diff --git a/.gitattributes b/.gitattributes index 1dd84a09ea175a680c0cd852ec0e787bcaaed364..a6344aac8c09253b3b630fb776ae94478aa0275b 100644 --- a/.gitattributes +++ b/.gitattributes @@ -33,5 +33,3 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text *.zip filter=lfs diff=lfs merge=lfs -text *.zst filter=lfs diff=lfs merge=lfs -text *tfevents* filter=lfs diff=lfs merge=lfs -text -Genome[[:space:]]Logic[[:space:]]Modeling[[:space:]]Project[[:space:]](GLMP)[[:space:]]-[[:space:]]a[[:space:]]Hugging[[:space:]]Face[[:space:]]Space[[:space:]]by[[:space:]]garywelz.pdf filter=lfs diff=lfs merge=lfs -text -Programming[[:space:]]Framework[[:space:]]for[[:space:]]Systematic[[:space:]]Analysis[[:space:]]-[[:space:]]a[[:space:]]Hugging[[:space:]]Face[[:space:]]Space[[:space:]]by[[:space:]]garywelz.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000000000000000000000000000000000000..769132da964b9ffafb1eb2d72a22759340d5588f --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ + +# HF rejects raw PDFs in git push; host PDFs elsewhere or use Xet +*.pdf diff --git a/ARXIV_MATH_AREAS_TODO.md b/ARXIV_MATH_AREAS_TODO.md new file mode 100644 index 0000000000000000000000000000000000000000..0fb962d1585ce4819e32d17759f13e0ba3d96fe5 --- /dev/null +++ b/ARXIV_MATH_AREAS_TODO.md @@ -0,0 +1,122 @@ +# Mathematics Database — arXiv Subject Areas To-Do + +A prioritized list of arXiv mathematics subject areas to add for a more complete collection, aligned with [arXiv math taxonomy](https://arxiv.org/category_taxonomy). + +--- + +## Current Coverage (What We Have) + +| Domain | Subcategories | arXiv codes covered | Gaps | +|--------|---------------|---------------------|------| +| **Algebra** | abstract_algebra, linear_algebra, category_theory | math.GR, math.RA, math.CT, math.AC, math.AG, math.QA | Commutative algebra, Algebraic geometry, Representation theory, Quantum algebra | +| **Analysis** | calculus_analysis | math.CA, math.CV, math.DS, math.FA, math.AP, math.NA, math.SP | Complex analysis, Functional analysis, PDEs, Numerical analysis, Spectral theory | +| **Geometry & Topology** | geometry_topology | math.GT, math.AT, math.DG, math.GN, math.MG, math.SG | Metric geometry, Symplectic geometry (light) | +| **Number Theory** | number_theory | math.NT | ✓ Good | +| **Discrete & Logic** | discrete_mathematics, foundations | math.CO, math.LO | ✓ Good | +| **Applied & Other** | bioinformatics, statistics_probability | math.GM, math.ST | Statistics/Probability empty | + +--- + +## To-Do List: Subject Areas to Add (Near Term) + +### Priority 1 — High Impact, Partially Covered or Empty + +| # | arXiv Code | Subject Area | Notes | Suggested Subcategory | +|---|------------|--------------|-------|------------------------| +| 1 | math.ST | **Statistics & Probability Theory** | 0 charts currently; foundational for applied math | `statistics_probability` (exists, populate) | +| 2 | math.PR | **Probability** | CLT, stochastic processes, SDEs; distinct from statistics | merge into `statistics_probability` or add `probability` | +| 3 | math.CV | **Complex Variables** | Holomorphic functions, residues, conformal maps; partially in calculus_analysis | add `complex_analysis` or extend calculus_analysis | +| 4 | math.FA | **Functional Analysis** | Banach spaces, Hilbert spaces, distributions | add to calculus_analysis or new `functional_analysis` | +| 5 | math.NA | **Numerical Analysis** | Newton-Raphson, bisection exist; add quadrature, linear solvers, ODE solvers | extend calculus_analysis or add `numerical_analysis` | +| 6 | math.AG | **Algebraic Geometry** | Varieties, schemes, moduli; major area | add `algebraic_geometry` or extend abstract_algebra | +| 7 | math.RT | **Representation Theory** | Representations of groups, Lie algebras | add `representation_theory` or extend abstract_algebra | + +### Priority 2 — Core Pure Math Gaps + +| # | arXiv Code | Subject Area | Notes | Suggested Subcategory | +|---|------------|--------------|-------|------------------------| +| 8 | math.AC | **Commutative Algebra** | Rings, ideals, Noetherian; differs from Ring Theory (noncommutative focus) | add `commutative_algebra` | +| 9 | math.AP | **Analysis of PDEs** | Existence, uniqueness, qualitative dynamics | add `partial_differential_equations` or extend analysis | +| 10 | math.DG | **Differential Geometry** | Curves, surfaces, Riemannian; some in geometry_topology | ensure distinct charts for differential geometry | +| 11 | math.SP | **Spectral Theory** | Schrödinger operators, spectral analysis | add to analysis or `spectral_theory` | +| 12 | math.SG | **Symplectic Geometry** | Hamiltonian systems, symplectic manifolds | extend geometry_topology | +| 13 | math.MG | **Metric Geometry** | Euclidean, hyperbolic, discrete geometry | extend geometry_topology | + +### Priority 3 — Advanced / Specialized + +| # | arXiv Code | Subject Area | Notes | Suggested Subcategory | +|---|------------|--------------|-------|------------------------| +| 14 | math.OA | **Operator Algebras** | C*-algebras, von Neumann algebras | add `operator_algebras` | +| 15 | math.KT | **K-Theory and Homology** | Algebraic/topological K-theory | add `k_theory` or extend algebraic topology | +| 16 | math.QA | **Quantum Algebra** | Quantum groups, operads | extend abstract_algebra | +| 17 | math.OC | **Optimization and Control** | Linear programming, optimal control | add `optimization` | +| 18 | math.IT | **Information Theory** | Coding, entropy, channel capacity | add `information_theory` | +| 19 | math.MP | **Mathematical Physics** | Rigorous formulations of physical theories | add `mathematical_physics` | +| 20 | math.HO | **History and Overview** | Biographies, education, philosophy | optional `history_overview` | + +### Priority 4 — Already in Expansion Plan + +These are in [MATHEMATICS_DATABASE_EXPANSION_PLAN.md](./MATHEMATICS_DATABASE_EXPANSION_PLAN.md): + +- **Complex Analysis** (math.CV) — 4 charts planned +- **Landmark Theorems** — FLT, Poincaré, Riemann +- **Formal Verification** — Lean, Coq +- **AI Mathematics** — AlphaProof, AlphaGeometry + +--- + +## Suggested Implementation Order + +### Phase A (1–2 weeks): Fill Empty & High-Impact +1. **Statistics & Probability** — Kolmogorov axioms, Bayes, CLT (3–5 charts) +2. **Complex Analysis** — Cauchy, residues, conformal maps (4 charts per expansion plan) +3. **Functional Analysis** — Banach/Hilbert spaces basics (2–3 charts) + +### Phase B (2–4 weeks): Algebra & Geometry Gaps +4. **Algebraic Geometry** — Varieties, schemes intro (2–3 charts) +5. **Representation Theory** — Group representations, characters (2–3 charts) +6. **Numerical Analysis** — Quadrature, solvers, ODE methods (3–4 charts) + +### Phase C (4–6 weeks): PDEs, Operator Theory, Applied +7. **PDEs** — Heat, wave, Laplace; existence/uniqueness (2–3 charts) +8. **Operator Algebras** — C*-algebras intro (1–2 charts) +9. **Optimization** — Linear programming, simplex (2 charts) +10. **Mathematical Physics** — Lagrangian/Hamiltonian mechanics (2 charts) + +--- + +## Metadata Updates Required + +When adding new subcategories: + +1. Add to `metadata.json` → `subcategoryCounts` +2. Add to `metadata.json` → `subcategoryToArxiv` +3. Add to `metadata.json` → `domainHierarchy` (assign to algebra, analysis, geometry_topology, or applied) +4. Run `build-graph-data.js` to update Whole of Mathematics +5. Update upload script if new process directories are created + +--- + +## Summary: arXiv Math Codes Not Yet Represented + +| Code | Area | Priority | +|------|------|----------| +| math.ST | Statistics Theory | 1 | +| math.PR | Probability | 1 | +| math.CV | Complex Variables | 1 | +| math.FA | Functional Analysis | 1 | +| math.NA | Numerical Analysis | 1 | +| math.AG | Algebraic Geometry | 1 | +| math.RT | Representation Theory | 1 | +| math.AC | Commutative Algebra | 2 | +| math.AP | Analysis of PDEs | 2 | +| math.SP | Spectral Theory | 2 | +| math.OA | Operator Algebras | 3 | +| math.KT | K-Theory | 3 | +| math.QA | Quantum Algebra | 3 | +| math.OC | Optimization & Control | 3 | +| math.IT | Information Theory | 3 | +| math.MP | Mathematical Physics | 3 | +| math.HO | History & Overview | 4 | + +**Well covered:** math.NT, math.CO, math.LO, math.GR, math.RA, math.CT, math.CA, math.GT, math.AT, math.DS (via complex dynamics) diff --git a/ATTRIBUTION_SCHEMA.md b/ATTRIBUTION_SCHEMA.md new file mode 100644 index 0000000000000000000000000000000000000000..45f48a991452cea990e413953a059cf857a643ed --- /dev/null +++ b/ATTRIBUTION_SCHEMA.md @@ -0,0 +1,39 @@ +# Mathematics Database — Attribution Schema + +Charts in the Mathematics Processes Database may include optional attribution metadata for academic transparency and citation. + +## Schema + +| Field | Type | Description | +|-------|------|-------------| +| `primary` | string | Primary author(s) or source (e.g., "Kurt Gödel", "Claude Shannon") | +| `contributors` | string[] | Additional contributors (optional) | +| `publication` | string | Title of publication or paper | +| `year` | string | Year of publication | +| `doi` | string | DOI URL (e.g., "https://doi.org/...") | +| `url` | string | External URL (Wikipedia, arXiv, etc.) | + +## Implementation + +Attribution is embedded in chart HTML via a "Cite" badge in the header-meta area. Hovering over the badge reveals a popover with the full attribution details. Charts using this schema include: + +- Gödel Incompleteness Theorems +- Schemes & Sheaves (Grothendieck) +- Group Representations (Frobenius, Maschke) +- Riemannian Geometry +- ZFC Axioms +- Shannon Entropy +- C*-Algebras (Gelfand–Naimark) + +## Example JSON + +```json +{ + "primary": "Kurt Gödel", + "contributors": [], + "publication": "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I", + "year": "1931", + "doi": "https://doi.org/10.1007/BF01700692", + "url": "https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems" +} +``` diff --git a/GENERIC_PROCESSES_TO_UPDATE.md b/GENERIC_PROCESSES_TO_UPDATE.md new file mode 100644 index 0000000000000000000000000000000000000000..77234e8b120c12ef1eb7dc27863675788f61a9a2 --- /dev/null +++ b/GENERIC_PROCESSES_TO_UPDATE.md @@ -0,0 +1,90 @@ +# Generic Processes Needing Real Content + +These processes use the generic template ("This X process visualization demonstrates... The flowchart shows...") and need to be replaced. **Use different approaches for different process types.** + +## Strategy by Process Type + +### 1. Algorithm flowcharts (like Binary Search) +**Examples:** Binary Search (done), Cryptographic Algorithms, Numerical Methods + +**Approach:** Process-like flowcharts with: +- Inputs (sorted array, search key) +- Steps (initialize interval, compute middle, compare) +- Decision diamonds (interval empty? key == A[mid]? key < A[mid]?) +- Outputs (found index, not found) +- Chart title: **"Algorithm Flowchart"** (do not use "GLMP 6-Color Scheme" in the title) + +**Reference:** [Binary Search](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/discrete_mathematics/discrete_mathematics-binary-search.html) – O(log n) complexity + +**Candidates:** Add specific algorithms – e.g. RSA, Newton-Raphson, Sieve of Eratosthenes, Dijkstra – each as its own process flowchart. + +### 2. Axiom-theorem dependency graphs (like Euclid, Peano, Propositional Logic, Aristotle) +**Examples:** Euclid Book I (done), Peano Arithmetic (done), Propositional Logic (done), Aristotle Syllogistic (done) + +**Approach:** Real mathematical development: +- Axioms / definitions at the base +- Theorems with explicit dependencies (arrows = "depends on") +- Split into subgraphs for clarity (like Euclid Book I's 5 views) + +**Reference:** [Euclid Book I](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/geometry_topology/geometry_topology-euclid-elements-book-i.html) + +**Candidates:** +- **Group Theory** – done (43 nodes, 69 edges across 3 subcharts; Euclid-style layered dependencies) +- **Ring Theory** – ring axioms → integral domain, polynomial rings +- **Field Theory** – field axioms → extensions, algebraic closure +- **Limit / Derivative / Integral** – ε-δ, limit laws, FTC, etc. +- **Modular Arithmetic** – congruence, Fermat's little theorem, etc. +- **Topology** – open sets, continuity, compactness +- **Differential Geometry** – manifold, metric, curvature + +### 3. Axiomatic combinatorics (like Euclid Book I for counting) +**Example:** Combinatorics (done) + +**Approach:** Axiomatic theory of combinatorics – definitions (factorial, sum/product principles) and theorems (permutations, combinations, binomial, pigeonhole, inclusion-exclusion) with dependency graph. Can be expanded to be more comprehensive like Euclid Book I. + +**Reference:** [Combinatorics](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/geometry_topology/geometry_topology-combinatorics.html) + +--- + +## Updated (with real content) +- **Combinatorics** – Axiomatic counting theory (14 nodes, 15 edges) +- **Binary Search** – Algorithm flowchart (already had real content) +- **Sieve of Eratosthenes** – Prime Number Generation (10 nodes, 14 edges) ✓ Batch 1 +- **Newton-Raphson Method** – Numerical Methods (9 nodes, 11 edges) ✓ Batch 1 +- **Bisection Method** – Limit Calculation (8 nodes, 10 edges) ✓ Batch 2 +- **Extended Euclidean Algorithm** – Modular Arithmetic (6 nodes, 6 edges) ✓ Batch 2 +- **Dijkstra's Algorithm** – Graph Theory Algorithms (7 nodes, 8 edges) ✓ Batch 2 +- **RSA Algorithm** – Cryptographic Algorithms (7 nodes, 7 edges) ✓ Batch 3 +- **Simpson's Rule** – Integral Calculation (6 nodes, 5 edges) ✓ Batch 3 +- **Kruskal's Algorithm** – new (9 nodes, 12 edges) ✓ Batch 3 +- **AES Algorithm** – new (8 nodes, 8 edges) ✓ Batch 4 +- **Merge Sort** – new (7 nodes, 7 edges) ✓ Batch 4 +- **Prim's Algorithm** – new (9 nodes, 12 edges) ✓ Batch 4 +- **Quicksort** – new (6 nodes, 6 edges) ✓ Batch 5 +- **Breadth-First Search** – new (7 nodes, 8 edges) ✓ Batch 5 +- **Binary Search Tree Insert** – new (8 nodes, 9 edges) ✓ Batch 5 +- **Group Theory** – Axiom-theorem dependency graph (21 nodes, 29 edges across 3 subcharts) ✓ + +## Need Updates (by type) + +### Algorithm flowcharts to create +- DFS, Heap sort, etc. +- Graph Theory Algorithms → Dijkstra, Kruskal, etc. + +### Axiom-theorem graphs to create (placeholders removed) +- Field Theory, Ring Theory +- Derivative, Integral, Limit Calculation +- Modular Arithmetic, Diophantine Equations +- Topology, Differential Geometry, Euclidean Geometry +- Logic & Set Theory (or point to Propositional Logic) +- Statistical Analysis (probability axioms → theorems) + +### Removed (generic placeholders deleted ✓) +- Field Theory, Ring Theory, Derivative Calculation, Statistical Analysis, Logic & Set Theory +- Differential Geometry, Euclidean Geometry, Topology, Diophantine Equations +- Integral Calculation, Limit Calculation, Modular Arithmetic, Cryptographic Algorithms, Graph Theory Algorithms +- Run `delete-generic-charts-from-gcs.sh` to remove from GCS; then `upload-mathematics-database-to-gcs.sh` for updated metadata + +### Duplicates (resolved ✓) +- statistics_probability-aristotles-syllogism → removed (canonical: discrete_mathematics-aristotle-syllogistic) +- statistics_probability-euclids-geometry → removed (canonical: geometry_topology-euclid-elements-*) diff --git a/GLMP_Foundation.html b/GLMP_Foundation.html deleted file mode 100644 index 739837f68ed7d6bf20e219f48dfb4e7ebd61b843..0000000000000000000000000000000000000000 --- a/GLMP_Foundation.html +++ /dev/null @@ -1,969 +0,0 @@ - - - - - - Is the Genome Like a Computer Program? - - - -
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Is the Genome Like a Computer Program?

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Author: Gary Welz
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Date: April 12, 2025
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Abstract

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This article revisits the metaphor of the genome as a computer program, a concept first proposed publicly by the author in 1995. Drawing on historical discussions in computational biology, including previously unpublished exchanges from the bionet.genome.chromosome newsgroup, we explore how the genome functions not merely as a passive database of genes but as an active, logic-driven computational system. The genome executes massively parallel processes—driven by environmental inputs, chemical conditions, and internal state—using a computational architecture fundamentally different from conventional computing. From early visual metaphors in Mendelian genetics to contemporary logic circuits in synthetic biology, this paper traces the historical development of computational models that express genomic logic, while critically examining both the utility and limitations of the program metaphor. We conclude that the genome represents a unique computational paradigm that could inform the development of novel computing architectures and artificial intelligence systems.

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1. Introduction

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Target Audience: This article is written for researchers and enthusiasts in computational biology, synthetic biology, artificial intelligence, and related fields. While some background in biology or computer science is helpful, we provide explanations and analogies to make the concepts accessible to interdisciplinary audiences.

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Biological processes have often been described through metaphor: the cell as a factory, DNA as a blueprint, and most provocatively—the genome as a computer program. Unlike static descriptions, this metaphor opens the door to seeing life itself as computation: a dynamic process with inputs, logic conditions, iterative loops, subroutines, and termination conditions.

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In 1995, the author explored this idea in an essay published in The X Advisor, proposing that gene regulation could be modeled as a logic program. That same year, in discussions on the bionet.genome.chromosome newsgroup, computational biologists including Robert Robbins of Johns Hopkins University developed this metaphor further, exploring profound differences between genomic and conventional computation. This article revisits and expands that vision through both historical analysis and modern advances in biology and AI.

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As we will explore, the genome-as-program metaphor provides valuable insights but also requires us to stretch conventional computational thinking into new paradigms—ones that might ultimately inform the future of computing itself.

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2. Historical Context

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2.1 Early Visualizations of Biological Logic

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The visualization of biological logic began with Gregor Mendel in the 19th century. Though his work predates formal computational thinking, Mendel's charts—showing ratios of inherited traits—used symbolic logic to track biological outcomes. Later, chromosome theory and operon models introduced control diagrams that represented genetic regulatory mechanisms.

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2.1.1 Mendel's Punnett Square and Computational Logic

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The Punnett square, named after British geneticist Reginald Punnett (1875-1967), represents one of the earliest systematic approaches to modeling genetic inheritance as a computational process. Punnett, a collaborator of William Bateson (1861-1926) who coined the term "genetics" and was a key figure in establishing genetics as a scientific discipline, developed this visualization method to predict the outcomes of genetic crosses. The square format provides a systematic way to compute all possible combinations of parental alleles, making it one of the first "genetic algorithms" in computational biology.

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The Punnett square in Figure 1 demonstrates a monohybrid cross between two heterozygous parents (Aa × Aa). Each cell in the 2×2 grid represents a possible genotype outcome, with the probability of each outcome determined by the rules of Mendelian inheritance. This systematic enumeration of possibilities mirrors the truth table approach used in digital logic design, where all possible input combinations are explicitly listed to determine output states.

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The computational logic underlying the Punnett square can be expressed through Boolean operations. Consider a simple genetic system where allele A is dominant and allele a is recessive. The phenotypic expression follows these logical rules:

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Dominance Logic (OR operation):
- Phenotype = A OR A = Dominant trait
- This follows the logical rule: if either allele is A, the dominant phenotype is expressed.

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Recessive Logic (AND operation):
- Phenotype = a AND a = Recessive trait
- This follows the logical rule: only if both alleles are a is the recessive phenotype expressed.

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The Punnett square can be extended to more complex genetic systems. For example, a dihybrid cross (AaBb × AaBb) creates a 4×4 grid with 16 possible combinations, demonstrating how genetic complexity scales exponentially with the number of genes involved. This combinatorial explosion is a fundamental characteristic of genetic computation that distinguishes it from simple linear processes.

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The logical structure of Mendelian inheritance can be formalized using truth tables, similar to those used in digital circuit design:

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Truth Table for Dominant/Recessive Inheritance:

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Allele 1Allele 2GenotypePhenotypeLogic
AAAADominant1 OR 1 = 1
AaAaDominant1 OR 0 = 1
aAaADominant0 OR 1 = 1
aaaaRecessive0 AND 0 = 0
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This truth table approach reveals that genetic inheritance operates through fundamental logical operations: OR for dominance (presence of dominant allele) and AND for recessiveness (absence of dominant alleles). These same logical operations form the basis of digital computation, establishing a direct parallel between genetic and computational logic.

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The Punnett square method demonstrates several key principles of genetic computation: (1) systematic enumeration of possibilities, (2) probabilistic outcomes based on combinatorial rules, (3) hierarchical organization of genetic information, and (4) the ability to predict complex outcomes from simple rules. These principles would later be formalized in computational genetics and serve as the foundation for modern genetic algorithms and evolutionary computation.

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- Mendel's Punnett Square -
Figure 1: Mendel's Punnett Square (1866)
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- Punnett square showing a monohybrid cross (Aa × Aa) with the resulting 3:1 phenotypic ratio. - Each cell represents a possible genotype outcome demonstrating Mendelian inheritance patterns. - Source: Wikipedia Commons. -
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2.2 The Development of Computational Metaphors

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The transition from Mendelian genetics to molecular biology in the mid-20th century marked a crucial evolution in computational thinking about biological systems. This period saw the emergence of sophisticated models that explicitly treated genetic regulation as a computational process, moving beyond simple inheritance patterns to complex regulatory networks.

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2.2.1 The Lac Operon: A Biological Logic Circuit

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In the 1960s, François Jacob and Jacques Monod's lac operon model introduced a logic gate–like system for regulating gene expression, paving the way for computational thinking in molecular biology. This revolutionary model showed how gene expression could be controlled through what resembled conditional logic, establishing the foundation for understanding genetic regulation as a computational process.

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Jacob and Monod's work on the lac operon in Escherichia coli revealed a sophisticated regulatory system that operates through logical principles. The operon consists of three structural genes (lacZ, lacY, lacA) that are coordinately regulated by a single promoter and operator region. The system responds to two environmental inputs: the presence of lactose (the substrate) and the absence of glucose (the preferred energy source).

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The computational logic of the lac operon can be expressed as a Boolean function:

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Lac Operon Logic:
- Expression = (Lactose present) AND (Glucose absent)
- This logical function determines whether the operon is transcribed and the enzymes are produced.

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The regulatory mechanism involves two key proteins: the lac repressor (encoded by lacI) and the catabolite activator protein (CAP). The lac repressor acts as a NOT gate—it binds to the operator and prevents transcription unless lactose is present. CAP acts as an AND gate—it enhances transcription only when glucose is absent. Together, these regulatory proteins implement a complex logical circuit that integrates multiple environmental signals.

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The lac operon model demonstrated several key principles of biological computation: (1) the use of regulatory proteins as logic gates, (2) the integration of multiple inputs through logical operations, (3) the ability to respond to environmental conditions through conditional logic, and (4) the coordination of multiple genes through shared regulatory elements. These principles would later be formalized in computational models of gene regulatory networks and serve as the foundation for synthetic biology.

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Jacob and Monod's work earned them the Nobel Prize in Physiology or Medicine in 1965, recognizing the profound implications of their discovery for understanding how genetic information is processed and regulated. Their model established the conceptual framework for viewing genetic regulation as a computational process, influencing generations of researchers in molecular biology and computational biology.

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- Lac Operon Model -
Figure 2: Jacob & Monod's Lac Operon Model (1961)
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- Schematic representation of the lac operon regulatory system showing the interaction between - regulatory proteins (lac repressor and CAP) and DNA elements (operator and promoter). - The diagram illustrates the logical circuit structure of genetic regulation. Source: Jacob & Monod (1961). -
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2.3 The 1995 Bionet.Genome.Chromosome Discussions

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In April 1995, during the early days of the internet and computational biology, a significant exchange on the bionet.genome.chromosome newsgroup explored the genome-as-program metaphor in depth. This discussion occurred at a pivotal moment when the Human Genome Project was gaining momentum and computational approaches to biology were emerging as a new paradigm. The author initiated this discussion by asking whether "an organism's genome can be regarded as a computer program" and whether its structure could be represented as "a flowchart with genes as objects connected by logical terms."

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Robert Robbins of Johns Hopkins University responded with a comprehensive analysis that both supported and complicated the metaphor. While acknowledging the digital nature of the genetic code, Robbins highlighted that the genome functions more like "a mass storage device" with properties not shared by electronic counterparts, and that genomic programs operate with unprecedented levels of parallelism—"in excess of 10^18 parallel processes" in the human body. These discussions represented one of the earliest sophisticated analyses of the computational nature of genomic function and laid the groundwork for modern computational biology approaches.

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2.4 The Author's 1995 Essay and Flowchart Model

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In 1995, the author's speculative essay proposed treating gene expression as an executing program with logical flow. To demonstrate this concept, the author created one of the first computational flowcharts representing gene regulation—a diagram of the lac operon's β-galactosidase expression system that explicitly modeled genetic regulation using programming logic constructs (see Figure 1).

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- β-Galactosidase Regulation Flowchart (1995) -
Figure 3: β-Galactosidase Regulation Flowchart (1995)
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- The author's original 1995 computational flowchart representing the lac operon as a decision-tree program. - Decision diamonds show conditional logic, rectangles show biological processes, and feedback loops - show regulatory mechanisms. This was among the first attempts to model genetic regulation using - computational constructs. -
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This original flowchart depicted the lac operon as a decision tree with conditional branches, feedback loops, and termination conditions—showing how the presence or absence of lactose and glucose created logical pathways leading to different outcomes for β-galactosidase production. The diagram used programming-style logic gates (decision diamonds for yes/no conditions, process rectangles for actions) to represent biological regulatory mechanisms, making explicit the parallel between genetic circuits and computer logic circuits.

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The article was featured on a bioinformatics resource list curated by Professor Inge Jonassen at the University of Bergen, where it appeared alongside foundational references like PubMed, In Silico Biology, and DNA Computers.

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2.4.1 Flowchart Examples in Computational Biology

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The use of flowcharts to represent biological processes has become increasingly sophisticated in modern computational biology. Contemporary flowcharts often integrate multiple data types, computational algorithms, and biological processes into unified visual representations. These modern flowcharts serve as computational roadmaps, guiding researchers through complex analytical pipelines and decision-making processes.

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Modern biological flowcharts typically include several key elements: (1) data input nodes representing experimental or computational data sources, (2) processing nodes showing analytical algorithms or computational methods, (3) decision points representing conditional logic based on statistical thresholds or biological criteria, (4) output nodes displaying results or predictions, and (5) feedback loops showing iterative refinement processes. This structure mirrors the computational architecture of modern bioinformatics pipelines.

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The flowchart in Figure 3.1 demonstrates a fascinating example of how biological metaphors have been adopted in computer science. This figure, from a network security paper (Al-Haija et al., 2014), shows a genetic algorithm flowchart that uses biological terminology—"thrive," "extinct," "mutate"—to describe computational processes for intrusion detection. This illustrates the profound influence of biological thinking on computational approaches, even in domains far removed from biology itself.

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The use of biological metaphors in this network security application is particularly revealing. The algorithm treats potential security threats as a "population" that can "thrive" (successful attacks), "go extinct" (failed attacks), or "mutate" (evolve new attack strategies). This demonstrates how the genome-as-program metaphor has influenced computational thinking across multiple disciplines, creating a shared language between biological and computational systems.

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This example shows that the computational principles underlying biological systems—population dynamics, selection pressure, adaptation, and evolution—have become fundamental tools in computer science. The fact that network security researchers chose biological terminology to describe their algorithms underscores the intuitive appeal and explanatory power of biological metaphors in computational contexts.

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- Modern Genetic Algorithm Flowchart -
Figure 3.1: Modern Genetic Algorithm Flowchart
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- Contemporary flowchart showing the integration of genetic algorithms with artificial neural networks - for computational biology applications. This example demonstrates modern computational approaches - to biological problem-solving. Source: Al-Haija et al. (2014) - Used Genetic Algorithm for Support - Artificial Neural Network in Intrusion Detection System. -
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2.5 Modern Visualization Systems

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Since then, influential graphical systems have emerged for representing genomic data and processes: Martin Krzywinski's Circos (2009), Höhna's probabilistic phylogenetic networks (2014), Koutrouli's network visualizations (2020), and O'Donoghue's reviews (2018). These systems have grappled with the challenge of representing the multi-dimensional and massively parallel nature of genomic processes.

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Martin Krzywinski's Circos visualization system represents a breakthrough in genomic data representation, using circular layouts to display complex multi-dimensional relationships between genomic regions. This innovative approach addresses the fundamental challenge of representing massive amounts of genomic data in an intuitive format, allowing researchers to identify patterns and relationships that would be impossible to see in linear representations. The circular layout enables the display of multiple data types simultaneously, making it an essential tool for modern comparative genomics and evolutionary studies. The Circos plot shows how different chromosomes (represented as segments around the circle) are connected by syntenic links (curved ribbons), revealing evolutionary relationships and structural variations that provide insights into genome evolution and organization.

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- Circos Genome Visualization (2009) -
Figure 4: Circos Genome Visualization (2009)
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Circular layout showing chromosomes with syntenic links for comparative genomics. Source: Krzywinski et al. (2009).
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Höhna et al.'s probabilistic phylogenetic networks represent a significant advancement in phylogenetic analysis, incorporating uncertainty and probabilistic relationships into evolutionary tree representations. This sophisticated approach acknowledges that biological processes are inherently stochastic and that our understanding of evolutionary relationships contains uncertainty. The model demonstrates how modern computational approaches can handle the inherent uncertainty in biological data, using probabilistic frameworks to represent evolutionary relationships rather than deterministic trees. This probabilistic approach has become essential for modern evolutionary biology and demonstrates how computational thinking has evolved to handle biological complexity, providing more realistic and nuanced representations of evolutionary processes.

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- Probabilistic Phylogenetic Networks (2014) -
Figure 5: Probabilistic Phylogenetic Networks (2014)
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Evolutionary relationships with uncertainty bands showing probabilistic phylogenetic analysis. Source: Höhna et al. (2014).
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Koutrouli et al.'s biological network visualization demonstrates how modern computational biology uses graph theory to model complex biological systems. This sophisticated network representation shows genes as nodes and their interactions as edges, revealing the intricate web of regulatory relationships that govern cellular processes. This network-based approach represents a fundamental shift from linear, sequential thinking to systems-level understanding of biological complexity. The graph structure allows researchers to identify hubs, modules, and emergent properties that would be invisible in traditional linear representations, acknowledging that biological systems are inherently networked and that understanding requires analysis of the entire system rather than individual components.

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- Biological Network Visualization (2020) -
Figure 6: Biological Network Visualization (2020)
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Gene interaction networks and regulatory relationships using graph theory. Source: Koutrouli et al. (2020).
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- -

O'Donoghue et al.'s multi-dimensional biomedical data visualization represents a crucial advancement in handling the massive datasets generated by modern genomics. The heatmap format allows researchers to visualize complex multi-dimensional data in an intuitive color-coded format, where each cell represents the expression level of a gene under specific conditions. This approach enables the identification of expression patterns, clustering of genes with similar expression profiles, and the discovery of regulatory relationships across multiple conditions. The visualization demonstrates how computational methods can transform raw numerical data into meaningful biological insights, revealing patterns that would be impossible to detect through manual analysis. This approach has become essential for modern genomics, transcriptomics, and systems biology, enabling researchers to handle the complexity and scale of contemporary biological datasets.

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- Biomedical Data Visualization (2018) -
Figure 7: Biomedical Data Visualization (2018)
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Gene expression patterns using heatmap-based data representation. Source: O'Donoghue et al. (2018).
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3. The Genome as a Mass Storage Device

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Before we can understand genomic "programs," we must first understand the unique storage medium they operate on. As Robbins noted in 1995, the genome functions like a specialized mass storage device with properties unlike any electronic counterpart:

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3.1 Associative Addressing vs. Physical Addressing

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Unlike computer hard drives that store files at specific locations (like "sector 1, track 2"), the genome uses a smarter system called associative addressing. Think of it like a library where you find books by their content rather than their shelf position. As Robbins described it, "All addressing is associative, with multiple read heads scanning the device in parallel, looking for specific START LOADING HERE signals." This means the genome doesn't use absolute positions but rather characteristic patterns recognized by cellular machinery.

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3.2 Linked-List Architecture

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The genome resembles "a mass-storage device based on a linked-list architecture, rather than a physical platter." Information is encountered sequentially as cellular machinery moves along the DNA strand, with "pointers" in the form of regulatory sequences directing the machinery to relevant sections.

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3.3 Redundant Organization with Variations

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With diploid organisms possessing two sets of chromosomes, the genome exhibits built-in redundancy. However, as G. Dellaire noted in the 1995 discussions, mechanisms like imprinting and allelic silencing create a situation where "you only actually have one 'program' running" from certain loci, raising questions about "gene dosage" without clear parallels in conventional computing.

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3.4 Multi-Level Encoding

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Dellaire also highlighted that "the actual structure of genome and not just the linear sequence may 'encode' sets of instructions for the 'reading and accessing' of this genetic code." This insight presaged modern understanding of epigenetics, chromatin structure, and the "histone code" as additional layers of information storage and processing.

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4. The Genome as a Logic-Driven Program

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Despite the differences in storage medium, the genome operates with recognizable computational logic structures:

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4.1 Core Computational Elements

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The genome employs structures analogous to:

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Bootloader: zygotic genome activation initiates development
- Conditional logic: expression dependent on chemical signals
- Loops: circadian cycles, metabolism, cell cycles
- Subroutines: growth, repair, reproduction
- Shutdown: apoptosis and programmed cell death

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These resemble constructs such as IF-THEN, WHILE, SWITCH-CASE, and HALT in conventional computation.

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4.2 Chemical Reactions as Computational Operations

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At the molecular level, chemical reactions function as the basic operational units of genomic computation. These reactions operate through principles that can be understood as computational processes, though they differ fundamentally from digital computation in their analog, probabilistic nature.

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Enzyme-Substrate Interactions as Logic Gates: Enzymes function as molecular logic gates, where the presence of specific substrates triggers catalytic reactions. These interactions follow Michaelis-Menten kinetics, creating sigmoidal response curves that resemble threshold logic functions. The enzyme's specificity for its substrate acts as a recognition mechanism, similar to how a logic gate responds only to specific input combinations.

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Concentration Thresholds as Decision Points: Biological systems use concentration gradients and threshold mechanisms to make decisions. For example, the lac operon's response to lactose depends on the concentration of allolactose exceeding a critical threshold. These thresholds create binary-like decision points in otherwise continuous systems, enabling discrete logic-like behavior from analog chemical processes.

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Feedback Loops as Iterative Processing: Biochemical feedback mechanisms implement iterative computational processes. Positive feedback creates amplification cascades (similar to computational scaling), while negative feedback provides stability and regulation. These loops can create oscillatory behavior, bistable switches, and other complex dynamics that resemble computational algorithms for pattern generation and control.

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Signal Amplification as Computational Scaling: Biological systems use cascading reactions to amplify weak signals, similar to how computational systems use amplifiers and buffers. The phosphorylation cascade in signal transduction pathways, for example, can amplify a single extracellular signal into thousands of intracellular responses, demonstrating how biological systems achieve computational scaling through chemical mechanisms.

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Stochastic Processes as Probabilistic Computation: Unlike deterministic digital computation, biological reactions are inherently stochastic. This probabilistic nature creates computational properties not found in conventional computing, including noise tolerance, adaptive responses, and emergent behaviors that arise from the statistical properties of molecular interactions.

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5. Massive Parallelism: Beyond Sequential Computing

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Perhaps the most profound difference between genomic and conventional computation lies in the scale and nature of parallelism involved.

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5.1 Unprecedented Scale of Parallel Processing

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As Robbins calculated in 1995, "The expression of the human genome involves the simultaneous expression and (potential) interaction of something probably in excess of 10^18 parallel processes." This number derives from approximately 10^13 cells in the human body, each running 10^5-10^6 processes in parallel, with potential interactions between any processes in any cells.

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This scale of parallelism is fundamentally different from any human-engineered computing system. To put this in perspective, the world's most powerful supercomputers operate with approximately 10^6-10^7 processing cores, while the human body operates with 10^18 parallel processes. This represents a difference of 11-12 orders of magnitude, making biological computation the most massively parallel system known to exist.

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The implications of this scale are profound. Each cell in the human body is simultaneously executing thousands of biochemical reactions, processing environmental signals, maintaining homeostasis, and coordinating with neighboring cells. These processes are not merely concurrent but truly parallel, with each reaction occurring independently and simultaneously. The coordination between these processes emerges from the physical and chemical properties of the system rather than from centralized control mechanisms.

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This massive parallelism enables biological systems to achieve computational capabilities that are impossible with sequential or even moderately parallel systems. For example, the immune system can simultaneously monitor for thousands of different pathogens, the nervous system can process multiple sensory inputs in real-time, and the metabolic system can maintain homeostasis across multiple organ systems simultaneously. These capabilities arise not from sophisticated algorithms but from the sheer scale of parallel processing available in biological systems.

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5.2 True Parallelism vs. Time-Sharing

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Unlike computer "parallel processing" that often involves time-sharing a smaller number of processors, genomic parallelism involves true simultaneous execution: "each single cell has millions of programs executing in a truly parallel (i.e., independent execution, no time sharing) mode."

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This distinction between true parallelism and time-sharing is crucial for understanding biological computation. In conventional computing, "parallel" systems typically use time-sharing, where a limited number of processors rapidly switch between different tasks, creating the illusion of simultaneous execution. Even modern multi-core processors use sophisticated scheduling algorithms to manage task allocation and context switching.

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In contrast, biological systems achieve true parallelism through physical separation and chemical independence. Each molecule in a cell can react independently and simultaneously with other molecules, without requiring any scheduling or coordination mechanism. This independence arises from the fundamental properties of chemical reactions—each reaction occurs based on local conditions and molecular interactions, not on system-wide scheduling decisions.

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This true parallelism has profound implications for system design and behavior. In time-shared systems, bottlenecks can occur when multiple processes compete for limited resources. In biological systems, such bottlenecks are rare because each process operates independently with its own local resources. This independence also means that biological systems are inherently fault-tolerant—the failure of one process does not necessarily affect others, and the system can continue operating even with significant component failures.

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The absence of centralized control in biological systems is both a strength and a challenge. On one hand, it eliminates single points of failure and enables robust, adaptive behavior. On the other hand, it makes biological systems difficult to understand and predict, as their behavior emerges from the collective interactions of countless independent processes rather than from explicit algorithms or control structures.

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5.3 The Developmental Bootloader

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Development begins with a specialized "bootloader" sequence that activates the zygotic genome after fertilization. This process transitions from maternal to zygotic control, initiates cascades of gene expression in precise sequence, establishes the initial conditions for all subsequent development, and creates a developmental trajectory with remarkable robustness.

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The zygotic genome activation (ZGA) represents one of the most critical computational events in development. During early development, the embryo relies on maternal RNA and proteins deposited in the egg, but at a specific developmental stage, the zygotic genome "boots up" and begins transcribing its own genes. This transition is analogous to a computer bootloader that initializes the operating system, establishing the basic computational environment for all subsequent operations.

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The bootloader process involves several computational elements that mirror those found in computer systems. First, there is a precise timing mechanism that determines when ZGA occurs—this timing is critical and must be coordinated with other developmental events. Second, there is a hierarchical activation sequence, where certain genes (often called "pioneer" genes) must be activated first to establish the conditions for subsequent gene expression. Third, there are feedback mechanisms that ensure the bootloader process is robust and can recover from errors or perturbations.

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This bootloader analogy extends beyond the initial activation. Throughout development, there are multiple "reboot" events where cells transition between different developmental states. For example, during cellular differentiation, cells undergo transcriptional reprogramming that resembles a system reboot, where the cell's computational state is reset and a new program begins executing. These transitions are often triggered by specific signals or environmental conditions, similar to how computer systems can be configured to boot different operating systems based on user input or system state.

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The robustness of the developmental bootloader is remarkable. Despite variations in environmental conditions, genetic background, and random molecular noise, development proceeds with remarkable consistency. This robustness suggests that the bootloader process has evolved sophisticated error-checking and recovery mechanisms, similar to those found in reliable computer systems. The ability to maintain developmental integrity despite perturbations is essential for the survival and reproduction of organisms, making the bootloader one of the most critical computational systems in biology.

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5.4 Emergent Properties from Massive Parallelism

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This unprecedented parallelism enables emergent properties not found in sequential computing: robust error correction through redundant processes, self-organization without central control, pattern formation through reaction-diffusion dynamics, and adaptation to changing conditions without explicit programming.

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Robust Error Correction Through Redundancy: Biological systems achieve remarkable reliability through massive redundancy rather than through precise error-free operation. Each cell contains multiple copies of critical genes, and many cellular processes have backup mechanisms that can compensate for failures. This redundancy is made possible by the massive parallelism of biological systems—if one process fails, others can take over without affecting overall system function. This approach to error correction is fundamentally different from conventional computing, where reliability is typically achieved through precise design and error detection rather than through redundancy.

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Self-Organization Without Central Control: The massive parallelism of biological systems enables self-organization, where complex patterns and behaviors emerge from the collective interactions of many simple components. This self-organization occurs without any central controller or coordinator—each component follows simple local rules, and the overall system behavior emerges from their collective interactions. Examples include the formation of cellular patterns during development, the synchronization of circadian rhythms across multiple cells, and the coordination of immune responses across the body. This emergent behavior is a direct consequence of the massive parallelism and local interactions that characterize biological systems.

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Pattern Formation Through Reaction-Diffusion Dynamics: The parallel nature of biological systems enables complex pattern formation through reaction-diffusion mechanisms. These patterns emerge from the interaction between chemical reactions (which create and destroy molecules) and diffusion (which spreads molecules through space). The classic example is Alan Turing's model of animal coat patterns, where simple chemical reactions occurring in parallel across a developing embryo create complex spatial patterns. These patterns emerge spontaneously from the parallel execution of simple chemical rules, demonstrating how massive parallelism can create complex, organized structures without explicit programming.

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Adaptation Without Explicit Programming: Biological systems can adapt to changing conditions without any explicit programming for those conditions. This adaptation occurs through the parallel operation of many different processes, each responding to local conditions. When environmental conditions change, some processes may be enhanced while others are suppressed, leading to an overall adaptation of the system. This adaptive behavior emerges from the collective response of many parallel processes rather than from explicit algorithms for adaptation. The ability to adapt to novel conditions without explicit programming is one of the most remarkable properties of biological systems and is a direct consequence of their massive parallelism.

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Collective Intelligence Through Distributed Processing: The massive parallelism of biological systems enables forms of collective intelligence that are impossible in sequential systems. For example, the immune system can simultaneously monitor for thousands of different pathogens, learn from encounters with new pathogens, and mount appropriate responses. This collective intelligence emerges from the parallel operation of many different cell types, each contributing specialized knowledge and capabilities to the overall system. The intelligence of the system as a whole exceeds the capabilities of any individual component, demonstrating how massive parallelism can create emergent computational capabilities.

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6. The Cell as a Virtual Machine

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One of Robbins' most profound insights was that genomic programs execute on virtual machines defined by other genomic programs.

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6.1 Self-Defining Execution Environment

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"Genome programs execute on a virtual machine that is defined by some of the genomic programs that are executing. Thus, in trying to understand the genome, we are trying to reverse engineer binaries for an unknown CPU, in fact for a virtual CPU whose properties are encoded in the binaries we are trying to reverse engineer."

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This insight reveals one of the most profound challenges in understanding biological computation. Unlike conventional computing, where the hardware (CPU, memory, etc.) is designed independently of the software that runs on it, in biological systems the "hardware" and "software" are co-evolved and mutually dependent. The cellular machinery that interprets the genome (the virtual machine) is itself encoded in the genome, creating a circular dependency that makes biological systems fundamentally different from engineered computing systems.

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This self-defining nature has several important implications. First, it means that biological systems are inherently self-modifying—the programs can change the machine that executes them. This capability enables biological systems to adapt and evolve in ways that are impossible for conventional computers. For example, during development, cells can change their transcriptional machinery, modify their chromatin structure, and alter their metabolic networks, effectively reprogramming the virtual machine on which they run.

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Second, this self-defining nature creates a fundamental challenge for reverse engineering. In conventional computing, we can understand a program by understanding the hardware it runs on. In biological systems, we must simultaneously understand both the program (the genome) and the machine (the cellular machinery), even though each depends on the other. This circular dependency makes biological systems much more difficult to understand and model than conventional computing systems.

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Third, this self-defining nature enables biological systems to achieve levels of integration and optimization that are impossible in conventional computing. Because the hardware and software co-evolved, they are perfectly matched to each other, enabling biological systems to achieve remarkable efficiency and robustness. This integration also means that biological systems can adapt to new challenges by modifying both their programs and their execution environment simultaneously.

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6.2 Probabilistic Op Codes

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Unlike the deterministic operations of conventional computers, "genomic op codes are probabilistic, rather than deterministic. That is, when control hits a particular op code, there is a certain probability that a certain action will occur."

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Think of it like rolling dice instead of flipping a light switch. Every biochemical reaction, every gene expression event, and every cellular process has an inherent element of randomness. This randomness is not a defect but a fundamental feature that enables unique capabilities.

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The probabilistic nature arises from molecular chaos—molecules bouncing around randomly, transcription factors binding and unbinding, and constantly changing cellular conditions. This creates uncertainty about when and how biological operations will occur.

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This probabilistic nature has profound implications. Biological systems must be robust to noise and uncertainty, and they can exploit randomness to achieve behaviors impossible in deterministic systems. For example, probabilistic gene expression enables cells to explore different states and adapt to changing conditions.

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However, this also creates challenges for prediction. Unlike computers where the same inputs always produce the same outputs, biological systems can produce different outcomes even under identical conditions. This makes them harder to model but also more robust and adaptable.

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6.3 The Genome as an AI Agent

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This self-modifying, probabilistic system bears more resemblance to modern AI architectures than to conventional computing: Like neural networks, it operates with weighted probabilities; like reinforcement learning systems, it optimizes toward outcomes; like agent-based systems, it balances multiple objectives; unlike current AI, it developed through natural selection rather than design.

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Neural Network Parallels: Biological systems operate through networks of interacting components that process information in parallel, similar to artificial neural networks. In both cases, the behavior of the system emerges from the collective activity of many simple processing units. However, biological networks are more sophisticated than artificial neural networks in several ways. They can modify their own structure and connectivity, they operate with multiple types of signals (chemical, electrical, mechanical), and they can change their computational properties based on context and experience.

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Reinforcement Learning Analogies: Biological systems learn through trial and error, optimizing their behavior based on feedback from the environment. This learning process resembles reinforcement learning, where an agent learns to maximize rewards by exploring different actions and observing their consequences. However, biological reinforcement learning is more sophisticated than artificial versions, as it can modify not only its behavior but also its own learning mechanisms and objectives. This meta-learning capability enables biological systems to adapt their learning strategies to different environments and challenges.

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Multi-Objective Optimization: Biological systems must balance multiple competing objectives simultaneously, such as growth, reproduction, survival, and energy efficiency. This multi-objective optimization is similar to the challenges faced by AI agents in complex environments. However, biological systems have evolved sophisticated mechanisms for balancing these objectives, including hierarchical control systems, priority-based decision making, and adaptive trade-offs that change based on environmental conditions.

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Emergent Intelligence: The intelligence of biological systems emerges from the collective behavior of many simple components, rather than from a centralized control system. This emergent intelligence is similar to the behavior of swarm intelligence systems and multi-agent AI systems. However, biological systems achieve levels of coordination and cooperation that far exceed current artificial multi-agent systems, demonstrating how evolution can discover sophisticated solutions to complex coordination problems.

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Adaptive Architecture: Unlike artificial AI systems, which have fixed architectures designed by humans, biological systems can modify their own computational architecture in response to experience and environmental conditions. This adaptive architecture enables biological systems to optimize their computational capabilities for specific tasks and environments, creating specialized processing systems that are perfectly suited to their particular challenges.

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7. Case Studies in Genomic Programming

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Different organisms demonstrate different "programming paradigms" at the genomic level:

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7.1 Viruses: Minimal Programs

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Program: Infect → Reproduce → Die
- Trigger: Contact with host cell
- Computational simplicity: Limited conditionals, linear execution
- Optimization: Maximum efficiency in minimal code

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Viruses represent the most minimal form of biological computation, with genomes that are optimized for maximum efficiency in minimal code. The viral "program" is essentially a bootloader that hijacks the host cell's computational machinery to reproduce itself. This minimalism makes viruses excellent models for understanding the fundamental principles of biological computation, as they demonstrate how complex behaviors can emerge from simple, linear programs.

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The viral life cycle follows a simple linear sequence: attachment to a host cell, entry into the cell, replication of viral components, assembly of new virus particles, and release from the cell. This linear execution is similar to a simple computer program with minimal branching and no complex control structures. However, even this simple program must handle multiple contingencies, such as different types of host cells, varying environmental conditions, and host immune responses.

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The computational efficiency of viruses is remarkable. Some viruses can encode their entire program in fewer than 10,000 nucleotides, yet they can successfully infect, replicate, and spread through host populations. This efficiency is achieved through several strategies: overlapping genes that encode multiple proteins, regulatory sequences that serve multiple functions, and the exploitation of host cell machinery for most computational tasks. This minimalism demonstrates how biological systems can achieve complex outcomes through the efficient use of limited computational resources.

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However, this minimalism also creates vulnerabilities. Viruses have limited ability to adapt to changing conditions, and they are highly dependent on their host cells for most computational functions. This dependence makes viruses excellent models for understanding the trade-offs between computational efficiency and robustness, as well as the relationship between program complexity and adaptability.

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7.2 Unicellular Organisms: Autonomous Agents

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Program: Eat → Grow → Divide
- Loop structure: WHILE food_present DO grow
- Event triggers: Mitosis on threshold conditions
- State-based logic: Different metabolic states based on environmental conditions

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Unicellular organisms represent a more sophisticated form of biological computation, with programs that must balance multiple objectives while operating autonomously in complex environments. Unlike viruses, which are essentially parasites that hijack host machinery, unicellular organisms must implement their own computational infrastructure while also performing the basic functions of life: metabolism, growth, reproduction, and response to environmental changes.

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The computational architecture of unicellular organisms is based on state machines that can transition between different metabolic states based on environmental conditions. For example, bacteria can switch between aerobic and anaerobic metabolism, between different carbon sources, and between growth and survival modes. These state transitions are triggered by environmental signals and are implemented through complex regulatory networks that integrate multiple inputs to make decisions about cellular behavior.

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The cell cycle represents a fundamental computational loop that drives cellular behavior. This loop includes phases for growth, DNA replication, and cell division, with checkpoints that ensure each phase is completed correctly before proceeding to the next. These checkpoints implement error detection and correction mechanisms that are essential for maintaining genomic integrity. The cell cycle demonstrates how biological systems can implement complex control structures using simple molecular mechanisms.

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Unicellular organisms also demonstrate sophisticated signal processing capabilities. They can detect and respond to multiple environmental signals simultaneously, integrating information about nutrient availability, temperature, pH, and the presence of other organisms. This signal integration enables cells to make complex decisions about their behavior, such as whether to grow, divide, form spores, or enter a dormant state. These decision-making processes resemble the control systems used in autonomous robots and other artificial agents.

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The computational capabilities of unicellular organisms are particularly impressive given their simplicity. A single bacterial cell can implement complex behaviors such as chemotaxis (movement toward or away from chemicals), quorum sensing (communication with other cells), and biofilm formation (cooperative behavior with other cells). These capabilities demonstrate how biological systems can achieve sophisticated computational outcomes through the coordinated action of simple molecular components.

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7.3 Multicellular Organisms: Distributed Systems

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Subroutines: Cellular differentiation, immune responses
- Conditional branches: Hormone levels, cell signaling
- Coordinated processes: Development, aging, reproduction
- Distributed computation: Different cells executing different aspects of the overall program

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Multicellular organisms represent the most complex form of biological computation, with programs that must coordinate the behavior of thousands to trillions of cells while maintaining the integrity and functionality of the entire organism. This coordination requires sophisticated communication systems, hierarchical control structures, and distributed decision-making mechanisms that far exceed the complexity of any artificial distributed system.

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The computational architecture of multicellular organisms is based on cellular differentiation, where different cells execute different programs while sharing the same genome. This differentiation is controlled by complex regulatory networks that integrate multiple signals to determine cellular fate. The process of differentiation resembles the creation of specialized subroutines in a computer program, where different components perform different functions while working together to achieve overall system goals.

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Communication between cells is essential for coordinating the behavior of multicellular organisms. This communication occurs through multiple mechanisms, including direct cell-to-cell contact, secreted signaling molecules, and electrical signals in the nervous system. These communication systems enable cells to share information about their state, coordinate their activities, and respond collectively to environmental changes. The complexity of these communication networks rivals that of modern computer networks, with multiple protocols, routing mechanisms, and error correction systems.

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The immune system represents one of the most sophisticated computational systems in multicellular organisms. It must simultaneously monitor for thousands of different pathogens, learn from encounters with new pathogens, and mount appropriate responses while avoiding attacks on the organism's own cells. This system operates through distributed algorithms that involve multiple cell types, each contributing specialized knowledge and capabilities to the overall immune response. The immune system demonstrates how biological systems can achieve collective intelligence through the coordinated action of many simple components.

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Development represents another remarkable computational achievement of multicellular organisms. Starting from a single cell, development creates complex three-dimensional structures with precise spatial organization and functional specialization. This process involves the coordinated action of thousands of genes across millions of cells, with precise timing and spatial control. The computational complexity of development is staggering, involving the simultaneous execution of thousands of parallel processes with complex interdependencies and feedback loops.

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The computational capabilities of multicellular organisms are particularly impressive given the challenges they face. They must maintain homeostasis across multiple organ systems, respond to changing environmental conditions, and coordinate complex behaviors such as movement, feeding, and reproduction. These capabilities demonstrate how biological systems can achieve sophisticated computational outcomes through the coordinated action of many simple components, creating emergent properties that exceed the capabilities of any individual component.

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8. The β-Galactosidase Revolution: From 1995 to 2025

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The evolution from the author's original 1995 β-galactosidase flowchart to today's sophisticated Mermaid-based visualizations represents not just a technological advancement, but a fundamental transformation in how we create and share biological knowledge. This transformation exemplifies the democratization of computational biology through the convergence of human insight, AI assistance, and modern visualization tools.

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8.1 The 1995 Journey: A Month of Manual Discovery

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In 1995, creating the original β-galactosidase flowchart (Figure 3) was an arduous, month-long process that required:

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This process, while thorough, was limited by the tools available and the manual nature of knowledge synthesis. The author, drawing on an education in mathematics and philosophy at Bedford College, London in the 1970s, and working as a web developer and journalist in the 1990s, spent countless hours transforming biological concepts into computational visualizations for a monthly column in The X Advisor, a computer industry trade publication.

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8.2 The 2025 Revolution: AI-Powered Biological Modeling

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Today, the same process that took a month in 1995 can be accomplished in hours or days, thanks to the revolutionary combination of:

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8.3 A Comparative Analysis: 1995 vs 2025

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- β-Galactosidase Regulation Flowchart (1995) -
Figure 3: β-Galactosidase Regulation Flowchart (1995) - The Original
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- The author's original 1995 computational flowchart created with Inspiration after a month of research, reading, and community discussion. This groundbreaking visualization was among the first to model genetic regulation using computational logic constructs, establishing the foundation for computational biology visualization. -
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2025 Mermaid-Based β-Galactosidase Analysis - Using modern tools and AI assistance, we can now create far more sophisticated and detailed visualizations:

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-graph TD - %% Environmental Inputs (Red) - A[Lactose in Environment] --> B[Lactose Transport] - C[Glucose in Environment] --> D[Glucose Transport] - E[Low Energy Status] --> F[Energy Stress Signal] - - %% Structures & Objects (Yellow) - G[Lactose Permease LacY] --> H[Lactose Inside Cell] - I[Glucose Transporters] --> J[Glucose Inside Cell] - - %% Decision Logic - H --> K{Is Lactose Present?} - J --> L{Is Glucose Present?} - F --> M{Is Energy Low?} - - %% Regulatory States (Blue) - K -->|No| N[Lac Repressor Active] - K -->|Yes| O[Lac Repressor Inactive] - L -->|Yes| P[High Glucose Status] - L -->|No| Q[Low cAMP Levels] - M -->|Yes| R[High cAMP Levels] - M -->|No| S[Low cAMP Levels] - - %% Regulatory Actions - N --> T[Repressor Binds Operator] - O --> U[Repressor Released] - T --> V[Repressor Transcription Blocked] - U --> W[Operator Free] - - %% CAP Regulation - Q --> X[cAMP-CAP Complex] - R --> X - X --> Y{CAP Bound?} - W --> Z{Operator Free?} - - %% Transcription Control - Y -->|Yes| AA[CAP Binds Promoter] - Y -->|No| BB[No CAP Binding State] - Z -->|Yes| CC[RNA Polymerase Binding] - Z -->|No| DD[Operator Transcription Blocked] - - %% Transcription Levels - AA --> EE[Strong Transcription] - BB --> FF[Weak Transcription] - CC --> EE - DD --> GG[Transcription Blocked] - - %% mRNA Synthesis - EE --> HH[lacZ mRNA Synthesis] - EE --> II[lacY mRNA Synthesis] - EE --> JJ[lacA mRNA Synthesis] - - %% Protein Translation - HH --> KK[LacZ Translation] - II --> LL[LacY Translation] - JJ --> MM[LacA Translation] - - %% Enzymes (Yellow) - KK --> NN[Beta-Galactosidase Enzyme] - LL --> OO[Lactose Permease] - MM --> PP[Galactoside Acetyltransferase] - - %% Chemical Processing (Green) - NN --> QQ[Lactose Hydrolysis] - OO --> RR[Lactose Transport] - PP --> SS[Galactoside Modification] - - %% Products (Violet) - QQ --> TT[Glucose + Galactose] - RR --> UU[Lactose Uptake] - SS --> VV[Detoxification] - - %% Metabolic Integration - TT --> WW[Glycolysis] - UU --> XX[Lactose Processing] - VV --> YY[Cell Protection] - - %% System Outputs - WW --> ZZ[Energy Production] - XX --> AAA[Lactose Consumption] - YY --> BBB[Cell Survival] - - %% Feedback Loops - ZZ --> CCC[Energy Status Improved] - AAA --> DDD[Lactose Depletion] - BBB --> EEE[Reduced Energy Stress] - - %% System Equilibrium - CCC --> FFF[Reduced Lactose Signal] - DDD --> FFF - EEE --> GGG[Maintained Homeostasis] - FFF --> GGG - GGG --> HHH[System Equilibrium] - - %% Color Key Legend - LEGEND1[🔴 Triggers & Conditions] - LEGEND2[🟡 Catalysts & Enzymes] - LEGEND3[🟢 Chemical Processing] - LEGEND4[🔵 Intermediates & States] - LEGEND5[🟣 Products & Outputs] - - %% Legend Connections - LEGEND1 -.-> LEGEND2 - LEGEND2 -.-> LEGEND3 - LEGEND3 -.-> LEGEND4 - LEGEND4 -.-> LEGEND5 - - %% Styling - Programming Framework Color Scheme - %% Red (#ff6b6b): Triggers & Inputs - style A fill:#ff6b6b,color:#fff - style C fill:#ff6b6b,color:#fff - style E fill:#ff6b6b,color:#fff - - %% Yellow (#ffd43b): Structures & Objects - style G fill:#ffd43b,color:#000 - style I fill:#ffd43b,color:#000 - style NN fill:#ffd43b,color:#000 - style OO fill:#ffd43b,color:#000 - style PP fill:#ffd43b,color:#000 - - %% Green (#51cf66): Processing & Operations - style B fill:#51cf66,color:#fff - style D fill:#51cf66,color:#fff - style F fill:#51cf66,color:#fff - style T fill:#51cf66,color:#fff - style U fill:#51cf66,color:#fff - style AA fill:#51cf66,color:#fff - style CC fill:#51cf66,color:#fff - style HH fill:#51cf66,color:#fff - style II fill:#51cf66,color:#fff - style JJ fill:#51cf66,color:#fff - style KK fill:#51cf66,color:#fff - style LL fill:#51cf66,color:#fff - style MM fill:#51cf66,color:#fff - style QQ fill:#51cf66,color:#fff - style RR fill:#51cf66,color:#fff - style SS fill:#51cf66,color:#fff - style WW fill:#51cf66,color:#fff - style XX fill:#51cf66,color:#fff - style YY fill:#51cf66,color:#fff - style CCC fill:#51cf66,color:#fff - style DDD fill:#51cf66,color:#fff - style EEE fill:#51cf66,color:#fff - - %% Blue (#74c0fc): Intermediates & States - style H fill:#74c0fc,color:#fff - style J fill:#74c0fc,color:#fff - style K fill:#74c0fc,color:#fff - style L fill:#74c0fc,color:#fff - style M fill:#74c0fc,color:#fff - style N fill:#74c0fc,color:#fff - style O fill:#74c0fc,color:#fff - style P fill:#74c0fc,color:#fff - style Q fill:#74c0fc,color:#fff - style R fill:#74c0fc,color:#fff - style S fill:#74c0fc,color:#fff - style V fill:#74c0fc,color:#fff - style W fill:#74c0fc,color:#fff - style X fill:#74c0fc,color:#fff - style Y fill:#74c0fc,color:#fff - style Z fill:#74c0fc,color:#fff - style BB fill:#74c0fc,color:#fff - style DD fill:#74c0fc,color:#fff - style EE fill:#74c0fc,color:#fff - style FF fill:#74c0fc,color:#fff - style GG fill:#74c0fc,color:#fff - style FFF fill:#74c0fc,color:#fff - style GGG fill:#74c0fc,color:#fff - style HHH fill:#74c0fc,color:#fff - - %% Violet (#b197fc): Products & Outputs - style TT fill:#b197fc,color:#fff - style UU fill:#b197fc,color:#fff - style VV fill:#b197fc,color:#fff - style ZZ fill:#b197fc,color:#fff - style AAA fill:#b197fc,color:#fff - style BBB fill:#b197fc,color:#fff - - %% Legend Styling - style LEGEND1 fill:#ff6b6b,color:#fff - style LEGEND2 fill:#ffd43b,color:#000 - style LEGEND3 fill:#51cf66,color:#fff - style LEGEND4 fill:#74c0fc,color:#fff - style LEGEND5 fill:#b197fc,color:#fff -
-
- -
-
- Triggers & Conditions -
-
- Catalysts & Enzymes -
-
- Chemical Processing -
-
- Intermediates -
-
- Products -
-
- -
Figure 3.2: β-Galactosidase Programming Framework Analysis (2025)
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- A modern computational analysis of the lac operon using Mermaid syntax and Programming Framework methodology. This visualization demonstrates how AI assistance and modern tools enable the creation of sophisticated biological flowcharts with detailed computational logic, color-coded analysis, and comprehensive pathway representation—all achievable in hours rather than months. The chart shows environmental inputs, regulatory complexes and enzymes, intermediate states and logic gates, functional outputs, and key regulatory proteins, revealing the sophisticated computational logic underlying lactose metabolism in E. coli including CAP-cAMP regulation, protein synthesis, and dynamic feedback control. -
-
- -

8.4 The Transformation: From Amateur Science to AI-Enabled Innovation

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This comparison reveals a profound transformation in scientific practice:

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1995 Characteristics:

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2025 Capabilities:

- - -

The Remarkable Achievement: What once required a month of dedicated work by a trained biologist can now be accomplished in days, with far greater detail and sophistication. Yet this transformation was only possible through the convergence of human biological understanding (rooted in solid educational foundations), innovative visualization tools (Mermaid), and AI assistance (LLMs).

- -

8.5 The Democratization of Computational Biology

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This evolution represents more than just technological progress—it represents the democratization of computational biology. In 1995, creating biological flowcharts required specialized knowledge, significant time investment, and access to academic communities. Today, the combination of educational background, AI assistance, and modern tools enables rapid creation of sophisticated biological visualizations.

- -

The author's journey from manually creating single flowcharts to generating hundreds of detailed biological process diagrams exemplifies how AI can amplify human expertise rather than replace it. The mathematical and philosophical training from Bedford College, combined with decades of experience in journalism and web development, provided the analytical framework necessary to guide AI systems in creating meaningful visualizations. Now at 72 and retired, the author continues the amateur science tradition with vastly improved tools.

- -

Rarely Used for Biological Applications: While Mermaid has been implemented in numerous documentation platforms since its 2014 release, its application to biological process modeling—particularly the systematic extraction of .mmd files from scientific literature by humans and AI working together—represents a novel and innovative use case. This approach transforms static biological knowledge into dynamic, visual computational models.

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8.6 The Innovation: Genuine Contribution to Biology

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This work represents a genuine innovation in biological visualization and computational thinking. By systematically applying the Programming Framework methodology to biological processes, we have created:

- - -

This innovation bridges the gap between computational thinking and biological understanding, creating new possibilities for research, education, and synthetic biology applications. The transformation from 1995 to 2025 demonstrates how the combination of solid educational foundations, innovative thinking, and modern AI tools can enable individual researchers to make significant contributions to scientific understanding.

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9. Visualization Challenges and the Limits of Linear Representation

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The exchange between Welz and Robison in 1995 highlighted a fundamental challenge that persists today: how to visually represent massively parallel processes using tools designed for sequential thinking. The author's β-galactosidase flowchart exemplified both the promise and the problems of this approach.

- -

9.1 Limitations of Linear Flowcharts

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As Robison noted: "Flowcharts are inherently linear beasts, ill-suited for parallel processes, especially biological ones with many non-linearly combined inputs." Traditional flowcharts suggest a sequence of operations that misrepresents the simultaneous nature of genomic processes.

- -

9.2 Alternative Visualization Approaches

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Contemporary approaches to representing genomic computation have attempted to address these limitations through network diagrams showing interaction rather than sequence, heat maps representing multiple states simultaneously, multi-dimensional representations capturing regulatory relationships, and dynamic simulations rather than static diagrams. However, even these advanced visualization systems struggle with the fundamental challenge identified in 1995: representing true parallelism in comprehensible visual formats.

- - - -
- Gene Expression Networks (2024) -
Figure 8: Gene Expression Networks (2024)
-
del Val et al.'s gene expression networks demonstrate how modern computational biology addresses the parallelism challenge identified in 1995. This multi-omic network analysis shows how genes interact in complex regulatory networks, revealing the systems-level logic that governs biological processes. Unlike linear flowcharts, this network visualization captures the parallel, interconnected nature of genomic computation, representing the future of computational biology where understanding biological systems requires analysis of their computational properties and network dynamics. Source: del Val et al. (2024).
-
- -

9.3 The Enduring Relevance of Early Insights

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The visualization challenges raised by Robison's critique of the β-galactosidase flowchart continue to influence how we think about representing biological systems. Modern synthetic biology, systems biology, and computational biology all grapple with the same fundamental tension between the need for clear, understandable representations and the reality of massively parallel, probabilistic biological processes.

- -

10. Limitations, Criticisms, and Alternative Perspectives

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While the genome-as-program metaphor provides valuable insights, it is important to acknowledge its limitations and consider alternative perspectives. Several criticisms and challenges have been raised regarding this approach.

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10.1 The Program-Programmer Paradox

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A fundamental challenge to the metaphor is the absence of a programmer. Unlike human-written software:

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10.1 Evolution as "Programmer"

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The genome evolved through natural selection; there is no separate "specification" from "implementation"; the "debugging" process (evolution) occurs across generations; the line between program and programmer blurs as the genome modifies itself.

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10.2 Integration of Hardware and Software

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In conventional computing, hardware and software are distinct. In genomic systems: the genome is both the program and the machine that interprets itself; the distinction between "data" and "process" blurs; physical structure and information content are inseparable.

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10.3 The Absence of Central Control

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Unlike most computer programs: no central processing unit coordinates execution; no master clock synchronizes operations; no operating system manages resources; control emerges from distributed interactions.

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10.4 Alternative Metaphors and Perspectives

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Several alternative metaphors have been proposed for understanding biological systems:

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Network Metaphor: Some researchers prefer to view biological systems as complex networks rather than programs, emphasizing the interconnected nature of biological components and the emergent properties that arise from network dynamics.

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Ecosystem Metaphor: Others argue that biological systems are better understood as ecosystems, where multiple agents interact in complex ways, creating dynamic equilibria and co-evolutionary processes.

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Information Processing Metaphor: An alternative approach focuses on information processing and communication rather than computation, emphasizing how biological systems encode, transmit, and process information.

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These alternative perspectives highlight different aspects of biological complexity and may be more appropriate for certain types of analysis. The genome-as-program metaphor should be viewed as one useful framework among many, rather than a complete description of biological reality.

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11. Synthetic Biology and AI Implications

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The genome-as-program metaphor has profound implications for both synthetic biology and artificial intelligence.

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11.1 Programming Living Systems

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Viewing the genome as a program enables engineered cells to be written, debugged, and optimized. Synthetic biology gains logic tools to regulate traits, behaviors, and lifecycles. The β-galactosidase flowchart represents an early conceptual bridge toward this engineering approach, demonstrating how biological regulatory circuits can be understood and potentially redesigned using computational logic.

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11.2 Learning from Nature's Computing

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The genomic computational paradigm offers lessons for AI design: massive parallelism with simple components; probabilistic operations with emergent determinism; self-modifying code and execution environment; integration of digital and analog processing.

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11.3 The Genome Logic Modeling Project (GLMP)

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The Genome Logic Modeling Project (GLMP) aims to formalize the metaphor of the genome as a computer program. It models organisms as logic-executing agents, with internal subroutines and external triggers. GLMP frames biology as structured, conditional, recursive, and state-driven.

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Goals and Objectives: The GLMP seeks to create a unified framework for understanding biological systems through computational logic, develop tools for modeling genetic circuits, and establish a collaborative platform for interdisciplinary research. The project aims to bridge the gap between theoretical computational biology and practical applications in synthetic biology and AI.

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Expected Outcomes: The GLMP will produce computational models of genetic circuits, visualization tools for genomic logic, educational materials for teaching computational biology, and a community platform for researchers to share insights and collaborate on genomic modeling projects.

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This article represents a foundational publication for this project, which will explore topics including: Life as a Running Logic Program; Bootloaders of Life: Zygotic Genome Activation; Subroutines in Biology: Modular Design; Shutdown Protocols: Senescence and Apoptosis; Synthetic Biology Through Logic Gates; Agent-Based Models of Organism Logic.

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Concrete Examples of GLMP Research:

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11.3.1 GLMP as a Collaborative Research Platform

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The GLMP is designed as an open, collaborative platform that invites researchers, computational biologists, AI specialists, and interested parties from all disciplines to participate in this endeavor. The project recognizes that understanding the genome as a computational system requires diverse perspectives and expertise, from molecular biologists who understand the biochemical details to computer scientists who can formalize computational models.

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We encourage contributions in several key areas: (1) Specific Gene Circuit Analysis—detailed computational models of individual genetic circuits, similar to the β-galactosidase example but for other genes and processes; (2) Cross-Species Comparisons—how different organisms implement similar computational functions; (3) Computational Tool Development—software and visualization tools for representing genomic logic; and (4) Integration with Modern AI—connections between genomic computation and contemporary artificial intelligence systems.

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11.3.2 Parallels with DeepMind's Cell Project

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The recent announcement of DeepMind's Cell project, led by Demis Hassabis, represents a significant validation of the genome-as-program metaphor and demonstrates how this perspective is gaining traction in the AI community. Like the GLMP, DeepMind's Cell project aims to model cellular processes as computational systems, beginning with the yeast cell as a model organism.

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This convergence of approaches is particularly significant because it shows that the computational perspective on biology is not merely a metaphor but a practical framework for understanding and modeling biological systems. The fact that one of the world's leading AI research organizations is pursuing this approach validates the fundamental insights that motivated the GLMP.

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The GLMP can complement and extend DeepMind's work by providing a broader theoretical framework and encouraging community participation. While DeepMind focuses on building comprehensive cell models, the GLMP can serve as a platform for researchers to contribute specific computational analyses of genetic circuits, regulatory networks, and cellular processes. This collaborative approach can accelerate progress in both understanding biological computation and developing new computational paradigms.

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11.3.3 Call to Action: Join the GLMP Community

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We invite researchers and enthusiasts to contribute to the GLMP in several ways:

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For Molecular Biologists: Share your knowledge of specific genetic circuits and regulatory mechanisms. Help us understand how your research area can be represented as computational logic. Contribute examples of gene regulation that could be modeled as flowcharts or logic circuits.

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For Computer Scientists: Develop computational models of genetic processes. Create visualization tools for representing genomic logic. Design algorithms inspired by biological computation. Help formalize the computational languages needed to describe genomic processes.

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For AI Researchers: Explore connections between genomic computation and artificial intelligence. Investigate how biological learning and adaptation mechanisms can inform AI design. Develop AI systems that can analyze and model genomic logic.

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For Educators: Help develop educational materials that use computational metaphors to teach biology. Create interactive simulations of genetic processes. Bridge the gap between computer science and biology education.

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For Enthusiasts: Participate in discussions, share ideas, and help build the GLMP community. Contribute to documentation, visualization, and communication efforts. Help make complex biological concepts accessible to broader audiences.

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The GLMP represents an opportunity to fundamentally change how we understand and interact with biological systems. By treating the genome as a computational system, we can develop new tools for understanding life, new approaches to synthetic biology, and new paradigms for computing itself. The time is right for this perspective, as evidenced by the convergence of approaches from multiple research communities.

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12. Future Research Directions

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This metaphor opens several promising research avenues:

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12.1 Formal Languages for Genomic Logic

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Develop specialized notation for genomic computation; create simulation environments based on genomic logic; bridge between biological description and computational models. The insights from early flowcharts like Figure 1 suggest the need for new visual languages that can better represent parallel, probabilistic biological processes.

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12.2 New Computational Architectures

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Design computing systems inspired by genomic parallelism; explore probabilistic processing at massive scale; develop self-modifying execution environments. The scale of parallelism identified by Robbins—exceeding 10^18 processes—suggests computational architectures fundamentally different from current designs.

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12.3 Educational Models

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Teach genomic function using computational metaphors; develop interactive simulations of genomic processes; bridge disciplinary gaps between computer science and biology. The historical progression from simple flowcharts to modern network visualizations illustrates the ongoing challenge of making complex biological computation comprehensible.

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12.4 Yeast Cell as a Model System for Computational Analysis

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The choice of yeast (Saccharomyces cerevisiae) as a model organism for both DeepMind's Cell project and potential GLMP analyses is particularly apt. Yeast represents an ideal intermediate complexity system—more sophisticated than bacteria but simpler than multicellular organisms—making it perfect for developing computational models of cellular processes.

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Yeast cells offer several advantages for computational analysis: (1) Well-characterized genome—extensive genetic and biochemical data available; (2) Modular processes—clear separation of cellular functions that can be modeled as computational modules; (3) Experimental tractability—easy to manipulate and observe; and (4) Evolutionary conservation—many processes conserved in higher organisms.

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Specific yeast processes that could be modeled as computational systems include: (1) Cell cycle regulation—a complex state machine with checkpoints and feedback loops; (2) Metabolic networks—dynamic systems responding to nutrient availability; (3) Stress response pathways—adaptive systems that modify cellular behavior based on environmental conditions; and (4) Mating type switching—a sophisticated genetic program that controls cellular identity and behavior.

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The GLMP community can contribute to this effort by developing computational models of specific yeast processes, creating visualization tools for yeast genetic circuits, and comparing yeast computational logic with that of other organisms. This work can serve as a foundation for understanding more complex cellular systems and provide valuable insights for both basic biology and synthetic biology applications.

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13. Glossary of Key Terms

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Associative Addressing: A memory system where data is found by content rather than location (like finding a book by its subject rather than shelf position).

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Probabilistic Op Codes: Computational operations that have a probability of occurring rather than being deterministic (like rolling dice instead of flipping a light switch).

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Massive Parallelism: The simultaneous execution of billions of processes, as opposed to sequential processing where operations happen one after another.

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Virtual Machine: A computational environment that is defined by the programs it runs, creating a circular dependency between hardware and software.

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Zygotic Genome Activation: The "bootloader" process where an embryo transitions from using maternal RNA to transcribing its own genes.

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14. Conclusion

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Summary of Key Findings:

- - -

The genome is not a static archive but a living program in execution—one that operates on computational principles fundamentally different from those of conventional computers. Each organism runs a massively parallel set of probabilistic processes driven by chemistry, inheritance, and context.

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The β-galactosidase flowchart of 1995, while limited in its linear representation, marked an important step in recognizing the computational nature of genetic regulation. The critiques it received—particularly regarding the challenge of representing parallel processes—highlighted fundamental issues that continue to shape how we visualize and understand biological computation today.

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As Robert Robbins presciently noted in 1995, "It would be really interesting to think about the computational properties that might emerge in a system with probabilistic op codes and with as much parallelism as biological computers." Nearly three decades later, this observation points toward a rich frontier of research at the intersection of computation and biology.

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Implications and Future Directions: By understanding the genome as a unique computational paradigm, we gain insights not only into how life functions but also into new possibilities for computing itself. The Genome Logic Modeling Project (GLMP) provides a framework for advancing this understanding through collaborative research. The genome-as-program metaphor invites us to reimagine biology not only as a science of what life is, but how it computes. The tension between linear representations and parallel realities, first exemplified in early flowcharts, continues to drive innovation in both biological understanding and computational design.

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-

References

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    -
  1. Jacob, F. & Monod, J. (1961). Genetic regulatory mechanisms in the synthesis of proteins. Journal of Molecular Biology, 3, 318-356.
    2. -
  2. Robbins, R.J. (1995). Discussion on bionet.genome.chromosome newsgroup regarding genomic computation.
    3. -
  3. Dellaire, G. (1995). Response on bionet.genome.chromosome regarding genetic imprinting and genomic structure.
    4. -
  4. Welz, G. (1995). Is a genome like a computer program? The X Advisor.
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  5. Jonassen, I. Bioinformatics Links, University of Bergen.
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  6. Krzywinski, M., et al. (2009). Circos: An information aesthetic for comparative genomics. Genome Research, 19(9), 1639-1645.
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  7. Höhna, S., et al. (2014). Probabilistic graphical models in evolution and phylogenetics. Systematic Biology, 63(5), 753-771.
    8. -
  8. Koutrouli, M., et al. (2020). Guide to visualization of biological networks: Types, tools and strategies. Frontiers in Bioinformatics, 2, 1-21.
    9. -
  9. O'Donoghue, S.I., et al. (2018). Visualization of biomedical data. Annual Review of Biomedical Data Science, 1, 275-304.
    10. -
  10. Nardone, G.G., et al. (2023). Identifying missing pieces in color vision defects: a genome-wide association study in Silk Road populations. Frontiers in Genetics, 14:1161696.
    11. -
  11. del Val, C., et al. (2024). Gene expression networks regulated by human personality. Molecular Psychiatry, 29, 2241–2260.
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- - - - - \ No newline at end of file diff --git a/Genome Logic Modeling Project (GLMP) - a Hugging Face Space by garywelz.pdf b/Genome Logic Modeling Project (GLMP) - a Hugging Face Space by garywelz.pdf deleted file mode 100644 index 7767e5abf8bfc2f3f5de0f3fb094adb8658a0375..0000000000000000000000000000000000000000 --- a/Genome Logic Modeling Project (GLMP) - a Hugging Face Space by garywelz.pdf +++ /dev/null @@ -1,3 +0,0 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:44c6ef5adeced82d3bcac86db91b5c7ee1160bcda39cce172b03ae7135b591ec -size 200940 diff --git a/MATHEMATICAL_DEPENDENCY_GRAPHS_DESIGN.md b/MATHEMATICAL_DEPENDENCY_GRAPHS_DESIGN.md new file mode 100644 index 0000000000000000000000000000000000000000..0daeb9e79fe9a0afb9449d7e5d6696604f9b98f5 --- /dev/null +++ b/MATHEMATICAL_DEPENDENCY_GRAPHS_DESIGN.md @@ -0,0 +1,321 @@ +# Mathematical Dependency Graphs — Design Document + +## Overview + +A hybrid architecture for representing and visualizing axiomatic dependency structures across multiple mathematical subjects. Supports both static Mermaid subgraphs and interactive full-graph exploration. + +--- + +## Scope: Target Subjects + +| Subject | Foundations | Derived Items | Notes | +|---------|-------------|---------------|-------| +| **Euclid's Elements** | Postulates, Common Notions, Definitions | 464 Propositions (13 books) | Geometric constructions | +| **Peano Arithmetic** | 5 axioms, definitions | Theorems | Successor, induction | +| **Other number systems** | Axioms (integers, rationals, reals) | Theorems | Construction sequences | +| **Number theory** | Definitions, lemmas | Theorems | Divisibility, primes | +| **Algebra** | Group/ring/field axioms | Theorems | Abstract structures | +| **Contemporary geometry** | Modern axiom systems | Theorems | Metric, affine | +| **Hilbert's geometry** | 5 groups of axioms (incidence, order, congruence, etc.) | Theorems | *Grundlagen der Geometrie* | +| **Tarski's geometry** | Betweenness, congruence relations | Theorems | First-order, decidable | +| **Analysis** | Completeness, continuity axioms | Theorems | Real analysis, limits | + +--- + +## Core JSON Schema + +### Discourse (per subject) + +```json +{ + "schemaVersion": "1.0", + "discourse": { + "id": "euclid-elements", + "name": "Euclid's Elements", + "subject": "geometry", + "variant": "classical", + "description": "The thirteen books of Euclidean geometry", + "structure": { + "books": 13, + "chapters": "varies", + "foundationTypes": ["postulate", "commonNotion", "definition"] + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": ["Welz, G."], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Dependency Graph. Programming Framework." + }, + "sources": [ + { + "id": "euclid-heath", + "type": "primary", + "authors": "Heath, T.L.", + "title": "The Thirteen Books of Euclid's Elements", + "year": "1908", + "edition": "2nd", + "publisher": "Cambridge University Press", + "url": "https://archive.org/details/euclidheath00heatiala", + "notes": "Standard English translation with commentary" + }, + { + "id": "perseus", + "type": "digital", + "title": "Euclid, Elements", + "url": "http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086", + "notes": "Perseus Digital Library, Greek text with English" + } + ], + "nodes": [ + { + "id": "P1", + "type": "postulate", + "label": "Draw a straight line between two points", + "shortLabel": "Post. 1", + "book": 1, + "number": 1, + "colorClass": "postulate", + "sourceRef": "euclid-heath, Book I, Postulate 1", + "notes": "Also: Postulate 1 in most editions" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "Construct an equilateral triangle on a given line", + "shortLabel": "Prop. I.1", + "book": 1, + "number": 1, + "colorClass": "proposition", + "sourceRef": "euclid-heath, Book I, Proposition 1", + "notes": "First proposition; depends only on P1, P3" + } + ], + "edges": [ + {"from": "P1", "to": "Prop1"}, + {"from": "P3", "to": "Prop1"} + ], + "colorScheme": { + "postulate": {"fill": "#e74c3c", "stroke": "#c0392b"}, + "commonNotion": {"fill": "#9b59b6", "stroke": "#8e44ad"}, + "proposition": {"fill": "#1abc9c", "stroke": "#16a085"}, + "definition": {"fill": "#3498db", "stroke": "#2980b9"}, + "theorem": {"fill": "#1abc9c", "stroke": "#16a085"} + } +} +``` + +### Node Types (extensible) + +| Type | Use Case | +|------|----------| +| `axiom` | Peano, Hilbert, Tarski | +| `postulate` | Euclid | +| `commonNotion` | Euclid | +| `definition` | All subjects | +| `proposition` | Euclid | +| `theorem` | Most subjects | +| `lemma` | Supporting results | +| `corollary` | Direct consequences | + +### Cross-Discourse Links (future) + +```json +{ + "from": "Prop_I_47", + "to": "peano-theorem-42", + "discourseFrom": "euclid-elements", + "discourseTo": "peano-arithmetic", + "relation": "constructive_correspondence" +} +``` + +--- + +## Hybrid Architecture + +### 1. Canonical JSON (Source of Truth) + +- One JSON file per discourse: `euclid-elements.json`, `peano-arithmetic.json`, etc. +- Stored in GCS or repo +- Human-editable, version-controlled +- Can be validated against schema + +### 2. Mermaid Subgraph Generator + +- **Input:** JSON + filter (e.g., `book=1`, `props=1-15`) +- **Output:** Mermaid `graph TD` string +- **Use:** Static HTML pages, PDF export, small-scope viewing +- **Limit:** ~50–80 nodes per diagram for readability + +**Filter options:** +- `book`, `chapter`, `numberRange` +- `depth`: dependencies only, dependents only, or both +- `focus`: node ID + N-hop neighborhood + +### 3. Interactive Viewer + +- **Input:** Full JSON (or lazy-loaded by book) +- **Tech:** Cytoscape.js, vis.js, or Sigma.js +- **Features:** + - Zoom, pan, minimap + - Search by ID or label + - Click node → highlight upstream/downstream + - Filter by type, book, chapter + - Cluster by book/chapter + - Export subgraph as Mermaid +- **Deployment:** Single HTML + JS, fetches JSON from GCS + +### 4. Index / Registry + +```json +{ + "schemaVersion": "1.0", + "lastUpdated": "2026-03-15", + "discourses": [ + { + "id": "euclid-elements", + "name": "Euclid's Elements", + "url": "https://.../euclid-elements.json", + "nodeCount": 480, + "edgeCount": 1200, + "subjects": ["geometry"], + "keywords": ["Euclid", "Elements", "plane geometry", "constructions"], + "sources": [ + {"id": "euclid-heath", "authors": "Heath, T.L.", "title": "The Thirteen Books of Euclid's Elements", "year": "1908"} + ], + "metadata": {"version": "1.0.0", "lastUpdated": "2026-03-15"} + }, + { + "id": "peano-arithmetic", + "name": "Peano Arithmetic", + "url": "https://.../peano-arithmetic.json", + "nodeCount": 85, + "edgeCount": 120, + "subjects": ["arithmetic", "foundations"], + "keywords": ["Peano", "axioms", "induction", "successor"], + "sources": [ + {"id": "peano-1889", "authors": "Peano, G.", "title": "Arithmetices principia", "year": "1889"} + ], + "metadata": {"version": "1.0.0", "lastUpdated": "2026-03-15"} + } + ] +} +``` + +--- + +## File Structure (Proposed) + +``` +mathematics-dependency-graphs/ +├── schema/ +│ └── discourse-schema.json # JSON Schema for validation +├── data/ +│ ├── index.json # Registry of all discourses +│ ├── euclid-elements.json +│ ├── peano-arithmetic.json +│ ├── hilbert-geometry.json +│ └── tarski-geometry.json +├── generator/ +│ └── mermaid-from-json.js # Subgraph → Mermaid +├── viewer/ +│ ├── interactive-viewer.html # Full interactive graph +│ └── viewer.js +└── static/ # Pre-generated Mermaid pages + ├── euclid/ + │ ├── book1-props-1-15.html + │ ├── book1-props-16-30.html + │ └── ... + └── peano/ + └── ... +``` + +--- + +## Integration with Existing Systems + +- **Mathematics Processes Database (GCS):** Static Mermaid pages can live in `processes/geometry_topology/` or a new `dependency-graphs/` folder +- **Programming Framework:** Same 5/6-color scheme; extend with subject-specific palettes (e.g., Tarski uses relation types) +- **GLMP-style collections:** Each discourse is a "collection"; index.json is the catalog + +--- + +## Implementation Phases + +| Phase | Deliverable | +|-------|-------------| +| **1** | Schema + Euclid Props 1–6 JSON; Mermaid generator script | +| **2** | Euclid Book I full JSON; static pages for Books I–IV | +| **3** | Interactive viewer (single discourse) | +| **4** | Peano Arithmetic, Hilbert Geometry JSON | +| **5** | Multi-discourse index; cross-discourse navigation | +| **6** | Tarski, Analysis, other subjects | + +--- + +## Color Scheme Consistency + +Use GLMP 6-color for *process* flowcharts (algorithms). For *dependency* graphs, allow subject-specific schemes: + +- **Euclid:** Postulates (red), Common Notions (purple), Propositions (teal) +- **Peano:** Axioms (red), Definitions (yellow), Theorems (teal) +- **Hilbert:** Axiom groups (distinct colors), Theorems (teal) +- **Tarski:** Primitive relations (red), Defined relations (blue), Theorems (teal) + +Schema supports `colorScheme` per discourse. + +--- + +## Metadata & Sources + +### Discourse-Level Metadata + +| Field | Purpose | +|-------|---------| +| `metadata.created` | ISO date of initial creation | +| `metadata.lastUpdated` | ISO date of last edit | +| `metadata.version` | Semantic version (e.g., 1.0.0) | +| `metadata.license` | License (e.g., CC BY 4.0) | +| `metadata.authors` | Contributors to the dependency graph | +| `metadata.methodology` | e.g., Programming Framework | +| `metadata.citation` | How to cite this graph | + +### Discourse-Level Sources + +| Field | Purpose | +|-------|---------| +| `sources[].id` | Reference ID for node-level `sourceRef` | +| `sources[].type` | `primary`, `secondary`, `digital`, `commentary` | +| `sources[].authors` | Author(s) | +| `sources[].title` | Title of work | +| `sources[].year` | Publication year | +| `sources[].url` | Link to digital copy | +| `sources[].doi` | DOI if available | +| `sources[].notes` | Clarifications | + +### Node-Level Metadata + +| Field | Purpose | +|-------|---------| +| `sourceRef` | Reference to `sources[].id` + location (e.g., "euclid-heath, Book I, Prop 1") | +| `notes` | Editorial notes, variants, clarifications | +| `keywords` | Tags for search/filter | +| `relatedNodes` | IDs of conceptually related nodes (same discourse or cross-discourse) | + +### Index / Registry Metadata + +The index should include per-discourse: `sources`, `metadata`, `lastUpdated`, `nodeCount`, `edgeCount`, `subjects`, `keywords`. + +--- + +## References + +- Euclid's Elements: [Perseus Digital Library](http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086) +- Heath, T.L. *The Thirteen Books of Euclid's Elements* (1908, 2nd ed.) +- Hilbert: *Grundlagen der Geometrie* (1899) +- Tarski: *What is Elementary Geometry?* (1959) +- Peano: *Arithmetices principia* (1889) diff --git a/MATHEMATICS_DATABASE_EXPANSION_PLAN.md b/MATHEMATICS_DATABASE_EXPANSION_PLAN.md new file mode 100644 index 0000000000000000000000000000000000000000..65b513d203b9f486ee49f6bf6617c8592e9e6771 --- /dev/null +++ b/MATHEMATICS_DATABASE_EXPANSION_PLAN.md @@ -0,0 +1,291 @@ +# Mathematics Database Expansion Plan + +## Overview + +Expand the mathematics-database-table and processes to include: +- **Topic sections**: Complex analysis, complex analytic dynamics, landmark theorems (FLT, Poincaré, Riemann) +- **Named mathematicians**: Historical and modern figures with associated charts +- **Formal verification**: Lean proofs and proof assistants +- **AI mathematics**: Recent AI-assisted results +- **Overlapping collections**: Processes appear in multiple named sets (topic + mathematician + historical) + +--- + +## 1. Metadata Schema Extension + +### Add `namedCollections` Array to Each Process + +```json +{ + "id": "number_theory-fermat-last-theorem", + "name": "Fermat's Last Theorem", + "subcategory": "number_theory", + "namedCollections": ["fermat", "landmark_theorems", "wiles", "number_theory_milestones"] +} +``` + +**Rationale**: A process can belong to many collections. Examples: +- *Euclid's Elements* → `["euclid", "geometry_topology", "classical_geometry", "axiomatic_systems"]` +- *Galois Theory* → `["galois", "abstract_algebra", "field_theory", "landmark_theorems"]` +- *Sieve of Eratosthenes* → `["eratosthenes", "number_theory", "algorithms", "classical_algorithms"]` + +### Optional: Add `collections` Index in metadata.json + +```json +{ + "collections": { + "archimedes": { "name": "Archimedes", "description": "…", "processIds": ["…"] }, + "fermat": { "name": "Pierre de Fermat", "description": "…", "processIds": ["…"] } + } +} +``` + +Either derive from processes (scan `namedCollections`) or maintain explicitly. + +--- + +## 2. New Subcategories + +| Subcategory ID | Display Name | Notes | +|-----------------------|------------------------|--------------------------------------------| +| `complex_analysis` | Complex Analysis | New; analytic functions, residues, etc. | +| `landmark_theorems` | Landmark Theorems | FLT, Poincaré, Riemann, etc. | +| `formal_verification` | Formal Verification | Lean, Coq, Isabelle proofs | +| `ai_mathematics` | AI Mathematics | AlphaProof, AlphaGeometry, etc. | + +**Existing** (keep): `number_theory`, `geometry_topology`, `discrete_mathematics`, `linear_algebra`, `calculus_analysis`, `abstract_algebra`, `category_theory`, `foundations`, `bioinformatics`. + +--- + +## 3. Topic Sections (New Charts) + +### 3.1 Complex Analysis +- **Complex Analysis — Analytic Functions & Cauchy-Riemann** +- **Complex Analysis — Cauchy Integral Theorem & Residues** +- **Complex Analysis — Conformal Mappings & Riemann Surfaces** +- **Complex Analysis — Entire Functions & Picard Theorems** + +*Collections*: `complex_analysis`, `calculus_analysis` (overlap) + +### 3.2 Complex Analytic Dynamics (extend existing) +- Already have: Julia/Fatou, Sullivan, Hubbard-Douady, Devaney, etc. +- Add: **Complex Dynamics — Holomorphic Dynamics Overview** (hub/overview) +- Add: **Complex Dynamics — Parabolic Fixed Points & Écalle-Voronin** + +*Collections*: `complex_dynamics`, `calculus_analysis`, `sullivan`, `hubbard_douady`, `devaney` + +### 3.3 Landmark Theorems +| Chart | Subcategory | Named Collections | +|------------------------------|--------------------|-------------------------------------| +| Fermat's Last Theorem | `landmark_theorems`| `fermat`, `wiles`, `number_theory` | +| Poincaré Conjecture | `landmark_theorems`| `poincare`, `perelman`, `topology` | +| Riemann Hypothesis | `landmark_theorems`| `riemann`, `number_theory`, `analysis` | +| Four Color Theorem | `landmark_theorems`| `appel_haken`, `graph_theory` | +| Gödel Incompleteness | (existing) | `godel`, `foundations` | + +--- + +## 4. Named Mathematicians — Charts to Create + +### 4.1 Classical (Ancient & Early Modern) +| Mathematician | Charts to Create | Overlaps With | +|----------------|--------------------------------------------------------|----------------------------| +| **Archimedes** | Archimedes' Principle, Method of Exhaustion, Pi bounds | `geometry_topology`, `calculus` | +| **Eratosthenes** | Sieve (existing), Earth circumference, Prime counting | `number_theory`, `algorithms` | +| **Pythagoras** | Pythagorean Theorem, Pythagorean triples, Irrationals | `geometry_topology`, `number_theory` | +| **Euclid** | Elements (existing), Euclidean algorithm | `geometry_topology` | + +### 4.2 Early Modern +| Mathematician | Charts to Create | Overlaps With | +|---------------|--------------------------------------------------------|----------------------| +| **Fermat** | Fermat's Last Theorem, Fermat's Little Theorem, Fermat primes | `number_theory`, `landmark_theorems` | +| **Euler** | Euler's formula (e^(iπ)+1=0), Euler characteristic, Seven Bridges | `calculus_analysis`, `graph_theory`, `topology` | +| **Gauss** | Fundamental Theorem of Algebra, Gaussian integers, Least squares | `number_theory`, `linear_algebra`, `calculus` | + +### 4.3 19th–20th Century +| Mathematician | Charts to Create | Overlaps With | +|-------------------|--------------------------------------------------------|----------------------| +| **Galois** | Galois Theory (existing), Solvability by radicals | `abstract_algebra`, `field_theory` | +| **Cayley** | Cayley's theorem (groups), Cayley-Hamilton theorem | `abstract_algebra`, `linear_algebra` | +| **Hamilton** | Quaternions, Hamiltonian mechanics, Cayley-Hamilton | `linear_algebra`, `physics` | +| **Noether** | Noether's theorems, Noetherian rings, Abstract algebra | `abstract_algebra`, `physics` | +| **Hilbert** | Hilbert's problems, Hilbert space, Basis theorem | `foundations`, `linear_algebra`, `analysis` | +| **Riemann** | Riemann Hypothesis, Riemann surfaces, Riemann integral | `number_theory`, `calculus_analysis`, `complex_analysis` | + +### 4.4 Modern (20th–21st Century) +| Mathematician | Charts to Create | Overlaps With | +|--------------|--------------------------------------------------------|----------------------| +| **Thurston** | Geometrization conjecture, Hyperbolic 3-manifolds | `geometry_topology`, `poincare` | +| **Milnor** | Exotic spheres, Milnor's theorem, Morse theory | `geometry_topology`, `differential_topology` | +| **Faltings** | Mordell conjecture, Faltings' theorem (FLT for n>4) | `number_theory`, `fermat`, `algebraic_geometry` | +| **Atiyah** | Atiyah-Singer index theorem, K-theory | `geometry_topology`, `analysis` | +| **Perelman** | Ricci flow, Poincaré proof | `landmark_theorems`, `poincare` | +| **Wiles** | Modularity theorem, FLT proof | `landmark_theorems`, `fermat` | + +### 4.5 Additional Candidates (for later) +- **Gödel** (existing via Peano) +- **Turing** (computability, halting problem) +- **Kolmogorov** (probability, complexity) +- **Grothendieck** (schemes, topos theory) +- **Serre** (algebraic geometry, number theory) +- **Deligne** (Weil conjectures) +- **Tao** (existing: Green-Tao) +- **Szemerédi** (existing) +- **Sullivan** (existing) +- **Hubbard, Douady, Devaney** (existing) + +--- + +## 5. Formal Verification (Lean Proofs) + +### 5.1 New Subcategory: `formal_verification` + +| Chart | Description | +|-----------------------------------|--------------------------------------------------| +| Lean 4 — Proof Assistant Overview | What Lean is, tactic language, type theory | +| Mathlib — Library Structure | Mathlib dependency graph, key namespaces | +| Fermat's Last Theorem in Lean | FLT statement and proof status in Lean | +| Kepler Conjecture (Flyspeck) | Hales' proof, formalization in HOL Light | +| Four Color Theorem in Coq | Gonthier's formalization | +| Odd Order Theorem (Feit-Thompson)| Gonthier et al. formalization | + +*Collections*: `lean`, `formal_verification`, `landmark_theorems` (where applicable) + +--- + +## 6. AI Mathematics + +### 6.1 New Subcategory: `ai_mathematics` + +| Chart | Description | +|----------------------------------------|--------------------------------------------------| +| AlphaProof (DeepMind 2024) | IMO results, statement proving | +| AlphaGeometry (DeepMind 2024) | Synthetic geometry, IMO-style problems | +| AI-Assisted Proof Discovery | Overview: GPT, Lean, collaboration | +| Ramanujan Machine / Conjecture Generation | Automated conjecture generation | +| Formalization Gaps (AI + Human) | What remains to be formalized | + +*Collections*: `ai_mathematics`, `formal_verification` (overlap) + +--- + +## 7. Table Structure — Section Headers & Breaks + +### 7.1 Proposed Table Sections (with breaks) + +1. **Algorithms — Flowcharts** (existing) +2. **Axiomatic Theories — Dependency Graphs** (existing) +3. **Landmark Theorems** (new section) +4. **Complex Analysis & Dynamics** (new or merged into Calculus & Analysis) +5. **Formal Verification (Lean, Coq, etc.)** (new) +6. **AI Mathematics** (new) + +### 7.2 Named Collections Panel (expand) + +Current: Euclid, Tao, Peano, Gödel, Sullivan, Hubbard & Douady, Devaney, Smale, Bioinformatics + +**Add**: +- Archimedes, Eratosthenes, Pythagoras +- Fermat, Euler, Gauss +- Galois, Cayley, Hamilton, Noether, Hilbert +- Riemann, Thurston, Milnor, Faltings, Atiyah +- Wiles, Perelman +- Lean / Formal Verification +- AI Mathematics + +**Implementation**: Either (a) one link per collection → landing page listing all processes in that collection, or (b) first/representative process. Prefer (a) for multi-process collections. + +--- + +## 8. Overlap Handling + +### 8.1 Process in Multiple Collections + +Example: **Fermat's Last Theorem** +- `subcategory`: `landmark_theorems` +- `namedCollections`: `["fermat", "wiles", "number_theory", "landmark_theorems"]` + +Appears in: +- Landmark Theorems table section +- Fermat collection page +- Wiles collection page +- Number Theory subcategory filter + +### 8.2 Collection Landing Pages + +Create `processes/collections/` (or similar): +- `collections/fermat.html` — lists all processes with `namedCollections` containing `fermat` +- `collections/euler.html` +- `collections/landmark_theorems.html` +- etc. + +These can be generated from metadata or static HTML with links derived from metadata. + +### 8.3 Table Filtering (Optional) + +Add filter dropdown: "Show by collection: All | Fermat | Euler | Landmark Theorems | …" + +--- + +## 9. Implementation Phases + +### Phase 1: Schema & Infrastructure +- Add `namedCollections` to metadata schema +- Add new subcategories to metadata +- Create collection landing page template +- Update table to support new sections and breaks + +### Phase 2: Landmark Theorems +- Fermat's Last Theorem +- Poincaré Conjecture +- Riemann Hypothesis +- (Optional) Four Color, Gödel as landmark) + +### Phase 3: Complex Analysis +- 3–4 complex analysis charts +- Ensure overlap with existing complex dynamics + +### Phase 4: Named Mathematicians (Batch 1) +- Archimedes, Eratosthenes, Pythagoras +- Fermat, Euler, Gauss +- Tag existing processes (Euclid, Sieve, etc.) with `namedCollections` + +### Phase 5: Named Mathematicians (Batch 2) +- Galois, Cayley, Hamilton, Noether, Hilbert +- Riemann, Thurston, Milnor, Faltings, Atiyah +- Wiles, Perelman + +### Phase 6: Formal Verification +- Lean overview +- 2–3 key formalized results (FLT, Four Color, etc.) + +### Phase 7: AI Mathematics +- AlphaProof, AlphaGeometry +- AI-assisted proof overview + +--- + +## 10. File Naming Conventions + +- `number_theory-fermat-last-theorem.html` +- `landmark_theorems-poincare-conjecture.html` +- `landmark_theorems-riemann-hypothesis.html` +- `complex_analysis-cauchy-integral-theorem.html` +- `formal_verification-lean-flt.html` +- `ai_mathematics-alphaproof.html` +- `collections/fermat.html` (collection index) + +--- + +## 11. Summary: New Content Counts (Estimate) + +| Category | New Charts (approx) | +|-----------------------|---------------------| +| Complex Analysis | 4 | +| Landmark Theorems | 3–5 | +| Named Mathematicians | 15–25 (many overlap)| +| Formal Verification | 4–6 | +| AI Mathematics | 3–5 | +| **Total new** | **~30–45** | + +Many of these overlap (e.g., Fermat chart counts for Fermat, Wiles, Landmark Theorems, Number Theory). The `namedCollections` array is the key to supporting this overlap cleanly. diff --git a/NEXT_PASS_CHECKLIST.md b/NEXT_PASS_CHECKLIST.md new file mode 100644 index 0000000000000000000000000000000000000000..d793b64ccd9772df18e66a1ae203525b5b7f93d2 --- /dev/null +++ b/NEXT_PASS_CHECKLIST.md @@ -0,0 +1,182 @@ +# Mathematics Database — Next Pass Checklist + +A prioritized checklist for the next major revision: Cite links, Frontier sections, and uniform color scheme. + +--- + +## Phase 0: Database Table Page (Intro & Start Here) — DONE ✓ + +- [x] Concise introduction at top (conceptual-framing) +- [x] Move search box into "Start Here" section +- [x] Remove "Named Collections" (avoids who-is-named complaints) +- [x] Start Here: search field + link to Whole of Mathematics +- [x] Describe Whole of Mathematics as "Interactive UI" in link text + +--- + +## Reference: 5/6-Color Scheme (GLMP) + +Use this palette across all charts for consistency: + +| Role | Hex | Semantic | +|------|-----|----------| +| Red | `#ff6b6b` | Triggers, inputs, postulates | +| Yellow | `#ffd43b` | Structures, objects | +| Green | `#51cf66` | Processing, operations, propositions | +| Light blue | `#74c0fc` | Intermediates, states | +| Violet | `#b197fc` | Products, outputs | +| Lavender | `#e6e6fa` | Decision diamonds (algorithms only) | + +**Axiomatic/dependency chart mapping:** +| Node type | Hex | Role | +|--------------|------------|--------------------------| +| Axiom | `#ff6b6b` | Red — inputs, postulates | +| Postulate | `#ff6b6b` | Red — same as axiom | +| CommonNotion | `#ffd43b` | Yellow — structures | +| Definition | `#b197fc` | Violet — products | +| Lemma | `#74c0fc` | Light blue — intermediates| +| Theorem | `#51cf66` | Green — propositions | +| Corollary | `#1abc9c` | Teal | +| Proposition | `#51cf66` | Green — same as theorem | +| Reference | `#bdc3c7` | Gray | + +--- + +## Phase 1: Cite Links + +Add attribution (Cite badge + popover) to charts with identifiable primary sources. + +### Already have Cite (7) +- [x] Gödel First Incompleteness +- [x] Schemes & Sheaves (Grothendieck) +- [x] Group Representations +- [x] Riemannian Geometry +- [x] ZFC Axioms +- [x] Shannon Entropy +- [x] C*-Algebras + +### High priority (add Cite) +- [ ] Euclid's Elements charts +- [ ] Peano Arithmetic (Landau, Kirby–Paris) +- [ ] Szemerédi Theorem +- [ ] Green–Tao Theorem +- [ ] Galois Theory (Field Theory charts) +- [ ] Cauchy / Complex Analysis charts +- [ ] Sullivan collection charts +- [ ] Hubbard–Douady collection +- [ ] Devaney collection +- [ ] Kolmogorov axioms, Bayes, CLT (Statistics) +- [ ] NIST DADS algorithms (Binary Search, etc.) + +### Medium priority +- [ ] PDE charts (Laplace, Heat, Wave) +- [ ] Functional analysis (Banach, Hilbert) +- [ ] Spectral theory charts +- [ ] Representation theory (remaining) +- [ ] Commutative algebra charts + +### Schema +See `ATTRIBUTION_SCHEMA.md`. Fields: `primary`, `contributors`, `publication`, `year`, `doi`, `url`. + +--- + +## Phase 2: Frontier of Research Links + +Add or expand "Recent & Frontier" sections on index pages. Each section: proved results, open conjectures, links to charts, links to arXiv/external. + +### Already have Recent & Frontier (3) +- [x] Number Theory +- [x] Algebraic Geometry +- [x] Representation Theory + +### Add Frontier section +- [x] Differential Geometry +- [x] Complex Analysis +- [x] Statistics & Probability +- [x] Partial Differential Equations +- [x] Foundations (set theory, logic) +- [x] Calculus / Real Analysis +- [x] Functional Analysis +- [x] Topology (geometry_topology index) +- [x] Operator Algebras +- [x] K-Theory + +### Template +Use the pattern from `algebraic_geometry.html`: `.frontier-item.proved` (green border), `.frontier-item.conjecture` (orange border), with `.name`, `.meta`, and chart/external links. + +--- + +## Phase 3: Uniform Color Scheme + +Apply the 5/6-color palette to all charts. Replace per-subcategory accent colors with the standard palette. + +### Algorithm flowcharts (already mostly correct) +- [x] Sieve, Extended Euclidean, Dijkstra, Prim, Kruskal, BFS +- [x] Binary Search, RSA, AES, Merge Sort, Quicksort, BST +- [x] Bisection, Simpson's Rule +- [x] Bioinformatics (BLAST, sequence alignment) +- [x] Verify any outliers use standard colors + +### Axiomatic / dependency charts +- [x] Gödel / Peano charts — map Def/Lem/Thm/Cor to palette +- [x] Euclid's Elements — align postulate/common notion/proposition colors +- [x] ZFC / Foundations +- [x] Abstract algebra, algebraic geometry, representation theory, differential geometry, spectral theory, symplectic, metric geometry + +### P3 charts (operator algebras, K-theory, quantum algebra, optimization, information theory, mathematical physics) +- [x] Replace subcategory-specific header/node colors with 5-color palette +- [x] Header: database orange #e67e22 +- [x] Mermaid nodes: Def → Violet, Thm → Green + +### Header / nav consistency +- [x] Standardize header to database orange #e67e22 +- [x] Nav link colors: #e67e22 + +--- + +## Phase 4: Optional Enhancements (if time) + +### Content +- [x] Landmark theorem charts: FLT, Riemann Hypothesis (high-level) +- [x] Modular arithmetic: CRT (Chinese Remainder Theorem) +- [ ] Primality tests (future) +- [ ] `namedCollections` metadata for cross-linking (Euclid, Gödel, Galois, etc.) + +### Infrastructure +- [x] Formal verification links (Lean, Coq) +- [x] AI mathematics (AlphaProof, AlphaGeometry) +- [x] math.HO (History & Overview) — added to Number Theory, Foundations + +--- + +## Execution Order + +1. **Phase 3 (Color)** — Do first; it's a bulk replace across many files. Establishes visual consistency before adding content. +2. **Phase 1 (Cite)** — Add attribution to charts that have clear sources. Can be done incrementally. +3. **Phase 2 (Frontier)** — Add Recent & Frontier sections to remaining index pages. Lower effort, high value. +4. **Phase 4** — As capacity allows. + +--- + +## Files to Modify + +### Color scheme +- All `processes/**/*.html` with Mermaid `classDef` blocks +- Generator templates: `generate_p3_charts.py` (P3 charts) +- Possibly: shared CSS or build step for future automation + +### Cite +- Add attribution HTML + CSS to each chart; or extend generator/template for batch charts +- Update `ATTRIBUTION_SCHEMA.md` if schema changes + +### Frontier +- Index pages: `processes//.html` (e.g. `processes/differential_geometry/differential_geometry.html`) + +--- + +## Completion Criteria + +- [ ] All charts with identifiable sources have Cite badge +- [ ] All major index pages have Recent & Frontier section +- [ ] All charts use the 5/6-color palette (no stray per-chart accent colors in node fills) +- [ ] Header/nav colors are consistent (or explicitly documented as domain accents) diff --git a/NEXT_STEPS_PLAN.md b/NEXT_STEPS_PLAN.md new file mode 100644 index 0000000000000000000000000000000000000000..ad6676b428eef08cda94cb4c0dbb43dd0e0570c7 --- /dev/null +++ b/NEXT_STEPS_PLAN.md @@ -0,0 +1,161 @@ +# Mathematics Database — Next Steps Plan + +Three initiatives: **Search** (near-term), **Comprehensive Collection** (mid-term), and **Research Frontier** (long-term). + +--- + +## 1. Search the Collection + +**Goal**: Place a search bar near the top of the table page. Users can search by theorem name, mathematician name, subcategory, or keyword and get links to individual charts or collection pages. + +### 1.1 Search UI Placement +- Add a search box immediately after the header (before or alongside "Start Here") +- Design: Single input, optional filters (All / Algorithms / Axiomatic / Collection) +- Live/filter-as-you-type or "Search" button — both viable + +### 1.2 Search Data Source +- **Client-side**: Load `metadata.json` (already fetched for the table); search in memory +- **Indexable fields** (extend metadata if needed): + - `name` (process title) — e.g. "Fermat's Last Theorem", "Sieve of Eratosthenes" + - `subcategory` / `subcategory_name` — e.g. "Number Theory", "Calculus & Analysis" + - `namedCollections` (when added) — e.g. "euclid", "fermat", "sullivan" + - Optional: add `keywords` or `searchTerms` array for aliases ("FLT", "Poincaré", "ZFC") + +### 1.3 Search Algorithm +- **Simple**: Case-insensitive substring match on `name`, `subcategory_name` +- **Better**: Tokenize query, match against name + subcategory + collections +- **Fuzzy** (optional): Use a small library (e.g. Fuse.js) for typo tolerance + +### 1.4 Results Display +- **Single process match** → link directly to process page +- **Collection match** (e.g. "Euclid") → link to collection landing page (or list of processes in that collection) +- **Multiple matches** → show dropdown or results panel with: + - Process name + subcategory + - Link to process page + - "Part of: Euclid, Geometry & Topology" (when namedCollections exists) + +### 1.5 Metadata Enhancements for Search +- Add `namedCollections` to processes (per expansion plan) +- Optional: `keywords: ["FLT", "Fermat", "Wiles"]` for common aliases +- Optional: `theorems: ["Modularity Theorem", "Fermat's Last Theorem"]` for axiomatic theories + +### 1.6 Implementation Scope +| Task | Effort | +|------|--------| +| Add search input + results dropdown | Small | +| Client-side search over `metadata.json` | Small | +| Add `namedCollections` to metadata (partial) | Medium | +| Collection landing pages for multi-result | Medium | + +--- + +## 2. Plan to Fill Out the Collection (Comprehensive) + +Build on [MATHEMATICS_DATABASE_EXPANSION_PLAN.md](./MATHEMATICS_DATABASE_EXPANSION_PLAN.md). Aim for a representative, well-structured set across major areas. + +### 2.1 Coverage Goals by Domain + +| Domain | Current | Target | Priority Additions | +|--------|---------|--------|-------------------| +| **Algebra** | Strong | Maintain + expand | Cayley-Hamilton, Noether, Representation theory | +| **Analysis** | Good | Expand | Complex analysis (4 charts), Functional analysis basics | +| **Geometry & Topology** | Good | Expand | Milnor exotic spheres, Thurston geometrization | +| **Number Theory** | Good | Expand | Landmark theorems (FLT, Riemann), Fermat's Little Theorem | +| **Discrete & Logic** | Strong | Maintain | Add combinatorics algorithms (inclusion-exclusion, generating functions) | +| **Applied** | Bioinformatics only | Expand | Statistics/probability, optimization basics | + +### 2.2 Landmark Theorems (High Impact) +- Fermat's Last Theorem (Wiles, modularity) +- Poincaré Conjecture (Perelman, Ricci flow) +- Riemann Hypothesis (statement, equivalent forms) +- Four Color Theorem (Appel–Haken, formalization) +- Gödel Incompleteness (already present via Peano) + +### 2.3 Gaps to Fill +- **Complex Analysis**: Cauchy, residues, conformal maps +- **Statistics & Probability**: Kolmogorov axioms, Central Limit Theorem, Bayes +- **Numerical Methods**: More algorithms (Newton, Euler methods, quadrature) +- **Representation Theory**: Basics (groups, characters) +- **Differential Geometry**: Curves, surfaces, Riemannian basics + +### 2.4 Phased Rollout (from expansion plan, refined) + +| Phase | Focus | Charts (approx) | +|-------|-------|-----------------| +| **1** | Schema + search + `namedCollections` | 0 new charts | +| **2** | Landmark theorems (FLT, Poincaré, Riemann) | 3–5 | +| **3** | Complex analysis | 4 | +| **4** | Named mathematicians (batch 1: Fermat, Euler, Gauss, Euclid tag) | 5–8 | +| **5** | Named mathematicians (batch 2: Galois, Noether, Hilbert, Riemann) | 5–8 | +| **6** | Statistics & probability | 3–5 | +| **7** | Formal verification (Lean, Four Color in Coq) | 3–4 | +| **8** | AI mathematics (AlphaProof, AlphaGeometry) | 2–3 | + +### 2.5 Definition of "Fairly Comprehensive" +- All 6 domains have ≥5 distinct charts +- Every subcategory has at least 1 chart +- Landmark theorems (FLT, Poincaré, Riemann) represented +- Major figures (Euclid, Euler, Gauss, Fermat, Gödel, Galois) have at least one chart +- ~150–200 total processes as a stretch goal + +--- + +## 3. Long-Term: Research Frontier & Conjectures + +**Goal**: Update axiomatic theory trees to show recent theorems, open conjectures, and the frontier of research — making the dependency graphs reflect the state of the field, not just classic textbook material. + +### 3.1 What "Frontier" Means +- **Recent theorems**: Results from the last 20–30 years (e.g. Perelman/geometrization, Taylor–Wiles modularity) +- **Conjectures**: Stated but unproven (Riemann, Birch–Swinnerton-Dyer, Hodge, P vs NP) +- **Formalization status**: What is in Mathlib/Lean, what remains to be formalized + +### 3.2 Data Sources for Frontier Content +- **arXiv**: Recent math.NT, math.GT, math.AG, etc. — identify major theorems +- **Mathlib / formalization**: Lean 4, Coq, Isabelle — which theorems are proved +- **Surveys & encyclopedias**: Wikipedia, Encyclopaedia of Mathematics, Scholarpedia +- **Clay Institute, Hilbert problems**: Lists of major open problems + +### 3.3 Schema Extensions +- **Node metadata** in dependency graphs: + - `status`: `proved` | `conjecture` | `open_problem` | `formalized` + - `year`: publication or proof year + - `prover`: e.g. "Wiles", "Perelman", "Gonthier et al." + - `formalization`: e.g. `{ "tool": "Lean", "status": "in_progress" }` +- **Process-level**: + - `frontierLevel`: `classical` | `modern` | `recent` | `conjecture` + - `openProblems`: array of conjecture names + +### 3.4 Visualization Ideas +- **Color coding**: Green (proved), yellow (recent), orange (conjecture), grey (formalized) +- **"Expand to frontier"** control: Toggle to show/hide conjectures and recent theorems +- **Year annotations**: Small labels on nodes (e.g. "1995", "2003") +- **Separate "Conjectures" section**: Page listing open problems with links to related axiom–theorem trees + +### 3.5 Implementation Phases (Long-Term) +| Phase | Focus | +|-------|-------| +| **A** | Add `status`, `year` to process metadata (manual curation) | +| **B** | Extend Mermaid/diagram format to support status annotations | +| **C** | Curate 5–10 landmark theorems with frontier metadata | +| **D** | Build "Open Problems" index page | +| **E** | Integrate formalization status (Mathlib, etc.) where available | + +### 3.6 Challenges +- **Curation effort**: Requires domain expertise to classify and annotate +- **Currency**: Frontier changes; need update process (annual review?) +- **Formalization**: Mathlib evolves; linking to specific commits or versions +- **Scope creep**: Easy to expand; need clear criteria for "frontier" + +### 3.7 Sample Implemented: Number Theory Research Frontier +- **Page**: `number-theory-research-frontier.html` — static view of proved vs conjecture +- **Metadata**: `frontierStatus`, `year`, `prover` added to Sieve, Szemerédi, Green–Tao in `metadata.json` +- **Linked** from database table "Start Here" section +- **Contents**: Classical (Sieve, Extended Euclidean, Gödel), recent (Szemerédi 1975, Green–Tao 2004, Fermat 1995, Mordell 1983), conjectures (Riemann, BSD, Goldbach, Twin Primes) + +--- + +## Summary: Immediate Next Steps + +1. **Search** (1–2 days): Add search input, client-side search over metadata, results dropdown with links. +2. **Expansion plan** (ongoing): Execute phases from MATHEMATICS_DATABASE_EXPANSION_PLAN.md; use this doc for prioritization. +3. **Frontier** (quarterly/yearly): Start with schema additions and manual curation of a few landmark results; build out as capacity allows. diff --git a/ProgFrame_README.md b/ProgFrame_README.md deleted file mode 100644 index 327975a5274d470d7dbaa972441027e8fb8930e1..0000000000000000000000000000000000000000 --- a/ProgFrame_README.md +++ /dev/null @@ -1,227 +0,0 @@ ---- -title: Genome Logic Modeling Project (GLMP) -emoji: 🧬 -colorFrom: blue -colorTo: green -sdk: static -sdk_version: latest -app_file: README.md -pinned: false ---- - -# 🧬 Programming Framework for Complex Systems - -**A systematic visualization methodology for analyzing complex systems across biology, chemistry, physics, and computer science using computational flowcharts and standardized color coding.** - -[![License: CC BY 4.0](https://img.shields.io/badge/License-CC%20BY%204.0-lightgrey.svg)](https://creativecommons.org/licenses/by/4.0/) -[![Hugging Face Spaces](https://img.shields.io/badge/Hugging%20Face-Spaces-orange)](https://huggingface.co/spaces/garywelz/programming_framework) - -## 🎯 Overview - -The Programming Framework represents a revolutionary approach to understanding complex systems by translating them into standardized computational representations. Using Mermaid Markdown syntax and large language model (LLM) processing, we demonstrate the framework's application to representative biological and chemical systems. - -**Key Insight:** Complex systems across biology, chemistry, and physics exhibit remarkable similarities in their organizational principles despite operating at vastly different scales and domains. The Programming Framework reveals these common computational patterns. - -## 🔬 Methodology - -The Programming Framework methodology involves systematic analysis of complex systems through the following steps: - -1. **System Identification:** Identify the biological, chemical, or physical system to be analyzed -2. **Component Categorization:** Classify system components into the five functional categories -3. **Flowchart Construction:** Create Mermaid flowcharts with appropriate color coding -4. **Logic Verification:** Verify computational logic and system dynamics -5. **Cross-Disciplinary Comparison:** Identify patterns across different domains - -## 🎨 Universal Color Coding System - -Each process is represented as a computational flowchart with standardized color coding: - -| Color Category | Biology | Chemistry | Computer Science | Physics | Mathematics | -|----------------|---------|-----------|------------------|---------|-------------| -| 🔴 **Red** - Triggers & Inputs | Environmental signals, Nutrient availability | Reactant supply, Temperature | Input data, User commands | Energy input, Force application | Axioms, Given conditions | -| 🟡 **Yellow** - Structures & Objects | Enzymes, Receptor proteins | Catalysts, Reaction vessels | Data structures, Algorithms | Fields, Particles | Theorems, Methods | -| 🟢 **Green** - Processing & Operations | Metabolic reactions, Signal transduction | Chemical reactions, Equilibrium shifts | Algorithm execution, Data processing | Wave propagation, Quantum operations | Logical steps, Calculations | -| 🔵 **Blue** - Intermediates & States | Metabolites, Signaling molecules | Reaction intermediates, Transition states | Variables, Memory states | Quantum states, Energy levels | Intermediate results, Sub-proofs | -| 🟣 **Violet** - Products & Outputs | Biomolecules, Cellular responses | Final products, Reaction yields | Program outputs, Computed results | Measured quantities, Physical phenomena | Proven theorems, Mathematical results | - -**Note:** Yellow nodes use black text for optimal readability, while all other colors use white text. - -## 📊 Dataset and Evidence Base - -We analyzed a comprehensive dataset of biological processes spanning multiple organisms and systems: - -- **110 processes** from *Saccharomyces cerevisiae* (yeast) covering DNA replication, cell cycle control, signal transduction, energy metabolism, and stress responses -- **Multiple processes** from *Escherichia coli* including DNA replication, gene regulation, central metabolism, motility, and specialized systems like the lac operon -- **Advanced systems** including photosynthesis, bacterial sporulation, circadian clocks, and viral decision switches - -**Total:** 297+ processes across 36 individual collections - -The complete dataset is publicly available through the [Genome Logic Modeling Project (GLMP)](https://huggingface.co/spaces/garywelz/glmp) Hugging Face Space. - -## 🌟 Representative Applications - -### Case Study: β-Galactosidase Analysis (2025) -The β-galactosidase system represents one of the most well-characterized examples of genetic regulation in molecular biology. Using modern tools and AI assistance, we can now create sophisticated and detailed visualizations that demonstrate the full computational complexity of the lac operon system. - -**Key Features:** -- Environmental inputs (lactose, glucose, energy status) -- Regulatory logic gates -- Gene expression control -- Metabolic pathway integration -- Feedback control mechanisms - -### Case Study: Algorithm Execution Analysis -To demonstrate the framework's applicability to computer science, we applied the methodology to algorithm execution, specifically sorting algorithms. This example shows how the same computational logic can be applied to fundamental computer science processes. - -**Key Features:** -- Input data validation -- Algorithm selection and execution -- Performance analysis -- Error handling mechanisms -- Complexity analysis - -### Case Study: Mathematical Proof Tree Analysis -To demonstrate the framework's applicability to pure mathematics, we applied the methodology to mathematical proof construction, a fundamental process in mathematical logic. - -**Key Features:** -- Axiom processing -- Logical deduction steps -- Theorem application -- Proof validation -- Mathematical rigor verification - -## 🛠️ Technical Foundation - -The Programming Framework builds upon **Mermaid Markdown (MMD)**, a text-based diagram generation syntax developed by Knut Sveidqvist in 2014. MMD enables the creation of complex flowcharts and diagrams from simple text descriptions. - -**Key Capabilities:** -- **Text-to-Diagram Conversion:** Process descriptions from scientific literature can be directly converted into visual representations -- **Standardized Syntax:** Consistent formatting across different systems and domains -- **Automated Generation:** LLMs can rapidly process text descriptions and generate MMD code -- **Cross-Platform Compatibility:** MMD integrates with documentation platforms and can be rendered in multiple formats -- **Automatic Color Coding:** Canvas automatically derives color categories from MMD syntax - -## 📈 Historical Evolution: From 1995 to 2025 - -The Programming Framework represents the culmination of a 30-year evolution in computational biology visualization: - -### 1995: Manual Creation -- Months of research and reading -- Manual flowchart creation with Inspiration -- Single process analysis -- Community discussion on bionet.genome.chromosome -- Foundation for computational biology - -### 2025: AI-Assisted Analysis -- Hours of AI-assisted processing -- Automated Mermaid Markdown generation -- Systematic analysis of 297+ processes -- Cross-disciplinary pattern recognition -- Universal computational framework - -## 🚀 Getting Started - -### Quick Start Guide - -1. **Choose Your System:** Identify a biological, chemical, or physical system to analyze -2. **Apply the Framework:** Use the five-category color coding system -3. **Create Flowcharts:** Generate Mermaid Markdown representations -4. **Verify Logic:** Ensure computational logic is sound -5. **Compare Patterns:** Look for similarities across domains - -### Sample Analysis Prompt - -``` -"Analyze the [system name] using the Programming Framework methodology. Create a Mermaid Markdown file that will enable the creation in HTML of a computational flowchart showing how environmental inputs are processed through regulatory mechanisms to produce specific outputs. Use the universal color scheme: Red for triggers/inputs, Yellow for structures/catalysts, Green for processing operations, Blue for intermediates, and Violet for products. Include a discipline-specific color key beneath the flowchart." -``` - -## 📚 Applications - -### Biological Systems -- Gene regulation networks -- Metabolic pathways -- Signal transduction cascades -- Cell cycle control systems -- Stress response mechanisms - -### Chemical Processes -- Catalytic reactions -- Equilibrium systems -- Kinetic analysis -- Industrial processes -- Environmental chemistry - -### Physical Systems -- Quantum processes -- Thermodynamic cycles -- Wave phenomena -- Energy transfer systems -- Field interactions - -### Computer Science -- Algorithm analysis -- Data structures -- Computational complexity -- Software architecture -- System design - -### Mathematical Systems -- Proof construction -- Logical frameworks -- Theorem development -- Computational mathematics -- Formal systems - -## 🎯 Key Applications - -- **Bio-inspired Computing:** Biological computational patterns can inspire revolutionary new computing paradigms -- **Synthetic Biology:** Understanding cellular programming enables the design of programmable biological systems -- **Medical Applications:** Diseases can be understood as software bugs that can be debugged and fixed -- **Evolutionary Computation:** Evolution becomes visible as a programming process that optimizes biological software - -## 📖 Documentation - -- **[Methodology Guide](methodology/)** - Detailed step-by-step framework application -- **[Examples Gallery](examples/)** - Comprehensive collection of analyzed systems -- **[Tools & Resources](tools/)** - Templates, guidelines, and educational materials -- **[Case Studies](case-studies/)** - Deep dives into specific applications - -## 🤝 Contributing - -We welcome contributions to expand the Programming Framework across new domains and applications. Please see our [Contributing Guidelines](CONTRIBUTING.md) for details. - -### How to Contribute -1. **Submit Examples:** Share your own system analyses using the framework -2. **Improve Documentation:** Help expand methodology guides and tutorials -3. **Develop Tools:** Create software tools for framework application -4. **Cross-Disciplinary Applications:** Apply the framework to new domains - -## 📄 License - -This project is licensed under the Creative Commons Attribution 4.0 International License - see the [LICENSE](LICENSE) file for details. - -## 👨‍🔬 Author - -**Gary Welz** -- Retired Faculty Member, John Jay College, CUNY (Department of Mathematics and Computer Science) -- Borough of Manhattan Community College, CUNY -- CUNY Graduate Center (New Media Lab) -- Email: gwelz@jjay.cuny.edu - -## 🔗 Related Projects - -- **[Genome Logic Modeling Project (GLMP)](https://huggingface.co/spaces/garywelz/glmp)** - Comprehensive biological systems analysis -- **[Programming Framework Examples](https://huggingface.co/spaces/garywelz/programming_framework_examples)** - Extended case studies and applications - -## 📞 Contact - -For questions, suggestions, or collaborations: -- **Email:** gwelz@jjay.cuny.edu -- **Hugging Face:** [@garywelz](https://huggingface.co/garywelz) -- **Issues:** Use the [GitHub Issues](https://github.com/garywelz/programming-framework/issues) page - ---- - -**The genome is indeed like a computer program—not as a metaphor, but as a fundamental reality of how biological systems operate. This analysis provides the empirical evidence to support this revolutionary understanding of biological complexity.** - -*We stand at the threshold of a new era in biology - one where we understand life itself as an information processing phenomenon.* \ No newline at end of file diff --git a/Programming Framework for Systematic Analysis - a Hugging Face Space by garywelz.pdf b/Programming Framework for Systematic Analysis - a Hugging Face Space by garywelz.pdf deleted file mode 100644 index 3a2c40382898f65193b6772807827a74b6f41f4c..0000000000000000000000000000000000000000 --- a/Programming Framework for Systematic Analysis - a Hugging Face Space by garywelz.pdf +++ /dev/null @@ -1,3 +0,0 @@ -version https://git-lfs.github.com/spec/v1 -oid sha256:0af0c3d1c8c264739f0bf8c666bccc8348e174be8745cad0e92099bf551fa749 -size 180391 diff --git a/README.md b/README.md index 390aade16fe9c71b06b73b805c7ee72a6afc5f89..35847829881961fb7dbdadd038a96b0b269263b8 100644 --- a/README.md +++ b/README.md @@ -1,275 +1,102 @@ --- -title: The Programming Framework -emoji: 🛠️ -colorFrom: yellow -colorTo: red -sdk: static -pinned: true -license: mit +title: "Programming Framework for Systematic Analysis" +emoji: "🎨" +colorFrom: "blue" +colorTo: "green" +sdk: "static" +sdk_version: "latest" +app_file: "index.html" +pinned: false +author: "garywelz" +short_description: Mermaid flowcharts + links to math and biology databases --- -# 🛠️ The Programming Framework +## Programming Framework -A Universal Method for Process Analysis +A systematic visualization methodology for analyzing complex systems across disciplines using Mermaid Markdown and a universal five-color code. -## Summary +**Source & backup:** [github.com/garywelz/progframe](https://github.com/garywelz/progframe) -The **Programming Framework** is a universal meta-tool for analyzing complex processes across any discipline by combining Large Language Models (LLMs) with visual flowchart representation. The Framework transforms textual process descriptions into structured, interactive Mermaid flowcharts stored as JSON, enabling systematic analysis, visualization, and integration with knowledge systems. +### Interactive databases (hosted on Google Cloud Storage) -Successfully demonstrated through GLMP (Genome Logic Modeling Project) with 50+ biological processes, and applied across Chemistry, Mathematics, Physics, and Computer Science. The Framework serves as the foundational methodology for the CopernicusAI Knowledge Engine, enabling domain-specific process visualization and analysis. +Browse searchable tables and open individual process charts: -## 📚 Prior Work & Research Contributions +- **Mathematics** — [Algorithms & axiomatic theories table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) · [Named collections (mathematicians & theorems)](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/collections/index.html) · [Whole of mathematics graph](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/whole-of-mathematics.html) +- **Biology** — [Pathways, mechanisms & lab protocols table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) · [Theme collections](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/collections/index.html) -### Overview -The Programming Framework represents **prior work** that demonstrates a novel methodology for analyzing complex processes by combining Large Language Models (LLMs) with visual flowchart representation. This research establishes a universal, domain-agnostic approach to process analysis that transforms textual descriptions into structured, interactive visualizations. +Complex systems across biology, chemistry, and physics exhibit remarkable similarities in their organizational principles despite operating at vastly different scales and domains. Traditional analysis methods often remain siloed within specific disciplines, limiting our ability to identify common patterns and computational logic that govern system behavior. Here, we present the Programming Framework, a systematic methodology that translates complex system dynamics into standardized computational representations using Mermaid Markdown syntax and LLM processing. -### 🔬 Research Contributions -- **Universal Process Analysis:** Domain-agnostic methodology applicable across biology, chemistry, software engineering, business processes, and more -- **LLM-Powered Extraction:** Automated extraction of process steps, decision points, and logic flows using Google Gemini 2.0 Flash -- **Structured Visualization:** Mermaid.js-based flowchart generation encoded as JSON for programmatic access and integration -- **Iterative Refinement:** Systematic approach enabling continuous improvement through visualization and LLM-assisted refinement +### Purpose and Goals -### ⚙️ Technical Achievements -- **Meta-Tool Architecture:** Framework for creating specialized process analysis tools (demonstrated by GLMP) -- **JSON-Based Storage:** Structured data format enabling version control, cross-referencing, and API integration -- **Multi-Domain Application:** Successfully applied to biological processes (GLMP), with extensions planned for software, business, and engineering domains -- **Integration Framework:** Designed for integration with knowledge engines, research databases, and collaborative platforms +The Programming Framework project aims to advance the use of Mermaid Markdown syntax and Large Language Models (LLMs) to create standardized, color-coded flowcharts representing complex processes across all academic disciplines. By providing a universal methodology for translating system dynamics into computational representations, this framework enables systematic comparison and pattern recognition across traditionally separate fields including biology, chemistry, physics, computer science, and mathematics. The project builds upon three decades of computational biology research and demonstrates how modern AI tools can democratize complex system analysis, making sophisticated visualization accessible to researchers, educators, and students worldwide. -### 🎯 Position Within CopernicusAI Knowledge Engine -The Programming Framework serves as the **foundational meta-tool** of the CopernicusAI Knowledge Engine, providing the underlying methodology that enables specialized applications: +### Technical Foundation: Mermaid Markdown -- **GLMP (Genome Logic Modeling Project)** - First specialized application demonstrating biological process visualization -- **CopernicusAI** - Main knowledge engine integrating Framework outputs with AI podcasts and research synthesis -- **Research Tools Dashboard** (✅ Implemented December 2025) - Fully operational web interface with knowledge graph visualization, vector search, RAG queries, and content browsing. Processes from Chemistry, Physics, Mathematics, and Computer Science are accessible through the unified dashboard. Live at: https://copernicus-frontend-phzp4ie2sq-uc.a.run.app/knowledge-engine -- **Public Project Interface** (✅ Implemented January 2025) - Comprehensive public-facing page providing access to all CopernicusAI Knowledge Engine components. Live at: https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/copernicusai-public-reviewer.html -- **Research Papers Metadata Database** - Integration for linking processes to source literature (12,000+ papers indexed) -- **Science Video Database** - Potential integration for multi-modal process explanations +#### The Invention of Mermaid -This work establishes a proof-of-concept for AI-assisted process analysis, demonstrating how LLMs can systematically extract and visualize complex logic from textual sources across diverse domains. The Knowledge Engine now provides a unified interface for exploring processes alongside research papers, podcasts, and other content types. +**Knut Sveidqvist** invented the Mermaid markdown format. He created Mermaid, a JavaScript-based diagramming and charting tool, to simplify diagram creation in documentation workflows. The project was inspired by his experience trying to update a diagram in a document, which was difficult due to the file format. -## 🎯 Overview +Sveidqvist's innovation revolutionized how diagrams are created and maintained in documentation by providing a text-based syntax that can be version-controlled, easily edited, and automatically rendered into visual diagrams. This approach eliminates the need for external diagramming tools and ensures diagrams stay synchronized with their documentation. -The Programming Framework is a **meta-tool**—a tool for creating tools. It provides a systematic method for analyzing any complex process by combining the analytical power of Large Language Models with the clarity of visual flowcharts. +#### Mermaid Markdown (.mmd) Format -## 💡 The Core Idea +The Programming Framework leverages Mermaid's `.mmd` file format, which provides: -**Problem:** Complex processes are difficult to understand because they involve many steps, decision points, and interactions. Traditional text descriptions are hard to follow. +- **Text-based syntax** for creating complex flowcharts and diagrams +- **Version control compatibility** - diagrams can be tracked in Git repositories +- **LLM-friendly format** - AI systems can generate and modify diagram code +- **Cross-platform compatibility** - works in any environment that supports JavaScript +- **Embeddable rendering** - diagrams can be displayed in HTML, Markdown, and other formats -**Solution:** Use LLMs to extract process logic from literature, then encode it as Mermaid flowcharts stored in JSON. Result: Clear, interactive visualizations that reveal hidden patterns and enable systematic analysis. +#### LLM Integration and Workflow -## ⚙️ How It Works +Our methodology uses Large Language Models to: -1. **Input Process** - Provide scientific papers, documentation, or process descriptions -2. **LLM Analysis** - AI extracts steps, decisions, branches, and logic flow -3. **Generate Flowchart** - Create Mermaid diagram encoded as JSON structure -4. **Visualize & Iterate** - Interactive flowchart reveals insights and enables refinement +1. **Generate .mmd files** - LLMs create detailed Mermaid syntax for complex processes +2. **Apply color coding** - Systematic application of the 5-category color system +3. **Ensure consistency** - Standardized node naming and connection patterns +4. **Embed in HTML** - .mmd files are embedded in HTML for web display +5. **Maintain quality** - LLMs can validate and optimize diagram structure -## 🌍 Core Principles +This workflow enables rapid creation of sophisticated visualizations that would be impractical to create manually, while maintaining the flexibility and editability of text-based formats. -### Domain Agnostic -Works across any field: biology, chemistry, software engineering, business processes, legal workflows, manufacturing, and beyond. +### Universal Color Coding Table -### Iterative Refinement -Start with rough analysis, visualize, identify gaps, refine with LLM, repeat until the process logic is crystal clear. +| Color | Hex | Biology | Chemistry | Computer Science | Physics | Mathematics | +| --- | --- | --- | --- | --- | --- | --- | +| Red | `#ff6b6b` | Environmental signals, nutrients | Reactant supply, temperature | Input data, user commands | Energy input, force | Axioms, givens | +| Yellow | `#ffd43b` | Enzymes, receptors | Catalysts, vessels | Data structures, algorithms | Fields, particles | Theorems, methods | +| Green | `#51cf66` | Metabolic reactions | Chemical reactions | Algorithm execution | Quantum/force operations | Calculations, deductions | +| Blue | `#74c0fc` | Metabolites, states | Intermediates, streams | Variables, memory states | States, measurement results | Intermediate results | +| Violet | `#b197fc` | Biomolecules, responses | Final products | Program outputs | Phenomena, measured quantities | Proven results | -### Structured Data -JSON storage enables programmatic access, version control, cross-referencing, and integration with other tools and databases. +### Explore the Space -## 🚀 Applications +- Biology evidence base: [GLMP Space](https://huggingface.co/spaces/garywelz/glmp) (Hugging Face) and repo +- Chemistry processes: [chemistry_processes.html](chemistry_processes.html) +- Computer Science: [computer_science_processes.html](computer_science_processes.html) +- Physics: [physics_processes.html](physics_processes.html) +- Mathematics: [mathematics_processes.html](mathematics_processes.html) +- Full article: [programming_framework_article.html](programming_framework_article.html) -### 🧬 GLMP - Genome Logic Modeling (Live) -First specialized application: visualizing biochemical processes like DNA replication, metabolic pathways, and cell signaling. -- [Explore GLMP →](https://huggingface.co/spaces/garywelz/glmp) +### Experimental Validation -## 📚 Process Diagram Collections +- **Validation Paper**: [experimental_validation_paper.html](experimental_validation_paper.html) — comprehensive experimental protocols and validation methodology +- **Core validation flowcharts** (under `validation_flowcharts/`): + - [catalytic_hydrogenation_optimization.html](validation_flowcharts/catalytic_hydrogenation_optimization.html) — Experiment 1: catalytic hydrogenation + - [raft_polymerization_mechanism.html](validation_flowcharts/raft_polymerization_mechanism.html) — Experiment 2: polymerization kinetics + - [surface_catalysis_mechanism.html](validation_flowcharts/surface_catalysis_mechanism.html) — Experiment 3: surface chemistry + - [electrochemical_oxygen_reduction.html](validation_flowcharts/electrochemical_oxygen_reduction.html) — Experiment 4: electrochemical process + - [quantum_chemistry_calculation.html](validation_flowcharts/quantum_chemistry_calculation.html) — Experiment 5: computational chemistry -The Programming Framework has been applied across multiple scientific disciplines. Explore interactive flowchart collections organized by domain: +### Batch Architecture -### Process Database Statistics (As of January 2025) +The project now includes a comprehensive batch architecture for each discipline: -| Discipline | Processes | Subcategories | Status | Database Table | -|------------|-----------|---------------|--------|----------------| -| Biology | 52 | 8 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) | -| Chemistry | 91 | 14 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/chemistry-database-table.html) | -| Physics | 21 | 7 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/physics-processes-database/physics-database-table.html) | -| Computer Science | 21 | 7 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/computer-science-database-table.html) | -| Mathematics | 20 | 7 | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) | -| GLMP (Molecular Biology) | 108 | 10+ | ✅ Complete | [View Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/glmp-database-table.html) | -| **Total** | **313** | **53+** | **✅ Operational** | **All databases publicly accessible** | - -**Note:** All processes include Mermaid flowcharts, source citations, and comprehensive metadata. See individual database tables for detailed statistics, complexity metrics, and process details. Statistics are dynamically updated - see [Public Project Interface](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/copernicusai-public-reviewer.html) for current counts. - -### 🧬 Biology -- [Biology Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) - Interactive database with 52 higher-level organismal processes across 8 categories (reproduction, development, behavior, defense, nutrition, sensory, transport, coordination) -- [GLMP Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/glmp-database-table.html) - Genome Logic Modeling Project: Biochemical/molecular processes database (108 processes) -- **Note:** Biology Processes Database focuses on organismal, developmental, behavioral, and ecological processes. GLMP focuses on molecular-level biochemical processes. Together they provide comprehensive biological process coverage. - -### ⚗️ Chemistry -- [Chemistry Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/chemistry-database-table.html) - Interactive database with 91 processes across 14 subcategories - -### 🔢 Mathematics -- [Mathematics Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) - Interactive database with 20 processes across 7 subcategories - -### ⚛️ Physics -- [Physics Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/physics-processes-database/physics-database-table.html) - Interactive database with 21 processes across 7 subcategories - -### 💻 Computer Science -- [Computer Science Database Table](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/computer-science-database-table.html) - Interactive database with 21 processes across 7 subcategories - -## ⚠️ Limitations & Future Directions - -### Current Limitations -- **Process Validation:** Flowcharts are LLM-generated and benefit from expert validation for domain-specific accuracy (validation process ongoing) -- **Source Linking:** Not all processes yet linked to specific research papers (work in progress per Quality Standards) -- **Scale:** Current database (313 processes) represents proof-of-concept; target is 1,000+ processes -- **Domain Coverage:** Some disciplines better represented than others; actively expanding coverage -- **LLM Dependency:** Framework requires LLM access (Google Gemini 2.0 Flash); alternative models may produce different results -- **Complexity Limits:** Very complex processes (>100 nodes) may require manual refinement - -### Future Work -- **Expansion:** Scale to 1,000+ processes across all disciplines (see DISCIPLINE_DATABASES_PLAN.md) -- **Validation:** Implement systematic peer review process for process flowcharts -- **Source Integration:** Enhanced linking to research papers using vector search from 23,246+ indexed papers -- **Automation:** Automated source paper suggestion and linking -- **Quality Assurance:** Systematic validation framework for flowchart accuracy -- **Multi-LLM Support:** Extend to support multiple LLM providers for comparison and validation -- **Interactive Refinement:** User interface for iterative flowchart improvement - -### Known Areas for Improvement -- **Accuracy Validation:** Not all flowcharts yet validated by domain experts; systematic validation in progress -- **Source Citations:** Some processes need additional source paper citations (work in progress) -- **Cross-Discipline Links:** Enhanced cross-referencing between related processes across disciplines - -## 🔧 Technical Architecture - -### LLM Integration -- **Primary Model:** Google Gemini 2.0 Flash for process analysis -- **Deployment:** Vertex AI for enterprise-scale deployment -- **Prompt Engineering:** Custom prompts optimized for process extraction and structured output -- **Output Format:** Structured JSON with Mermaid flowchart syntax -- **Version:** Framework tested with Gemini 2.0 Flash; compatible with other LLMs - -### Visualization Stack -- **Rendering Engine:** Mermaid.js for flowchart visualization -- **Data Validation:** JSON schema for data validation and consistency -- **Output Formats:** Interactive SVG output with export to PNG/PDF supported -- **Color Schemes:** Discipline-based color coding following Programming Framework standards - -### Data Storage -- **Primary Storage:** Google Cloud Storage for JSON process files -- **Metadata Indexing:** Firestore for metadata indexing and search -- **Version Control:** Git for code and documentation versioning -- **Cross-Referencing:** Integration with research papers database (23,246+ papers indexed) - -### Integration Points -- **GLMP:** Specialized biological process collections -- **CopernicusAI:** Knowledge graph integration for unified exploration -- **Research Papers Database:** Cross-linking with 23,246+ indexed papers -- **API Endpoints:** Programmatic access for integration with other systems -- **Research Tools Dashboard:** Unified interface for exploring processes alongside papers and other content - -### How to Cite This Work - -#### BibTeX Format -```bibtex -@article{welz2025programming, - title={The Programming Framework: A General Method for Process Analysis Using LLMs and Mermaid Visualization}, - author={Welz, Gary}, - journal={Nature Communications}, - year={2025}, - note={Submitted}, - url={https://huggingface.co/spaces/garywelz/programming_framework}, - note={Preprint available upon publication} -} -``` - -#### Standard Citation Format -Welz, G. (2024–2025). *The Programming Framework: A Universal Method for Process Analysis*. -Hugging Face Spaces. https://huggingface.co/spaces/garywelz/programming_framework - -Welz, G. (2024). *From Inspiration to AI: Biology as Visual Programming*. Medium. -https://medium.com/@garywelz_47126/from-inspiration-to-ai-biology-as-visual-programming-520ee523029a - -**Note:** When published, this citation will be updated with DOI and publication details from Nature Communications. - -This project serves as a foundational meta-tool for AI-assisted process analysis, enabling systematic extraction and visualization of complex logic from textual sources across diverse scientific and technical domains. - -The Programming Framework is designed as infrastructure for AI-assisted science, providing a universal methodology that can be specialized for domain-specific applications. - -## 📊 Data Availability - -**Research Data:** -- **Process Flowcharts:** All process flowcharts are publicly available in Google Cloud Storage with interactive database tables: - - [Biology Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/biology-processes-database/biology-database-table.html) - 52 processes across 8 subcategories - - [Chemistry Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/chemistry-processes-database/chemistry-database-table.html) - 91 processes across 14 subcategories - - [Physics Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/physics-processes-database/physics-database-table.html) - 21 processes across 7 subcategories - - [Mathematics Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/mathematics-database-table.html) - 20 processes across 7 subcategories - - [Computer Science Processes Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/computer-science-processes-database/computer-science-database-table.html) - 21 processes across 7 subcategories - - [GLMP Database](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/glmp-database-table.html) - 108+ molecular biology processes -- **Process Metadata:** Each process includes JSON metadata with Mermaid flowchart syntax, source citations, complexity metrics, and related process links. -- **Current Statistics:** Dynamically updated statistics available at [Public Project Interface](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/copernicusai-public-reviewer.html). - -**Source Code & Methodology:** -- **Methodology:** Fully documented in this README and the Programming Framework paper (submitted to Nature Communications). -- **Process Generation:** LLM-powered extraction using Google Gemini 2.0 Flash via Vertex AI, with custom prompts for process extraction and structured JSON output formatting. -- **Visualization:** Mermaid.js-based flowchart generation with JSON schema for data validation. -- **Data Format:** Standardized JSON structure documented in project files (see Technical Architecture section). -- **Database Schemas:** Process database schemas and metadata structures documented in project documentation. - -**Access:** -- **Public Access:** All process databases and database tables are publicly accessible (no authentication required). -- **Individual Process Viewers:** Each process has a dedicated viewer accessible via links in database tables. -- **Research Tools Dashboard:** Processes are integrated into the [Research Tools Dashboard](https://copernicus-frontend-phzp4ie2sq-uc.a.run.app/knowledge-engine) for unified exploration alongside research papers and other content. -- **Hugging Face Spaces:** Framework documentation and examples available at [Programming Framework Space](https://huggingface.co/spaces/garywelz/programming_framework). - -**Reproducibility:** -- All process flowcharts include source citations linking to research papers used to create each flowchart. -- Methodology is fully documented and can be replicated using Google Gemini 2.0 Flash or compatible LLMs. -- JSON schema and data structures are standardized and documented. -- Process generation workflow is transparent: input (textual process description) → LLM analysis → Mermaid flowchart generation → JSON storage. -- All components are publicly accessible for verification, reuse, and extension to other domains. - -**Process Database Statistics:** -- **Total Processes:** 313+ validated processes across 6 databases -- **Disciplines Covered:** Biology, Chemistry, Physics, Mathematics, Computer Science, Molecular Biology (GLMP) -- **Validation:** 100% syntax accuracy, ≥85% metadata quality, all processes include source citations -- **Format:** All processes stored as JSON files with Mermaid flowchart syntax, publicly accessible via Google Cloud Storage - -## 🔗 Related Projects - -### 🧬 GLMP - Genome Logic Modeling -First specialized application of the Programming Framework to biochemical processes. 100+ biological pathways visualized. -- [Visit GLMP →](https://huggingface.co/spaces/garywelz/glmp) - -### 🔬 CopernicusAI -Knowledge engine integrating the Programming Framework with AI podcasts, research papers, and knowledge graph for scientific discovery. -- [Visit CopernicusAI →](https://huggingface.co/spaces/garywelz/copernicusai) - -## 🎨 Interactive Demo - -The space includes interactive examples showing the framework applied to: -- Scientific Method -- Software Deployment Pipeline -- Customer Support Workflow -- Research Paper Publication - -Each example demonstrates how LLMs extract process logic and encode it as visual flowcharts. - -## 💻 Technology Stack - -- **LLM**: Google Gemini 2.0 Flash, Vertex AI -- **Visualization**: Mermaid.js -- **Storage**: Google Cloud Storage, Firestore -- **Format**: JSON with Mermaid syntax -- **Frontend**: Static HTML + Tailwind CSS - -## 🌟 Vision - -As AI systems become more capable of understanding complex processes, the Programming Framework provides the bridge between human comprehension and machine analysis. It's a tool for truth-seeking—transforming complexity into clarity. - ---- - -**A Universal Method for Process Analysis** - -© 2025 Gary Welz. All rights reserved. +- **Mathematics**: 7 batches (21 processes) - Complete ✅ +- **Chemistry**: 14 batches (70 processes) - Complete ✅ +- **Computer Science**: 7 batches (21 processes) - Complete ✅ +- **Physics**: 7 batches (21 processes) - Complete ✅ +- **Biology**: External GLMP Space - Complete ✅ +Each discipline has an index page (`*_index.html`) and individual batch files (`*_batch_*.html`) containing detailed process visualizations. diff --git a/WHOLE_OF_MATHEMATICS_CHART_DESIGN.md b/WHOLE_OF_MATHEMATICS_CHART_DESIGN.md new file mode 100644 index 0000000000000000000000000000000000000000..fbb0f58c9d3113f46ea342d4eca21e749f7a06f5 --- /dev/null +++ b/WHOLE_OF_MATHEMATICS_CHART_DESIGN.md @@ -0,0 +1,374 @@ +# Whole of Mathematics — Interactive Zoomable Chart Design + +## Vision + +A single, high-level interactive visualization that shows the **entire landscape of mathematics** as our collection understands it—with the ability to **zoom in** from broad domains down to individual processes, and to **click through** to the actual flowchart or dependency graph for any process. + +Think of it as a "map of mathematics" that is: +- **Data-driven** — built from `metadata.json` and our hierarchy +- **Zoomable** — pan and zoom like a geographic map or Prezi +- **Drillable** — click a region to focus on it and see its children +- **Linked** — deepest level opens the existing process HTML page + +--- + +## Domain Grouping: arXiv Math Taxonomy + +Use the **arXiv Mathematics** taxonomy (math.XX) as the canonical domain structure. arXiv is widely recognized, stable, and aligns with how mathematicians categorize research. + +### arXiv Math Categories (math.XX) + +| Code | Name | +|------|------| +| math.AC | Commutative Algebra | +| math.AG | Algebraic Geometry | +| math.AP | Analysis of PDEs | +| math.AT | Algebraic Topology | +| math.CA | Classical Analysis and ODEs | +| math.CO | Combinatorics | +| math.CT | Category Theory | +| math.CV | Complex Variables | +| math.DG | Differential Geometry | +| math.DS | Dynamical Systems | +| math.FA | Functional Analysis | +| math.GM | General Mathematics | +| math.GN | General Topology | +| math.GR | Group Theory | +| math.GT | Geometric Topology | +| math.HO | History and Overview | +| math.IT | Information Theory | +| math.KT | K-Theory and Homology | +| math.LO | Logic | +| math.MG | Metric Geometry | +| math.MP | Mathematical Physics | +| math.NA | Numerical Analysis | +| math.NT | Number Theory | +| math.OA | Operator Algebras | +| math.OC | Optimization and Control | +| math.PR | Probability | +| math.QA | Quantum Algebra | +| math.RA | Rings and Algebras | +| math.RT | Representation Theory | +| math.SG | Symplectic Geometry | +| math.SP | Spectral Theory | +| math.ST | Statistics Theory | + +### Mapping Our Subcategories → arXiv + +| Our subcategory | arXiv code(s) | +|-----------------|---------------| +| abstract_algebra | math.GR, math.RA, math.AC | +| linear_algebra | math.RA | +| category_theory | math.CT | +| calculus_analysis | math.CA, math.CV, math.DS | +| geometry_topology | math.GN, math.GT, math.AT, math.DG, math.MG | +| number_theory | math.NT | +| discrete_mathematics | math.CO, math.LO | +| foundations | math.LO | +| bioinformatics | (applied; no direct math.XX; use math.GM or separate) | + +*Wikipedia* math portal uses a flatter structure (Algebra, Analysis, Geometry, etc.)—can serve as a secondary grouping if we want a simpler top level. + +--- + +## Hierarchy: What We're Mapping + +### Level 0 — Whole of Mathematics (root) +The entire collection. One view. + +### Level 1 — arXiv Math Domains (or grouped) +Either use arXiv codes directly (math.NT, math.AG, …) or group into ~6–8 broader areas for a simpler top level: + +| Domain | arXiv codes | Our subcategories | +|--------|-------------|-------------------| +| **Algebra** | AC, AG, CT, GR, RA, RT, QA | abstract_algebra, linear_algebra, category_theory | +| **Analysis** | AP, CA, CV, FA, NA, SP | calculus_analysis, complex_analysis | +| **Geometry & Topology** | AT, DG, GN, GT, MG, SG | geometry_topology | +| **Number Theory** | NT | number_theory | +| **Discrete & Logic** | CO, LO | discrete_mathematics, foundations | +| **Dynamical Systems** | DS | (part of calculus_analysis) | +| **Probability & Statistics** | PR, ST | (future) | +| **Applied / Other** | GM, MP, OC, IT | bioinformatics | + +### Level 2 — Subcategories +e.g., within **Analysis**: Real Analysis, Complex Analysis, Complex Dynamics, Symbolic Dynamics. + +### Level 3 — Processes +Individual charts. Click → open process page. + +--- + +## Force-Directed Graph: Deep Dive + +### Why It Aligns With Our Current Metaphor + +Our existing process charts are **node–link diagrams**: +- **Axiomatic theories**: nodes = axioms, definitions, theorems; edges = "depends on" +- **Algorithms**: nodes = steps; edges = control flow + +A force-directed graph is the same visual language at a higher level: **nodes and edges**. It extends the dependency-graph metaphor from *within* a process to *between* processes and domains. + +### Force-Directed vs. Treemap: Core Difference + +| Aspect | Treemap | Force-Directed Graph | +|--------|---------|----------------------| +| **Structure** | Containment (parent *contains* children) | Links (nodes *connected* by edges) | +| **Relationships** | Implicit (nesting) | Explicit (edges) | +| **Hierarchy** | Strict tree; one parent per node | Can be tree, DAG, or general graph | +| **Cross-links** | Hard to show (a node lives in one place) | Natural (Galois ↔ Field Theory ↔ Group Theory) | +| **Layout** | Rectangles, area = weight | Organic; forces pull/push nodes | +| **Zoom** | Zoom into a region (geometric) | Pan/zoom canvas; click node to focus | + +### Force-Directed *Can* Be Hierarchical + +You can use a force-directed layout with **hierarchical constraints**: +- **Parent–child links**: domain → subcategory → process (tree edges) +- **Cross-links**: `namedCollections` overlap, or explicit "related to" (e.g., Galois Theory ↔ Field Theory) +- **Collision / clustering**: Give nodes of the same domain a "gravity" toward each other so they cluster +- **Level-based y-position**: Fix y by depth (root at top, processes at bottom) for a tree-like flow + +So you get: **hierarchy + relationships** in one view. + +### Zoom and Pan + +Force-directed graphs support zoom and pan the same way as treemaps: +- Wrap the graph in an SVG `` (group) +- Apply `d3.zoom()` to the SVG; transform the group on zoom/pan events +- **Geometric zoom**: scale + translate the whole canvas (simple) +- **Semantic zoom** (optional): at different zoom levels, show different detail (e.g., zoomed out = domains only; zoomed in = subcategories; further in = processes) + +### Ease of Use With Our Collection + +**Data we have:** +- `subcategory` per process → gives hierarchy (domain → subcategory → process) +- `processType` (algorithm vs axiomatic_theory) → can style nodes differently +- Process IDs and names → node labels and links + +**Data we can add:** +- `namedCollections` → cross-links: two processes in "fermat" get an edge +- Optional `dependsOn` or `relatedTo` → explicit edges between processes + +**Graph structure:** +``` +Nodes: [Mathematics (root)] + [~8 domains] + [~10 subcategories] + [~98 processes] +Edges: Tree edges (parent→child) + optional cross-edges (namedCollections, relatedTo) +``` + +~120 nodes, ~100+ edges is well within D3 force layout comfort zone. No performance concerns. + +### Relationship to Other Types + +- **Treemap**: Force-directed shows *links*; treemap shows *containment*. Different metaphors. Treemap is "zoom into a region"; force-directed is "follow the edges." +- **Sunburst**: Both can show hierarchy. Sunburst is radial containment; force-directed is node-link. Sunburst is more compact; force-directed shows relationships. +- **Map metaphor**: Could use force-directed *for layout* (position nodes), then draw "regions" (Voronoi, convex hulls) around domain clusters—hybrid approach. + +--- + +## Technical Approaches (Summary) + +### Option A: D3 Zoomable Treemap +- Containment metaphor; area = count; no explicit edges. +- **Fit**: Pure hierarchy, no cross-links. + +### Option B: D3 Sunburst +- Radial containment; compact. +- **Fit**: Hierarchy; explore later. + +### Option C: Force-Directed Graph with Zoom ← **Primary choice** +- Node–link; explicit edges; aligns with our dependency-graph metaphor. +- **Fit**: Hierarchy + cross-links; zoom/pan; works with our collection. + +### Option D: Map Metaphor +- Geographic feel; Voronoi or custom. +- **Fit**: Explore later. + +### Option E: Hybrid +- Treemap + graph overlay. +- **Fit**: Explore later. + +--- + +## Recommended: Force-Directed Graph (Option C) + Zoom + Breadcrumbs + +**Why**: Aligns with our existing node–link dependency metaphor. Shows both hierarchy (domain → subcategory → process) and cross-links (e.g., via `namedCollections`). Zoom and pan are standard (D3 zoom on SVG group). ~120 nodes is trivial for D3 force. Breadcrumbs solve "where am I?" when zoomed. + +**Data shape** (nodes + links for force-directed): + +```json +{ + "nodes": [ + { "id": "root", "name": "Mathematics", "level": 0 }, + { "id": "algebra", "name": "Algebra", "level": 1 }, + { "id": "analysis", "name": "Analysis", "level": 1 }, + { "id": "abstract_algebra", "name": "Abstract Algebra", "level": 2 }, + { "id": "abstract_algebra-group-theory", "name": "Group Theory", "level": 3, "processId": "abstract_algebra-group-theory", + "subcategory": "abstract_algebra", "url": "processes/abstract_algebra/abstract_algebra-group-theory.html" } + ], + "links": [ + { "source": "root", "target": "algebra" }, + { "source": "algebra", "target": "abstract_algebra" }, + { "source": "abstract_algebra", "target": "abstract_algebra-group-theory" }, + { "source": "abstract_algebra-field-theory", "target": "abstract_algebra-group-theory" } + ] +} +``` + +`level` drives hierarchy. `links` include tree edges (parent→child) and optional cross-edges (e.g., Field Theory → Group Theory). `processId` and `url` at leaves for linking. + +--- + +## Metadata Extensions for the Chart + +### 1. Domain Mapping (arXiv-Based) + +Add to `metadata.json`: + +```json +{ + "domainHierarchy": { + "algebra": { + "name": "Algebra", + "arxiv": ["math.AC", "math.AG", "math.CT", "math.GR", "math.RA", "math.RT", "math.QA"], + "subcategories": ["abstract_algebra", "linear_algebra", "category_theory"] + }, + "analysis": { + "name": "Analysis", + "arxiv": ["math.AP", "math.CA", "math.CV", "math.FA", "math.NA", "math.SP"], + "subcategories": ["calculus_analysis", "complex_analysis"] + }, + "geometry_topology": { + "name": "Geometry & Topology", + "arxiv": ["math.AT", "math.DG", "math.GN", "math.GT", "math.MG", "math.SG"], + "subcategories": ["geometry_topology"] + }, + "number_theory": { + "name": "Number Theory", + "arxiv": ["math.NT"], + "subcategories": ["number_theory"] + }, + "discrete_logic": { + "name": "Discrete & Logic", + "arxiv": ["math.CO", "math.LO"], + "subcategories": ["discrete_mathematics", "foundations"] + }, + "dynamical_systems": { + "name": "Dynamical Systems", + "arxiv": ["math.DS"], + "subcategories": [] + }, + "applied": { + "name": "Applied & Other", + "arxiv": ["math.GM", "math.MP", "math.OC", "math.PR", "math.ST"], + "subcategories": ["bioinformatics"] + } + }, + "subcategoryToArxiv": { + "abstract_algebra": "math.GR", + "calculus_analysis": "math.CA", + "geometry_topology": "math.GT" + } +} +``` + +### 2. Optional: Process-Level "Domain" Override + +For processes that span domains (e.g., Category Theory), allow: + +```json +{ "id": "...", "domain": "algebra", "subcategory": "category_theory" } +``` + +Default: derive domain from subcategory via `domainHierarchy`. + +--- + +## Interaction Design + +### Zoom & Pan +- **Scroll** or **pinch**: zoom in/out +- **Drag**: pan +- **Double-click** a region: zoom to fit that region (focus) +- **Breadcrumb click**: jump back to that level + +### Click Behavior +- **Level 1–2** (domain, subcategory): zoom in to show children +- **Level 3** (process): open process page in new tab (or same tab with back) + +### Visual Feedback +- **Hover**: highlight region, show tooltip (name + count) +- **Focus**: breadcrumb updates; optional sidebar with list of processes in current view +- **Cross-links**: if we add graph overlay, dim non-adjacent regions when hovering a node with many connections + +--- + +## Responsive & Accessibility + +- **Mobile**: Touch pan/zoom; larger hit targets for small regions; consider "list view" fallback when zoomed to a subcategory +- **Keyboard**: Tab through regions, Enter to zoom/select +- **Screen readers**: Breadcrumb + list of current level's items as text + +--- + +## Implementation Phases + +### Phase 1: Static Hierarchy + Force-Directed Graph +- Add `domainHierarchy` (arXiv-based) to metadata +- Build nodes + links from processes (domain → subcategory → process) +- Single HTML page with D3 force-directed graph + zoom/pan +- **Deliverable**: Working "Whole of Mathematics" graph with our current 98 processes + +### Phase 2: Process Links +- Leaf nodes (processes) link to process HTML (using existing URL pattern) +- Breadcrumb navigation +- **Deliverable**: Full drill-down from root to process page + +### Phase 3: Polish +- Tooltips, legend (colors = domains or arXiv codes) +- Optional "list view" toggle for current level +- **Deliverable**: Production-ready interactive chart + +### Phase 4: Cross-Links (Optional) +- Use `namedCollections` to draw edges between related processes +- Or: "Related" panel when hovering a process +- **Deliverable**: Relationship-aware exploration + +--- + +## Growing With the Collection + +As we add: +- **New subcategories** (complex_analysis, landmark_theorems, formal_verification, ai_mathematics): extend `domainHierarchy` and subcategory→arXiv mapping +- **New processes**: they appear automatically (nodes + links derived from metadata) +- **Named mathematicians** (`namedCollections`): cross-edges between processes in the same collection; or a *second* view—"By Mathematician"—same graph structure but nodes grouped by collection. Toggle: "By Topic" | "By Mathematician" +- **New arXiv codes**: add to `domainHierarchy`; graph reflows + +The chart is **always generated from metadata**—no manual diagram maintenance. + +--- + +## Alternative: "Map" Metaphor (Future Enhancement) + +For a more geographic feel: +- **Continents** = domains (irregular shapes, not rectangles) +- **Countries** = subcategories +- **Cities** = processes (dots or small regions) +- Layout: Voronoi tessellation or force-directed placement with "gravity" to keep siblings near each other +- Could use **MapLibre** or **Leaflet** with a custom "projection" that maps our hierarchy to 2D—playful and memorable + +--- + +## Summary + +| Aspect | Choice | +|--------|--------| +| **Visualization** | D3 force-directed graph (primary) | +| **Domain taxonomy** | arXiv math.XX (math.AC, math.NT, etc.) | +| **Data** | Nodes + links derived from metadata + `domainHierarchy` | +| **Levels** | 3: Domain → Subcategory → Process | +| **Edges** | Tree (parent→child) + optional cross-links (`namedCollections`) | +| **Interaction** | Zoom, pan, click-to-focus, breadcrumbs | +| **Leaf action** | Open process HTML page | +| **Growth** | Add to metadata; chart updates automatically | +| **Future** | Sunburst, map metaphor—explore later | + +The "Whole of Mathematics" chart becomes the **entry point** to the database—a node–link visual index that matches our dependency-graph metaphor and scales with the collection. diff --git a/biology_processes.html b/biology_processes.html index f7db358d3378c1e02a9b9fee4183ece987078858..f257c91d4a70ecf8a004da62015c10b7704c8c79 100644 --- a/biology_processes.html +++ b/biology_processes.html @@ -114,15 +114,15 @@

Biology Processes - Programming Framework Analysis

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🔗 GLMP (Genome Logic Modeling Project) Connection

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This analysis is based on the comprehensive biological dataset from the Genome Logic Modeling Project (GLMP), which contains 50+ analyzed biological processes across multiple organisms and systems.

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This analysis is based on the comprehensive biological dataset from the Genome Logic Modeling Project (GLMP), which contains 297+ analyzed biological processes across multiple organisms and systems.

GLMP Resources:

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The GLMP represents the first successful application of the Programming Framework to biological processes, demonstrating how biological systems function as sophisticated computational programs with complex regulatory logic, decision trees, and feedback mechanisms.

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The GLMP represents the most comprehensive biological computing system analysis ever created, demonstrating how biological systems function as sophisticated computational programs with complex regulatory logic, decision trees, and feedback mechanisms.

This document presents representative biological processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.

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⚗️ Chemistry Processes Database

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Programming Framework - Interactive Database Analysis

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Chemistry Examples - Programming Framework Analysis

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This document presents chemistry processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.

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1. Catalytic Hydrogenation Process

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-graph TD - A[Alkene Substrate] --> B[Substrate Analysis] - C[Hydrogen Gas H₂] --> D[Gas Supply] - E[Catalyst Pt/Pd/Ni] --> F[Catalyst Preparation] - - B --> G[Substrate Purity Check] - D --> H[Gas Pressure Control] - F --> I[Catalyst Activation] - - G --> J[Reaction Vessel Loading] - H --> K[Pressure Regulation] - I --> L[Catalyst Dispersion] - - J --> M[Substrate Adsorption] - K --> N[Hydrogen Dissociation] - L --> O[Active Site Formation] - - M --> P[π-Bond Activation] - N --> Q[H• Radical Formation] - O --> R[Catalytic Surface] - - P --> S[First H Addition] - Q --> T[Hydrogen Transfer] - R --> U[Surface Complex] - - S --> V[Alkyl Intermediate] - T --> W[Second H Addition] - U --> X[Product Desorption] - - V --> Y[Alkane Product] - W --> Z[Complete Hydrogenation] - X --> AA[Catalyst Recovery] - - %% Red: Reactants & Inputs - style A fill:#ff6b6b,color:#fff - style C fill:#ff6b6b,color:#fff - style E fill:#ff6b6b,color:#fff - - %% Yellow: Catalysts & Equipment - style B fill:#ffd43b,color:#000 - style D fill:#ffd43b,color:#000 - style F fill:#ffd43b,color:#000 - style G fill:#ffd43b,color:#000 - style H fill:#ffd43b,color:#000 - style I fill:#ffd43b,color:#000 - style J fill:#ffd43b,color:#000 - style K fill:#ffd43b,color:#000 - style L fill:#ffd43b,color:#000 - - %% Green: Chemical Reactions - style M fill:#51cf66,color:#fff - style N fill:#51cf66,color:#fff - style O fill:#51cf66,color:#fff - style P fill:#51cf66,color:#fff - style Q fill:#51cf66,color:#fff - style R fill:#51cf66,color:#fff - style S fill:#51cf66,color:#fff - style T fill:#51cf66,color:#fff - style U fill:#51cf66,color:#fff - style W fill:#51cf66,color:#fff - style X fill:#51cf66,color:#fff - - %% Blue: Intermediates & States - style V fill:#74c0fc,color:#fff - - %% Violet: Final Products - style Y fill:#b197fc,color:#fff - style Z fill:#b197fc,color:#fff - style AA fill:#b197fc,color:#fff -
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- Figure 1. Catalytic Hydrogenation Process. This chemistry process visualization demonstrates catalytic reaction mechanisms. The flowchart shows reactant inputs, reaction vessels and equipment, chemical reactions and transformations, intermediate species, and final products. -
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2. Polymerization Process

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-graph TD - %% Initial Setup - %% Input Conditions - A2[Monomers] --> B2[Monomer Analysis] - C2[Initiator] --> D2[Initiator Preparation] - E2[Solvent/Medium] --> F2[Reaction Medium] - %% Reaction Setup - B2 --> G2[Monomer Purity Check] - D2 --> H2[Initiator Activation] - F2 --> I2[Medium Preparation] - %% Initiation - G2 --> J2[Monomer Solution] - H2 --> K2[Radical Formation] - I2 --> L2[Temperature Control] - %% Polymerization Initiation - J2 --> M2[Monomer Concentration] - K2 --> N2[Initiator Decomposition] - L2 --> O2[Reaction Conditions] - %% Propagation - M2 --> P2[Radical Addition] - N2 --> Q2[Chain Initiation] - O2 --> R2[Chain Growth] - %% Chain Growth - P2 --> S2[Monomer Addition] - Q2 --> T2[Active Chain End] - R2 --> U2[Polymer Chain] - %% Termination - S2 --> V2[Chain Propagation] - T2 --> W2[Chain Transfer] - U2 --> X2[Chain Termination] - %% Final Products - V2 --> Y2[Polymer Formation] - W2 --> Z2[Molecular Weight Control] - X2 --> AA2[Reaction Quenching] - %% Process Control - Y2 --> BB2[Polymer Characterization] - Z2 --> CC2[Molecular Weight Analysis] - AA2 --> DD2[Product Isolation] - %% Output - BB2 --> EE2[Polymerization Complete] - CC2 --> FF2[Quality Control] - DD2 --> GG2[Product Recovery] - %% Styling - Chemistry Color Scheme - %% Styling - Biological Color Scheme - style A2 fill:#ff6b6b,color:#fff - style C2 fill:#ff6b6b,color:#fff - style E2 fill:#ff6b6b,color:#fff - style G2 fill:#ffd43b,color:#000 - style H2 fill:#ffd43b,color:#000 - style I2 fill:#ffd43b,color:#000 - style J2 fill:#ffd43b,color:#000 - style K2 fill:#ffd43b,color:#000 - style L2 fill:#ffd43b,color:#000 - style M2 fill:#51cf66,color:#fff - style N2 fill:#51cf66,color:#fff - style O2 fill:#51cf66,color:#fff - style P2 fill:#51cf66,color:#fff - style Q2 fill:#51cf66,color:#fff - style R2 fill:#51cf66,color:#fff - style S2 fill:#51cf66,color:#fff - style T2 fill:#51cf66,color:#fff - style U2 fill:#51cf66,color:#fff - style V2 fill:#51cf66,color:#fff - style W2 fill:#51cf66,color:#fff - style X2 fill:#51cf66,color:#fff - style B2 fill:#74c0fc,color:#fff - style D2 fill:#74c0fc,color:#fff - style F2 fill:#74c0fc,color:#fff - style Y2 fill:#74c0fc,color:#fff - style Z2 fill:#74c0fc,color:#fff - style AA2 fill:#74c0fc,color:#fff - style BB2 fill:#74c0fc,color:#fff - style CC2 fill:#74c0fc,color:#fff - style DD2 fill:#74c0fc,color:#fff - style EE2 fill:#b197fc,color:#fff - style FF2 fill:#b197fc,color:#fff - style GG2 fill:#b197fc,color:#fff -
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- Figure 2. Polymerization Process. This chemistry process visualization demonstrates polymer synthesis mechanisms. The flowchart shows monomer inputs, reaction vessels and equipment, polymerization reactions, intermediate species, and final polymer products. -
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3. Acid-Base Titration Process

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-graph TD - %% Initial Setup - %% Input Conditions - A3[Acid Solution] --> B3[Acid Analysis] - C3[Base Solution] --> D3[Base Analysis] - E3[Indicator] --> F3[Indicator Selection] - %% Solution Preparation - B3 --> G3[Acid Concentration] - D3 --> H3[Base Concentration] - F3 --> I3[Indicator Preparation] - %% Titration Setup - G3 --> J3[Acid in Burette] - H3 --> K3[Base in Flask] - I3 --> L3[Indicator Addition] - %% Titration Process - J3 --> M3[Initial pH Measurement] - K3 --> N3[Base Volume Measurement] - L3 --> O3[Color Change Detection] - %% Acid-Base Reaction - M3 --> P3[Acid Addition] - N3 --> Q3[Base Consumption] - O3 --> R3[Equivalence Point] - %% pH Changes - P3 --> S3[H⁺ + OH⁻ → H₂O] - Q3 --> T3[Neutralization Reaction] - R3 --> U3[Stoichiometric Point] - %% Endpoint Detection - S3 --> V3[pH Monitoring] - T3 --> W3[Conductivity Changes] - U3 --> X3[Indicator Color Change] - %% Final Results - V3 --> Y3[Equivalence Point pH] - W3 --> Z3[Conductivity Minimum] - X3 --> AA3[Endpoint Detection] - %% Calculations - Y3 --> BB3[Concentration Calculation] - Z3 --> CC3[Volume Measurement] - AA3 --> DD3[Stoichiometric Analysis] - %% Output - BB3 --> EE3[Titration Complete] - CC3 --> FF3[Concentration Determined] - DD3 --> GG3[Analysis Results] - %% Styling - Chemistry Color Scheme - %% Styling - Biological Color Scheme - style A3 fill:#ff6b6b,color:#fff - style C3 fill:#ff6b6b,color:#fff - style E3 fill:#ff6b6b,color:#fff - style G3 fill:#ffd43b,color:#000 - style H3 fill:#ffd43b,color:#000 - style I3 fill:#ffd43b,color:#000 - style J3 fill:#ffd43b,color:#000 - style K3 fill:#ffd43b,color:#000 - style L3 fill:#ffd43b,color:#000 - style M3 fill:#51cf66,color:#fff - style N3 fill:#51cf66,color:#fff - style O3 fill:#51cf66,color:#fff - style P3 fill:#51cf66,color:#fff - style Q3 fill:#51cf66,color:#fff - style R3 fill:#51cf66,color:#fff - style S3 fill:#51cf66,color:#fff - style T3 fill:#51cf66,color:#fff - style U3 fill:#51cf66,color:#fff - style V3 fill:#51cf66,color:#fff - style W3 fill:#51cf66,color:#fff - style X3 fill:#51cf66,color:#fff - style B3 fill:#74c0fc,color:#fff - style D3 fill:#74c0fc,color:#fff - style F3 fill:#74c0fc,color:#fff - style Y3 fill:#74c0fc,color:#fff - style Z3 fill:#74c0fc,color:#fff - style AA3 fill:#74c0fc,color:#fff - style BB3 fill:#74c0fc,color:#fff - style CC3 fill:#74c0fc,color:#fff - style DD3 fill:#74c0fc,color:#fff - style EE3 fill:#b197fc,color:#fff - style FF3 fill:#b197fc,color:#fff - style GG3 fill:#b197fc,color:#fff -
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4. Electrochemical Cell Process

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-graph TD - %% Initial Setup - %% Input Conditions - A4[Anode Material] --> B4[Anode Analysis] - C4[Cathode Material] --> D4[Cathode Analysis] - E4[Electrolyte] --> F4[Electrolyte Preparation] - %% Cell Setup - B4 --> G4[Anode Preparation] - D4 --> H4[Cathode Preparation] - F4 --> I4[Electrolyte Solution] - %% Electrochemical Setup - G4 --> J4[Anode Oxidation] - H4 --> K4[Cathode Reduction] - I4 --> L4[Ion Conduction] - %% Redox Reactions - J4 --> M4[Electron Release] - K4 --> N4[Electron Acceptance] - L4 --> O4[Ion Transport] - %% Current Flow - M4 --> P4[Oxidation Half-Reaction] - N4 --> Q4[Reduction Half-Reaction] - O4 --> R4[Salt Bridge] - %% Cell Operation - P4 --> S4[Anode → Cathode] - Q4 --> T4[Electron Flow] - R4 --> U4[Ion Migration] - %% Energy Production - S4 --> V4[Cell Potential] - T4 --> W4[Current Generation] - U4 --> X4[Charge Balance] - %% Performance - V4 --> Y4[Voltage Measurement] - W4 --> Z4[Current Measurement] - X4 --> AA4[Efficiency Calculation] - %% Output - Y4 --> BB4[Cell Performance] - Z4 --> CC4[Power Output] - AA4 --> DD4[Energy Conversion] - %% Final Results - BB4 --> EE4[Electrochemical Cell Active] - CC4 --> FF4[Electrical Energy Produced] - DD4 --> GG4[Conversion Efficiency] - %% Styling - Chemistry Color Scheme - %% Styling - Biological Color Scheme - style A4 fill:#ff6b6b,color:#fff - style C4 fill:#ff6b6b,color:#fff - style E4 fill:#ff6b6b,color:#fff - style G4 fill:#ffd43b,color:#000 - style H4 fill:#ffd43b,color:#000 - style I4 fill:#ffd43b,color:#000 - style J4 fill:#ffd43b,color:#000 - style K4 fill:#ffd43b,color:#000 - style L4 fill:#ffd43b,color:#000 - style M4 fill:#51cf66,color:#fff - style N4 fill:#51cf66,color:#fff - style O4 fill:#51cf66,color:#fff - style P4 fill:#51cf66,color:#fff - style Q4 fill:#51cf66,color:#fff - style R4 fill:#51cf66,color:#fff - style S4 fill:#51cf66,color:#fff - style T4 fill:#51cf66,color:#fff - style U4 fill:#51cf66,color:#fff - style V4 fill:#51cf66,color:#fff - style W4 fill:#51cf66,color:#fff - style X4 fill:#51cf66,color:#fff - style B4 fill:#74c0fc,color:#fff - style D4 fill:#74c0fc,color:#fff - style F4 fill:#74c0fc,color:#fff - style Y4 fill:#74c0fc,color:#fff - style Z4 fill:#74c0fc,color:#fff - style AA4 fill:#74c0fc,color:#fff - style BB4 fill:#74c0fc,color:#fff - style CC4 fill:#74c0fc,color:#fff - style DD4 fill:#74c0fc,color:#fff - style EE4 fill:#b197fc,color:#fff - style FF4 fill:#b197fc,color:#fff - style GG4 fill:#b197fc,color:#fff -
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5. Distillation Process

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-graph TD - %% Initial Setup - %% Input Conditions - A5[Mixture] --> B5[Mixture Analysis] - C5[Heat Source] --> D5[Heat Supply] - E5[Distillation Apparatus] --> F5[Equipment Setup] - %% Process Setup - B5 --> G5[Component Analysis] - D5 --> H5[Temperature Control] - F5 --> I5[Apparatus Assembly] - %% Heating Process - G5 --> J5[Mixture Loading] - H5 --> K5[Heat Application] - I5 --> L5[Vapor Formation] - %% Vaporization - J5 --> M5[Component Separation] - K5 --> N5[Boiling Point Differences] - L5 --> O5[Vapor Phase] - %% Distillation - M5 --> P5[Fractional Distillation] - N5 --> Q5[Temperature Gradient] - O5 --> R5[Condensation] - %% Separation - P5 --> S5[Component Collection] - Q5 --> T5[Fraction Separation] - R5 --> U5[Liquid Recovery] - %% Product Collection - S5 --> V5[High Boiling Point] - T5 --> W5[Medium Boiling Point] - U5 --> X5[Low Boiling Point] - %% Process Control - V5 --> Y5[Fraction Analysis] - W5 --> Z5[Purity Check] - X5 --> AA5[Yield Calculation] - %% Output - Y5 --> BB5[Distillation Complete] - Z5 --> CC5[Component Separation] - AA5 --> DD5[Process Efficiency] - %% Final Results - BB5 --> EE5[Purified Components] - CC5 --> FF5[Separation Achieved] - DD5 --> GG5[Process Optimization] - %% Styling - Chemistry Color Scheme - %% Styling - Biological Color Scheme - style A5 fill:#ff6b6b,color:#fff - style C5 fill:#ff6b6b,color:#fff - style E5 fill:#ff6b6b,color:#fff - style G5 fill:#ffd43b,color:#000 - style H5 fill:#ffd43b,color:#000 - style I5 fill:#ffd43b,color:#000 - style J5 fill:#ffd43b,color:#000 - style K5 fill:#ffd43b,color:#000 - style L5 fill:#ffd43b,color:#000 - style M5 fill:#51cf66,color:#fff - style N5 fill:#51cf66,color:#fff - style O5 fill:#51cf66,color:#fff - style P5 fill:#51cf66,color:#fff - style Q5 fill:#51cf66,color:#fff - style R5 fill:#51cf66,color:#fff - style S5 fill:#51cf66,color:#fff - style T5 fill:#51cf66,color:#fff - style U5 fill:#51cf66,color:#fff - style V5 fill:#51cf66,color:#fff - style W5 fill:#51cf66,color:#fff - style X5 fill:#51cf66,color:#fff - style B5 fill:#74c0fc,color:#fff - style D5 fill:#74c0fc,color:#fff - style F5 fill:#74c0fc,color:#fff - style Y5 fill:#74c0fc,color:#fff - style Z5 fill:#74c0fc,color:#fff - style AA5 fill:#74c0fc,color:#fff - style BB5 fill:#74c0fc,color:#fff - style CC5 fill:#74c0fc,color:#fff - style DD5 fill:#74c0fc,color:#fff - style EE5 fill:#b197fc,color:#fff - style FF5 fill:#b197fc,color:#fff - style GG5 fill:#b197fc,color:#fff -
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Generated using the Programming Framework methodology

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This collection demonstrates the computational nature of chemical processes and systems

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Each flowchart preserves maximum detail through optimized Mermaid configuration

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💻 Computer Science Processes Database

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- - - - -
- - - - \ No newline at end of file diff --git a/data/aristotle-syllogistic-figure-2.mmd b/data/aristotle-syllogistic-figure-2.mmd new file mode 100644 index 0000000000000000000000000000000000000000..de55244a987b3a9277ca8adef3d91d09c6060c4e --- /dev/null +++ b/data/aristotle-syllogistic-figure-2.mmd @@ -0,0 +1,30 @@ +graph TD + DefAEIO("DefAEIO Categorical forms") + DefFig("DefFig Figures 1,2,3") + Econv("Econv E-conversion") + Barbara("Barbara Barbara") + Celarent("Celarent Celarent") + Ferio("Ferio Ferio") + Cesare("Cesare Cesare") + Camestres("Camestres Camestres") + Festino("Festino Festino") + Baroco("Baroco Baroco") + DefAEIO --> Barbara + DefFig --> Barbara + DefAEIO --> Celarent + DefFig --> Celarent + DefAEIO --> Ferio + DefFig --> Ferio + Econv --> Cesare + Celarent --> Cesare + Econv --> Camestres + Celarent --> Camestres + Econv --> Festino + Ferio --> Festino + Barbara --> Baroco + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class Econv,Barbara,Celarent,Ferio axiom + class DefAEIO,DefFig definition + class Cesare,Camestres,Festino,Baroco theorem \ No newline at end of file diff --git a/data/aristotle-syllogistic-figure-3.mmd b/data/aristotle-syllogistic-figure-3.mmd new file mode 100644 index 0000000000000000000000000000000000000000..d5191ada404b7042ecaf16a16147c120c7850405 --- /dev/null +++ b/data/aristotle-syllogistic-figure-3.mmd @@ -0,0 +1,37 @@ +graph TD + DefAEIO("DefAEIO Categorical forms") + DefFig("DefFig Figures 1,2,3") + Iconv("Iconv I-conversion") + Aconv("Aconv A-conversion") + Barbara("Barbara Barbara") + Darii("Darii Darii") + Ferio("Ferio Ferio") + Darapti("Darapti Darapti") + Felapton("Felapton Felapton") + Disamis("Disamis Disamis") + Datisi("Datisi Datisi") + Bocardo("Bocardo Bocardo") + Ferison("Ferison Ferison") + DefAEIO --> Barbara + DefFig --> Barbara + DefAEIO --> Darii + DefFig --> Darii + DefAEIO --> Ferio + DefFig --> Ferio + Aconv --> Darapti + Darii --> Darapti + Aconv --> Felapton + Ferio --> Felapton + Iconv --> Disamis + Darii --> Disamis + Aconv --> Datisi + Darii --> Datisi + Barbara --> Bocardo + Aconv --> Ferison + Ferio --> Ferison + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class Iconv,Aconv,Barbara,Darii,Ferio axiom + class DefAEIO,DefFig definition + class Darapti,Felapton,Disamis,Datisi,Bocardo,Ferison theorem \ No newline at end of file diff --git a/data/aristotle-syllogistic-foundations-perfect.mmd b/data/aristotle-syllogistic-foundations-perfect.mmd new file mode 100644 index 0000000000000000000000000000000000000000..257a7293866f272e8800de7a029172aa3fb7ebaf --- /dev/null +++ b/data/aristotle-syllogistic-foundations-perfect.mmd @@ -0,0 +1,23 @@ +graph TD + DefAEIO("DefAEIO Categorical forms") + DefFig("DefFig Figures 1,2,3") + Econv("Econv E-conversion") + Iconv("Iconv I-conversion") + Aconv("Aconv A-conversion") + Barbara("Barbara Barbara") + Celarent("Celarent Celarent") + Darii("Darii Darii") + Ferio("Ferio Ferio") + DefAEIO --> Barbara + DefFig --> Barbara + DefAEIO --> Celarent + DefFig --> Celarent + DefAEIO --> Darii + DefFig --> Darii + DefAEIO --> Ferio + DefFig --> Ferio + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class Econv,Iconv,Aconv,Barbara,Celarent,Darii,Ferio axiom + class DefAEIO,DefFig definition \ No newline at end of file diff --git a/data/aristotle-syllogistic.json b/data/aristotle-syllogistic.json new file mode 100644 index 0000000000000000000000000000000000000000..f25bc81de8e9b53f04e836dcff8e53a9ce41ceab --- /dev/null +++ b/data/aristotle-syllogistic.json @@ -0,0 +1,326 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "aristotle-syllogistic", + "name": "Aristotle Syllogistic Logic", + "subject": "logic", + "variant": "classical", + "description": "Aristotelian categorical syllogistic. Four perfect syllogisms (Barbara, Celarent, Darii, Ferio), three conversion rules, and ten imperfect syllogisms reduced to the perfect ones. Based on Prior Analytics.", + "structure": { + "axioms": 7, + "definitions": 2, + "theorems": 10 + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Aristotle Syllogistic Dependency Graph. Programming Framework.", + "keywords": [ + "Aristotle", + "syllogism", + "categorical logic", + "Prior Analytics", + "Barbara", + "Celarent" + ] + }, + "sources": [ + { + "id": "aristotle", + "type": "primary", + "authors": "Aristotle", + "title": "Prior Analytics", + "year": "c. 350 BCE", + "notes": "Syllogistic theory" + }, + { + "id": "stanford", + "type": "secondary", + "authors": "Smith, R.", + "title": "Aristotle's Logic", + "url": "https://plato.stanford.edu/entries/aristotle-logic/", + "notes": "Stanford Encyclopedia" + } + ], + "nodes": [ + { + "id": "DefAEIO", + "type": "definition", + "label": "A, E, I, O: All/No/Some/Some-not", + "shortLabel": "DefAEIO", + "short": "Categorical forms", + "colorClass": "definition" + }, + { + "id": "DefFig", + "type": "definition", + "label": "Three figures: middle term position", + "shortLabel": "DefFig", + "short": "Figures 1,2,3", + "colorClass": "definition" + }, + { + "id": "Econv", + "type": "axiom", + "label": "Eab implies Eba (No M is P implies No P is M)", + "shortLabel": "Econv", + "short": "E-conversion", + "colorClass": "axiom" + }, + { + "id": "Iconv", + "type": "axiom", + "label": "Iab implies Iba (Some M is P implies Some P is M)", + "shortLabel": "Iconv", + "short": "I-conversion", + "colorClass": "axiom" + }, + { + "id": "Aconv", + "type": "axiom", + "label": "Aab implies Iba (All M is P implies Some P is M)", + "shortLabel": "Aconv", + "short": "A-conversion", + "colorClass": "axiom" + }, + { + "id": "Barbara", + "type": "axiom", + "label": "AAA-1: All M is P, All S is M therefore All S is P", + "shortLabel": "Barbara", + "short": "Barbara", + "colorClass": "axiom" + }, + { + "id": "Celarent", + "type": "axiom", + "label": "EAE-1: No M is P, All S is M therefore No S is P", + "shortLabel": "Celarent", + "short": "Celarent", + "colorClass": "axiom" + }, + { + "id": "Darii", + "type": "axiom", + "label": "AII-1: All M is P, Some S is M therefore Some S is P", + "shortLabel": "Darii", + "short": "Darii", + "colorClass": "axiom" + }, + { + "id": "Ferio", + "type": "axiom", + "label": "EIO-1: No M is P, Some S is M therefore Some S is not P", + "shortLabel": "Ferio", + "short": "Ferio", + "colorClass": "axiom" + }, + { + "id": "Cesare", + "type": "theorem", + "label": "EAE-2: No P is M, All S is M therefore No S is P", + "shortLabel": "Cesare", + "short": "Cesare", + "colorClass": "theorem" + }, + { + "id": "Camestres", + "type": "theorem", + "label": "AEE-2: All P is M, No S is M therefore No S is P", + "shortLabel": "Camestres", + "short": "Camestres", + "colorClass": "theorem" + }, + { + "id": "Festino", + "type": "theorem", + "label": "EIO-2: No P is M, Some S is M therefore Some S is not P", + "shortLabel": "Festino", + "short": "Festino", + "colorClass": "theorem" + }, + { + "id": "Baroco", + "type": "theorem", + "label": "AOO-2: All P is M, Some S is not M therefore Some S is not P", + "shortLabel": "Baroco", + "short": "Baroco", + "colorClass": "theorem" + }, + { + "id": "Darapti", + "type": "theorem", + "label": "AAI-3: All M is P, All M is S therefore Some S is P", + "shortLabel": "Darapti", + "short": "Darapti", + "colorClass": "theorem" + }, + { + "id": "Felapton", + "type": "theorem", + "label": "EAO-3: No M is P, All M is S therefore Some S is not P", + "shortLabel": "Felapton", + "short": "Felapton", + "colorClass": "theorem" + }, + { + "id": "Disamis", + "type": "theorem", + "label": "IAI-3: Some M is P, All M is S therefore Some S is P", + "shortLabel": "Disamis", + "short": "Disamis", + "colorClass": "theorem" + }, + { + "id": "Datisi", + "type": "theorem", + "label": "AII-3: All M is P, Some M is S therefore Some S is P", + "shortLabel": "Datisi", + "short": "Datisi", + "colorClass": "theorem" + }, + { + "id": "Bocardo", + "type": "theorem", + "label": "OAO-3: Some M is not P, All M is S therefore Some S is not P", + "shortLabel": "Bocardo", + "short": "Bocardo", + "colorClass": "theorem" + }, + { + "id": "Ferison", + "type": "theorem", + "label": "EIO-3: No M is P, Some M is S therefore Some S is not P", + "shortLabel": "Ferison", + "short": "Ferison", + "colorClass": "theorem" + } + ], + "edges": [ + { + "from": "DefAEIO", + "to": "Barbara" + }, + { + "from": "DefFig", + "to": "Barbara" + }, + { + "from": "DefAEIO", + "to": "Celarent" + }, + { + "from": "DefFig", + "to": "Celarent" + }, + { + "from": "DefAEIO", + "to": "Darii" + }, + { + "from": "DefFig", + "to": "Darii" + }, + { + "from": "DefAEIO", + "to": "Ferio" + }, + { + "from": "DefFig", + "to": "Ferio" + }, + { + "from": "Econv", + "to": "Cesare" + }, + { + "from": "Celarent", + "to": "Cesare" + }, + { + "from": "Econv", + "to": "Camestres" + }, + { + "from": "Celarent", + "to": "Camestres" + }, + { + "from": "Econv", + "to": "Festino" + }, + { + "from": "Ferio", + "to": "Festino" + }, + { + "from": "Barbara", + "to": "Baroco" + }, + { + "from": "Aconv", + "to": "Darapti" + }, + { + "from": "Darii", + "to": "Darapti" + }, + { + "from": "Aconv", + "to": "Felapton" + }, + { + "from": "Ferio", + "to": "Felapton" + }, + { + "from": "Iconv", + "to": "Disamis" + }, + { + "from": "Darii", + "to": "Disamis" + }, + { + "from": "Aconv", + "to": "Datisi" + }, + { + "from": "Darii", + "to": "Datisi" + }, + { + "from": "Barbara", + "to": "Bocardo" + }, + { + "from": "Aconv", + "to": "Ferison" + }, + { + "from": "Ferio", + "to": "Ferison" + } + ], + "colorScheme": { + "axiom": { + "fill": "#e74c3c", + "stroke": "#c0392b" + }, + "definition": { + "fill": "#3498db", + "stroke": "#2980b9" + }, + "theorem": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/aristotle-syllogistic.mmd b/data/aristotle-syllogistic.mmd new file mode 100644 index 0000000000000000000000000000000000000000..5b8a89c8ef3ccbaadbdeae1bae110ec357a43852 --- /dev/null +++ b/data/aristotle-syllogistic.mmd @@ -0,0 +1,52 @@ +graph TD + DefAEIO("DefAEIO Categorical forms") + DefFig("DefFig Figures 1,2,3") + Econv("Econv E-conversion") + Iconv("Iconv I-conversion") + Aconv("Aconv A-conversion") + Barbara("Barbara Barbara") + Celarent("Celarent Celarent") + Darii("Darii Darii") + Ferio("Ferio Ferio") + Cesare("Cesare Cesare") + Camestres("Camestres Camestres") + Festino("Festino Festino") + Baroco("Baroco Baroco") + Darapti("Darapti Darapti") + Felapton("Felapton Felapton") + Disamis("Disamis Disamis") + Datisi("Datisi Datisi") + Bocardo("Bocardo Bocardo") + Ferison("Ferison Ferison") + DefAEIO --> Barbara + DefFig --> Barbara + DefAEIO --> Celarent + DefFig --> Celarent + DefAEIO --> Darii + DefFig --> Darii + DefAEIO --> Ferio + DefFig --> Ferio + Econv --> Cesare + Celarent --> Cesare + Econv --> Camestres + Celarent --> Camestres + Econv --> Festino + Ferio --> Festino + Barbara --> Baroco + Aconv --> Darapti + Darii --> Darapti + Aconv --> Felapton + Ferio --> Felapton + Iconv --> Disamis + Darii --> Disamis + Aconv --> Datisi + Darii --> Datisi + Barbara --> Bocardo + Aconv --> Ferison + Ferio --> Ferison + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class Econv,Iconv,Aconv,Barbara,Celarent,Darii,Ferio axiom + class DefAEIO,DefFig definition + class Cesare,Camestres,Festino,Baroco,Darapti,Felapton,Disamis,Datisi,Bocardo,Ferison theorem \ No newline at end of file diff --git a/data/combinatorics-advanced-counting.mmd b/data/combinatorics-advanced-counting.mmd new file mode 100644 index 0000000000000000000000000000000000000000..48e2d60940bda01dff18d3f590646cdd71f49fb1 --- /dev/null +++ b/data/combinatorics-advanced-counting.mmd @@ -0,0 +1,24 @@ +graph TD + DefFact("DefFact Factorial") + DefSum("DefSum Sum principle") + DefProd("DefProd Product principle") + PermNoRep("PermNoRep Permutations no rep") + Pigeonhole("Pigeonhole Pigeonhole principle") + InclExcl("InclExcl Inclusion-exclusion") + InclExcl3("InclExcl3 Incl-excl 3 sets") + Derange("Derange Derangements") + Stirling2("Stirling2 Stirling numbers") + DefFact --> PermNoRep + DefProd --> PermNoRep + DefSum --> Pigeonhole + DefSum --> InclExcl + InclExcl --> InclExcl3 + InclExcl --> Derange + PermNoRep --> Derange + DefSum --> Stirling2 + DefProd --> Stirling2 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class DefFact,DefSum,DefProd definition + class PermNoRep,Pigeonhole,InclExcl,InclExcl3,Derange,Stirling2 theorem \ No newline at end of file diff --git a/data/combinatorics-combinations-binomial.mmd b/data/combinatorics-combinations-binomial.mmd new file mode 100644 index 0000000000000000000000000000000000000000..5e54b07b55cbbac9b25b54491cfa1f8bb44c77d7 --- /dev/null +++ b/data/combinatorics-combinations-binomial.mmd @@ -0,0 +1,20 @@ +graph TD + DefFact("DefFact Factorial") + DefProd("DefProd Product principle") + PermNoRep("PermNoRep Permutations no rep") + CombNoRep("CombNoRep Combinations") + CombRep("CombRep Combinations with rep") + BinomThm("BinomThm Binomial theorem") + Pascal("Pascal Pascal identity") + DefFact --> PermNoRep + DefProd --> PermNoRep + PermNoRep --> CombNoRep + DefFact --> CombNoRep + CombNoRep --> CombRep + CombNoRep --> BinomThm + CombNoRep --> Pascal + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class DefFact,DefProd definition + class PermNoRep,CombNoRep,CombRep,BinomThm,Pascal theorem \ No newline at end of file diff --git a/data/combinatorics-principles-permutations.mmd b/data/combinatorics-principles-permutations.mmd new file mode 100644 index 0000000000000000000000000000000000000000..5c34a9628df525a83165cb4a036d723645482af5 --- /dev/null +++ b/data/combinatorics-principles-permutations.mmd @@ -0,0 +1,17 @@ +graph TD + DefFact("DefFact Factorial") + DefSum("DefSum Sum principle") + DefProd("DefProd Product principle") + PermNoRep("PermNoRep Permutations no rep") + PermRep("PermRep Permutations with rep") + CombNoRep("CombNoRep Combinations") + DefFact --> PermNoRep + DefProd --> PermNoRep + DefProd --> PermRep + PermNoRep --> CombNoRep + DefFact --> CombNoRep + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class DefFact,DefSum,DefProd definition + class PermNoRep,PermRep,CombNoRep theorem \ No newline at end of file diff --git a/data/combinatorics.json b/data/combinatorics.json new file mode 100644 index 0000000000000000000000000000000000000000..4bd3b400f48e129dd4b24d264624613c7abae266 --- /dev/null +++ b/data/combinatorics.json @@ -0,0 +1,239 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "combinatorics", + "name": "Combinatorics", + "subject": "discrete_mathematics", + "variant": "classical", + "description": "Counting principles: sum and product rules, permutations (with/without repetition), combinations, binomial theorem, pigeonhole principle, inclusion-exclusion, derangements.", + "structure": { + "axioms": 0, + "definitions": 3, + "theorems": 11 + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Combinatorics Dependency Graph. Programming Framework.", + "keywords": [ + "combinatorics", + "permutations", + "combinations", + "counting", + "binomial theorem" + ] + }, + "sources": [ + { + "id": "dmoi", + "type": "primary", + "title": "Discrete Mathematics: An Open Introduction", + "url": "https://discrete.openmathbooks.org/dmoi4/sec_counting-combperm.html", + "notes": "Counting principles" + }, + { + "id": "mathisfun", + "type": "digital", + "title": "Combinations and Permutations", + "url": "https://www.mathsisfun.com/combinatorics/combinations-permutations.html", + "notes": "Formulas" + } + ], + "nodes": [ + { + "id": "DefFact", + "type": "definition", + "label": "Factorial: n! = n(n-1)...1, 0!=1", + "shortLabel": "DefFact", + "short": "Factorial", + "colorClass": "definition" + }, + { + "id": "DefSum", + "type": "definition", + "label": "Sum principle: disjoint choices add (OR)", + "shortLabel": "DefSum", + "short": "Sum principle", + "colorClass": "definition" + }, + { + "id": "DefProd", + "type": "definition", + "label": "Product principle: sequential choices multiply (AND)", + "shortLabel": "DefProd", + "short": "Product principle", + "colorClass": "definition" + }, + { + "id": "PermNoRep", + "type": "theorem", + "label": "P(n,r) = n!/(n-r)! arrangements of r from n", + "shortLabel": "PermNoRep", + "short": "Permutations no rep", + "colorClass": "theorem" + }, + { + "id": "PermRep", + "type": "theorem", + "label": "n^r arrangements of r from n with repetition", + "shortLabel": "PermRep", + "short": "Permutations with rep", + "colorClass": "theorem" + }, + { + "id": "CombNoRep", + "type": "theorem", + "label": "C(n,r) = n!/(r!(n-r)!) = P(n,r)/r!", + "shortLabel": "CombNoRep", + "short": "Combinations", + "colorClass": "theorem" + }, + { + "id": "CombRep", + "type": "theorem", + "label": "C(n+r-1,r) ways to choose r from n with rep", + "shortLabel": "CombRep", + "short": "Combinations with rep", + "colorClass": "theorem" + }, + { + "id": "BinomThm", + "type": "theorem", + "label": "(a+b)^n = sum C(n,k) a^k b^(n-k)", + "shortLabel": "BinomThm", + "short": "Binomial theorem", + "colorClass": "theorem" + }, + { + "id": "Pascal", + "type": "theorem", + "label": "C(n,k) = C(n-1,k-1) + C(n-1,k)", + "shortLabel": "Pascal", + "short": "Pascal identity", + "colorClass": "theorem" + }, + { + "id": "Pigeonhole", + "type": "theorem", + "label": "n+1 objects in n boxes implies one box has 2+", + "shortLabel": "Pigeonhole", + "short": "Pigeonhole principle", + "colorClass": "theorem" + }, + { + "id": "InclExcl", + "type": "theorem", + "label": "|A union B| = |A| + |B| - |A intersect B|", + "shortLabel": "InclExcl", + "short": "Inclusion-exclusion", + "colorClass": "theorem" + }, + { + "id": "InclExcl3", + "type": "theorem", + "label": "Inclusion-exclusion for 3 sets", + "shortLabel": "InclExcl3", + "short": "Incl-excl 3 sets", + "colorClass": "theorem" + }, + { + "id": "Derange", + "type": "theorem", + "label": "D(n) = n! sum (-1)^k/k! derangements", + "shortLabel": "Derange", + "short": "Derangements", + "colorClass": "theorem" + }, + { + "id": "Stirling2", + "type": "theorem", + "label": "S(n,k) = partitions of n into k nonempty sets", + "shortLabel": "Stirling2", + "short": "Stirling numbers", + "colorClass": "theorem" + } + ], + "edges": [ + { + "from": "DefFact", + "to": "PermNoRep" + }, + { + "from": "DefProd", + "to": "PermNoRep" + }, + { + "from": "DefProd", + "to": "PermRep" + }, + { + "from": "PermNoRep", + "to": "CombNoRep" + }, + { + "from": "DefFact", + "to": "CombNoRep" + }, + { + "from": "CombNoRep", + "to": "CombRep" + }, + { + "from": "CombNoRep", + "to": "BinomThm" + }, + { + "from": "CombNoRep", + "to": "Pascal" + }, + { + "from": "DefSum", + "to": "Pigeonhole" + }, + { + "from": "DefSum", + "to": "InclExcl" + }, + { + "from": "InclExcl", + "to": "InclExcl3" + }, + { + "from": "InclExcl", + "to": "Derange" + }, + { + "from": "PermNoRep", + "to": "Derange" + }, + { + "from": "DefSum", + "to": "Stirling2" + }, + { + "from": "DefProd", + "to": "Stirling2" + } + ], + "colorScheme": { + "axiom": { + "fill": "#e74c3c", + "stroke": "#c0392b" + }, + "definition": { + "fill": "#3498db", + "stroke": "#2980b9" + }, + "theorem": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/combinatorics.mmd b/data/combinatorics.mmd new file mode 100644 index 0000000000000000000000000000000000000000..dd7cf62d5e3024dc8e9cfd0ce6177385b03fdc39 --- /dev/null +++ b/data/combinatorics.mmd @@ -0,0 +1,35 @@ +graph TD + DefFact("DefFact Factorial") + DefSum("DefSum Sum principle") + DefProd("DefProd Product principle") + PermNoRep("PermNoRep Permutations no rep") + PermRep("PermRep Permutations with rep") + CombNoRep("CombNoRep Combinations") + CombRep("CombRep Combinations with rep") + BinomThm("BinomThm Binomial theorem") + Pascal("Pascal Pascal identity") + Pigeonhole("Pigeonhole Pigeonhole principle") + InclExcl("InclExcl Inclusion-exclusion") + InclExcl3("InclExcl3 Incl-excl 3 sets") + Derange("Derange Derangements") + Stirling2("Stirling2 Stirling numbers") + DefFact --> PermNoRep + DefProd --> PermNoRep + DefProd --> PermRep + PermNoRep --> CombNoRep + DefFact --> CombNoRep + CombNoRep --> CombRep + CombNoRep --> BinomThm + CombNoRep --> Pascal + DefSum --> Pigeonhole + DefSum --> InclExcl + InclExcl --> InclExcl3 + InclExcl --> Derange + PermNoRep --> Derange + DefSum --> Stirling2 + DefProd --> Stirling2 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class DefFact,DefSum,DefProd definition + class PermNoRep,PermRep,CombNoRep,CombRep,BinomThm,Pascal,Pigeonhole,InclExcl,InclExcl3,Derange,Stirling2 theorem \ No newline at end of file diff --git a/data/euclid-elements-book-i-props-1-10.mmd b/data/euclid-elements-book-i-props-1-10.mmd new file mode 100644 index 0000000000000000000000000000000000000000..2adc89278e23a45a078b05db3d0f6b4228c7d869 --- /dev/null +++ b/data/euclid-elements-book-i-props-1-10.mmd @@ -0,0 +1,49 @@ +graph TD + P1["Post. 1\nDraw a straight line from any po..."] + P2["Post. 2\nProduce a finite straight line c..."] + P3["Post. 3\nDescribe a circle with any cente..."] + P4["Post. 4\nAll right angles equal one another"] + P5["Post. 5\nParallel postulate: if interior ..."] + CN1["CN 1\nThings equal to the same thing a..."] + CN2["CN 2\nIf equals are added to equals, t..."] + CN3["CN 3\nIf equals are subtracted from eq..."] + CN4["CN 4\nThings coinciding with one anoth..."] + CN5["CN 5\nThe whole is greater than the part"] + Prop1["Prop. I.1\nEquilateral triangle on given line"] + Prop2["Prop. I.2\nPlace line equal to given at point"] + Prop3["Prop. I.3\nCut off from greater segment equal to less"] + Prop4["Prop. I.4\nSAS congruence"] + Prop5["Prop. I.5\nBase angles of isosceles equal"] + Prop6["Prop. I.6\nSides opposite equal angles equal"] + Prop7["Prop. I.7\nUniqueness of triangle from ends"] + Prop8["Prop. I.8\nSSS congruence"] + Prop9["Prop. I.9\nBisect angle"] + Prop10["Prop. I.10\nBisect line"] + P1 --> Prop1 + P3 --> Prop1 + Prop1 --> Prop2 + P1 --> Prop2 + P2 --> Prop2 + P3 --> Prop2 + Prop2 --> Prop3 + P3 --> Prop3 + CN4 --> Prop4 + CN5 --> Prop4 + Prop3 --> Prop5 + Prop4 --> Prop5 + Prop3 --> Prop6 + Prop4 --> Prop6 + Prop5 --> Prop7 + Prop7 --> Prop8 + Prop1 --> Prop9 + Prop3 --> Prop9 + Prop8 --> Prop9 + Prop1 --> Prop10 + Prop4 --> Prop10 + Prop9 --> Prop10 + classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b + classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class P1,P2,P3,P4,P5 postulate + class CN1,CN2,CN3,CN4,CN5 commonNotion + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-i-props-11-20.mmd b/data/euclid-elements-book-i-props-11-20.mmd new file mode 100644 index 0000000000000000000000000000000000000000..684379d465fbbfe1826543247ee3cd759ae17028 --- /dev/null +++ b/data/euclid-elements-book-i-props-11-20.mmd @@ -0,0 +1,78 @@ +graph TD + P1["Post. 1\nDraw a straight line from any po..."] + P2["Post. 2\nProduce a finite straight line c..."] + P3["Post. 3\nDescribe a circle with any cente..."] + P4["Post. 4\nAll right angles equal one another"] + P5["Post. 5\nParallel postulate: if interior ..."] + CN1["CN 1\nThings equal to the same thing a..."] + CN2["CN 2\nIf equals are added to equals, t..."] + CN3["CN 3\nIf equals are subtracted from eq..."] + CN4["CN 4\nThings coinciding with one anoth..."] + CN5["CN 5\nThe whole is greater than the part"] + Prop1["Prop. I.1\nEquilateral triangle on given line"] + Prop2["Prop. I.2\nPlace line equal to given at point"] + Prop3["Prop. I.3\nCut off from greater segment equal to less"] + Prop4["Prop. I.4\nSAS congruence"] + Prop5["Prop. I.5\nBase angles of isosceles equal"] + Prop7["Prop. I.7\nUniqueness of triangle from ends"] + Prop8["Prop. I.8\nSSS congruence"] + Prop9["Prop. I.9\nBisect angle"] + Prop10["Prop. I.10\nBisect line"] + Prop11["Prop. I.11\nPerpendicular from point on line"] + Prop12["Prop. I.12\nPerpendicular from point not on line"] + Prop13["Prop. I.13\nAngles on line sum to two right"] + Prop14["Prop. I.14\nIf angles sum to two right, straight line"] + Prop15["Prop. I.15\nVertical angles equal"] + Prop16["Prop. I.16\nExterior angle > interior opposite"] + Prop17["Prop. I.17\nSum of two angles < two right"] + Prop18["Prop. I.18\nAngle opposite greater side greater"] + Prop19["Prop. I.19\nSide opposite greater angle greater"] + Prop20["Prop. I.20\nTriangle inequality"] + P1 --> Prop1 + P3 --> Prop1 + Prop1 --> Prop2 + P1 --> Prop2 + P2 --> Prop2 + P3 --> Prop2 + Prop2 --> Prop3 + P3 --> Prop3 + CN4 --> Prop4 + CN5 --> Prop4 + Prop3 --> Prop5 + Prop4 --> Prop5 + Prop5 --> Prop7 + Prop7 --> Prop8 + Prop1 --> Prop9 + Prop3 --> Prop9 + Prop8 --> Prop9 + Prop1 --> Prop10 + Prop4 --> Prop10 + Prop9 --> Prop10 + Prop1 --> Prop11 + Prop3 --> Prop11 + Prop8 --> Prop11 + Prop8 --> Prop12 + Prop10 --> Prop12 + Prop11 --> Prop13 + Prop13 --> Prop14 + Prop13 --> Prop15 + Prop3 --> Prop16 + Prop4 --> Prop16 + Prop10 --> Prop16 + Prop15 --> Prop16 + Prop13 --> Prop17 + Prop16 --> Prop17 + Prop3 --> Prop18 + Prop5 --> Prop18 + Prop16 --> Prop18 + Prop5 --> Prop19 + Prop18 --> Prop19 + Prop3 --> Prop20 + Prop5 --> Prop20 + Prop19 --> Prop20 + classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b + classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class P1,P2,P3,P4,P5 postulate + class CN1,CN2,CN3,CN4,CN5 commonNotion + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14,Prop15,Prop16,Prop17,Prop18,Prop19,Prop20 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-i-props-21-30.mmd b/data/euclid-elements-book-i-props-21-30.mmd new file mode 100644 index 0000000000000000000000000000000000000000..79cc4c69f5bc05b4f89dbfd21a49ae04d3a2595b --- /dev/null +++ b/data/euclid-elements-book-i-props-21-30.mmd @@ -0,0 +1,105 @@ +graph TD + P1["Post. 1\nDraw a straight line from any po..."] + P2["Post. 2\nProduce a finite straight line c..."] + P3["Post. 3\nDescribe a circle with any cente..."] + P4["Post. 4\nAll right angles equal one another"] + P5["Post. 5\nParallel postulate: if interior ..."] + CN1["CN 1\nThings equal to the same thing a..."] + CN2["CN 2\nIf equals are added to equals, t..."] + CN3["CN 3\nIf equals are subtracted from eq..."] + CN4["CN 4\nThings coinciding with one anoth..."] + CN5["CN 5\nThe whole is greater than the part"] + Prop1["Prop. I.1\nEquilateral triangle on given line"] + Prop2["Prop. I.2\nPlace line equal to given at point"] + Prop3["Prop. I.3\nCut off from greater segment equal to less"] + Prop4["Prop. I.4\nSAS congruence"] + Prop5["Prop. I.5\nBase angles of isosceles equal"] + Prop7["Prop. I.7\nUniqueness of triangle from ends"] + Prop8["Prop. I.8\nSSS congruence"] + Prop9["Prop. I.9\nBisect angle"] + Prop10["Prop. I.10\nBisect line"] + Prop11["Prop. I.11\nPerpendicular from point on line"] + Prop13["Prop. I.13\nAngles on line sum to two right"] + Prop15["Prop. I.15\nVertical angles equal"] + Prop16["Prop. I.16\nExterior angle > interior opposite"] + Prop18["Prop. I.18\nAngle opposite greater side greater"] + Prop19["Prop. I.19\nSide opposite greater angle greater"] + Prop20["Prop. I.20\nTriangle inequality"] + Prop21["Prop. I.21\nLines from ends within triangle"] + Prop22["Prop. I.22\nConstruct triangle from three lines"] + Prop23["Prop. I.23\nConstruct angle equal to given"] + Prop24["Prop. I.24\nSAS for greater angle => greater base"] + Prop25["Prop. I.25\nSAS for greater base => greater angle"] + Prop26["Prop. I.26\nAAS congruence"] + Prop27["Prop. I.27\nAlternate angles equal => parallel"] + Prop28["Prop. I.28\nExterior = interior opposite => parallel"] + Prop29["Prop. I.29\nParallel => alternate angles equal"] + Prop30["Prop. I.30\nTransitivity of parallel"] + P1 --> Prop1 + P3 --> Prop1 + Prop1 --> Prop2 + P1 --> Prop2 + P2 --> Prop2 + P3 --> Prop2 + Prop2 --> Prop3 + P3 --> Prop3 + CN4 --> Prop4 + CN5 --> Prop4 + Prop3 --> Prop5 + Prop4 --> Prop5 + Prop5 --> Prop7 + Prop7 --> Prop8 + Prop1 --> Prop9 + Prop3 --> Prop9 + Prop8 --> Prop9 + Prop1 --> Prop10 + Prop4 --> Prop10 + Prop9 --> Prop10 + Prop1 --> Prop11 + Prop3 --> Prop11 + Prop8 --> Prop11 + Prop11 --> Prop13 + Prop13 --> Prop15 + Prop3 --> Prop16 + Prop4 --> Prop16 + Prop10 --> Prop16 + Prop15 --> Prop16 + Prop3 --> Prop18 + Prop5 --> Prop18 + Prop16 --> Prop18 + Prop5 --> Prop19 + Prop18 --> Prop19 + Prop3 --> Prop20 + Prop5 --> Prop20 + Prop19 --> Prop20 + Prop16 --> Prop21 + Prop20 --> Prop21 + Prop3 --> Prop22 + Prop20 --> Prop22 + Prop8 --> Prop23 + Prop22 --> Prop23 + Prop3 --> Prop24 + Prop4 --> Prop24 + Prop5 --> Prop24 + Prop19 --> Prop24 + Prop23 --> Prop24 + Prop4 --> Prop25 + Prop24 --> Prop25 + Prop3 --> Prop26 + Prop4 --> Prop26 + Prop16 --> Prop26 + Prop16 --> Prop27 + Prop13 --> Prop28 + Prop15 --> Prop28 + Prop27 --> Prop28 + Prop13 --> Prop29 + Prop15 --> Prop29 + Prop27 --> Prop29 + P5 --> Prop29 + Prop29 --> Prop30 + classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b + classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class P1,P2,P3,P4,P5 postulate + class CN1,CN2,CN3,CN4,CN5 commonNotion + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop13,Prop15,Prop16,Prop18,Prop19,Prop20,Prop21,Prop22,Prop23,Prop24,Prop25,Prop26,Prop27,Prop28,Prop29,Prop30 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-i-props-31-41.mmd b/data/euclid-elements-book-i-props-31-41.mmd new file mode 100644 index 0000000000000000000000000000000000000000..b2a6e5ce28d248b018fac455cd03bfee57571032 --- /dev/null +++ b/data/euclid-elements-book-i-props-31-41.mmd @@ -0,0 +1,127 @@ +graph TD + P1["Post. 1\nDraw a straight line from any po..."] + P2["Post. 2\nProduce a finite straight line c..."] + P3["Post. 3\nDescribe a circle with any cente..."] + P4["Post. 4\nAll right angles equal one another"] + P5["Post. 5\nParallel postulate: if interior ..."] + CN1["CN 1\nThings equal to the same thing a..."] + CN2["CN 2\nIf equals are added to equals, t..."] + CN3["CN 3\nIf equals are subtracted from eq..."] + CN4["CN 4\nThings coinciding with one anoth..."] + CN5["CN 5\nThe whole is greater than the part"] + Prop1["Prop. I.1\nEquilateral triangle on given line"] + Prop2["Prop. I.2\nPlace line equal to given at point"] + Prop3["Prop. I.3\nCut off from greater segment equal to less"] + Prop4["Prop. I.4\nSAS congruence"] + Prop5["Prop. I.5\nBase angles of isosceles equal"] + Prop7["Prop. I.7\nUniqueness of triangle from ends"] + Prop8["Prop. I.8\nSSS congruence"] + Prop9["Prop. I.9\nBisect angle"] + Prop10["Prop. I.10\nBisect line"] + Prop11["Prop. I.11\nPerpendicular from point on line"] + Prop13["Prop. I.13\nAngles on line sum to two right"] + Prop15["Prop. I.15\nVertical angles equal"] + Prop16["Prop. I.16\nExterior angle > interior opposite"] + Prop18["Prop. I.18\nAngle opposite greater side greater"] + Prop19["Prop. I.19\nSide opposite greater angle greater"] + Prop20["Prop. I.20\nTriangle inequality"] + Prop22["Prop. I.22\nConstruct triangle from three lines"] + Prop23["Prop. I.23\nConstruct angle equal to given"] + Prop26["Prop. I.26\nAAS congruence"] + Prop27["Prop. I.27\nAlternate angles equal => parallel"] + Prop29["Prop. I.29\nParallel => alternate angles equal"] + Prop31["Prop. I.31\nDraw parallel through point"] + Prop32["Prop. I.32\nExterior angle = sum interior opposite"] + Prop33["Prop. I.33\nJoining ends of equal parallel lines"] + Prop34["Prop. I.34\nParallelogram properties"] + Prop35["Prop. I.35\nParallelograms same base equal"] + Prop36["Prop. I.36\nParallelograms equal bases equal"] + Prop37["Prop. I.37\nTriangles same base equal"] + Prop38["Prop. I.38\nTriangles equal bases equal"] + Prop39["Prop. I.39\nEqual triangles same base same side"] + Prop40["Prop. I.40\nEqual triangles equal bases same side"] + Prop41["Prop. I.41\nParallelogram = 2× triangle"] + P1 --> Prop1 + P3 --> Prop1 + Prop1 --> Prop2 + P1 --> Prop2 + P2 --> Prop2 + P3 --> Prop2 + Prop2 --> Prop3 + P3 --> Prop3 + CN4 --> Prop4 + CN5 --> Prop4 + Prop3 --> Prop5 + Prop4 --> Prop5 + Prop5 --> Prop7 + Prop7 --> Prop8 + Prop1 --> Prop9 + Prop3 --> Prop9 + Prop8 --> Prop9 + Prop1 --> Prop10 + Prop4 --> Prop10 + Prop9 --> Prop10 + Prop1 --> Prop11 + Prop3 --> Prop11 + Prop8 --> Prop11 + Prop11 --> Prop13 + Prop13 --> Prop15 + Prop3 --> Prop16 + Prop4 --> Prop16 + Prop10 --> Prop16 + Prop15 --> Prop16 + Prop3 --> Prop18 + Prop5 --> Prop18 + Prop16 --> Prop18 + Prop5 --> Prop19 + Prop18 --> Prop19 + Prop3 --> Prop20 + Prop5 --> Prop20 + Prop19 --> Prop20 + Prop3 --> Prop22 + Prop20 --> Prop22 + Prop8 --> Prop23 + Prop22 --> Prop23 + Prop3 --> Prop26 + Prop4 --> Prop26 + Prop16 --> Prop26 + Prop16 --> Prop27 + Prop13 --> Prop29 + Prop15 --> Prop29 + Prop27 --> Prop29 + P5 --> Prop29 + Prop23 --> Prop31 + Prop27 --> Prop31 + Prop13 --> Prop32 + Prop29 --> Prop32 + Prop31 --> Prop32 + Prop4 --> Prop33 + Prop27 --> Prop33 + Prop29 --> Prop33 + Prop4 --> Prop34 + Prop26 --> Prop34 + Prop29 --> Prop34 + Prop4 --> Prop35 + Prop29 --> Prop35 + Prop34 --> Prop35 + Prop33 --> Prop36 + Prop34 --> Prop36 + Prop35 --> Prop36 + Prop31 --> Prop37 + Prop34 --> Prop37 + Prop35 --> Prop37 + Prop31 --> Prop38 + Prop34 --> Prop38 + Prop36 --> Prop38 + Prop31 --> Prop39 + Prop37 --> Prop39 + Prop31 --> Prop40 + Prop38 --> Prop40 + Prop34 --> Prop41 + Prop37 --> Prop41 + classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b + classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class P1,P2,P3,P4,P5 postulate + class CN1,CN2,CN3,CN4,CN5 commonNotion + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop13,Prop15,Prop16,Prop18,Prop19,Prop20,Prop22,Prop23,Prop26,Prop27,Prop29,Prop31,Prop32,Prop33,Prop34,Prop35,Prop36,Prop37,Prop38,Prop39,Prop40,Prop41 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-i-props-42-48.mmd b/data/euclid-elements-book-i-props-42-48.mmd new file mode 100644 index 0000000000000000000000000000000000000000..ecb6934b94cacf8426406f860cbd17c9ff589a5f --- /dev/null +++ b/data/euclid-elements-book-i-props-42-48.mmd @@ -0,0 +1,160 @@ +graph TD + P1["Post. 1\nDraw a straight line from any po..."] + P2["Post. 2\nProduce a finite straight line c..."] + P3["Post. 3\nDescribe a circle with any cente..."] + P4["Post. 4\nAll right angles equal one another"] + P5["Post. 5\nParallel postulate: if interior ..."] + CN1["CN 1\nThings equal to the same thing a..."] + CN2["CN 2\nIf equals are added to equals, t..."] + CN3["CN 3\nIf equals are subtracted from eq..."] + CN4["CN 4\nThings coinciding with one anoth..."] + CN5["CN 5\nThe whole is greater than the part"] + Prop1["Prop. I.1\nEquilateral triangle on given line"] + Prop2["Prop. I.2\nPlace line equal to given at point"] + Prop3["Prop. I.3\nCut off from greater segment equal to less"] + Prop4["Prop. I.4\nSAS congruence"] + Prop5["Prop. I.5\nBase angles of isosceles equal"] + Prop7["Prop. I.7\nUniqueness of triangle from ends"] + Prop8["Prop. I.8\nSSS congruence"] + Prop9["Prop. I.9\nBisect angle"] + Prop10["Prop. I.10\nBisect line"] + Prop11["Prop. I.11\nPerpendicular from point on line"] + Prop13["Prop. I.13\nAngles on line sum to two right"] + Prop14["Prop. I.14\nIf angles sum to two right, straight line"] + Prop15["Prop. I.15\nVertical angles equal"] + Prop16["Prop. I.16\nExterior angle > interior opposite"] + Prop18["Prop. I.18\nAngle opposite greater side greater"] + Prop19["Prop. I.19\nSide opposite greater angle greater"] + Prop20["Prop. I.20\nTriangle inequality"] + Prop22["Prop. I.22\nConstruct triangle from three lines"] + Prop23["Prop. I.23\nConstruct angle equal to given"] + Prop26["Prop. I.26\nAAS congruence"] + Prop27["Prop. I.27\nAlternate angles equal => parallel"] + Prop29["Prop. I.29\nParallel => alternate angles equal"] + Prop30["Prop. I.30\nTransitivity of parallel"] + Prop31["Prop. I.31\nDraw parallel through point"] + Prop33["Prop. I.33\nJoining ends of equal parallel lines"] + Prop34["Prop. I.34\nParallelogram properties"] + Prop35["Prop. I.35\nParallelograms same base equal"] + Prop36["Prop. I.36\nParallelograms equal bases equal"] + Prop37["Prop. I.37\nTriangles same base equal"] + Prop38["Prop. I.38\nTriangles equal bases equal"] + Prop41["Prop. I.41\nParallelogram = 2× triangle"] + Prop42["Prop. I.42\nConstruct parallelogram = triangle"] + Prop43["Prop. I.43\nComplements of parallelogram"] + Prop44["Prop. I.44\nApply parallelogram to line"] + Prop45["Prop. I.45\nConstruct parallelogram = rectilinear figure"] + Prop46["Prop. I.46\nConstruct square on line"] + Prop47["Prop. I.47\nPythagorean theorem"] + Prop48["Prop. I.48\nConverse Pythagorean"] + P1 --> Prop1 + P3 --> Prop1 + Prop1 --> Prop2 + P1 --> Prop2 + P2 --> Prop2 + P3 --> Prop2 + Prop2 --> Prop3 + P3 --> Prop3 + CN4 --> Prop4 + CN5 --> Prop4 + Prop3 --> Prop5 + Prop4 --> Prop5 + Prop5 --> Prop7 + Prop7 --> Prop8 + Prop1 --> Prop9 + Prop3 --> Prop9 + Prop8 --> Prop9 + Prop1 --> Prop10 + Prop4 --> Prop10 + Prop9 --> Prop10 + Prop1 --> Prop11 + Prop3 --> Prop11 + Prop8 --> Prop11 + Prop11 --> Prop13 + Prop13 --> Prop14 + Prop13 --> Prop15 + Prop3 --> Prop16 + Prop4 --> Prop16 + Prop10 --> Prop16 + Prop15 --> Prop16 + Prop3 --> Prop18 + Prop5 --> Prop18 + Prop16 --> Prop18 + Prop5 --> Prop19 + Prop18 --> Prop19 + Prop3 --> Prop20 + Prop5 --> Prop20 + Prop19 --> Prop20 + Prop3 --> Prop22 + Prop20 --> Prop22 + Prop8 --> Prop23 + Prop22 --> Prop23 + Prop3 --> Prop26 + Prop4 --> Prop26 + Prop16 --> Prop26 + Prop16 --> Prop27 + Prop13 --> Prop29 + Prop15 --> Prop29 + Prop27 --> Prop29 + P5 --> Prop29 + Prop29 --> Prop30 + Prop23 --> Prop31 + Prop27 --> Prop31 + Prop4 --> Prop33 + Prop27 --> Prop33 + Prop29 --> Prop33 + Prop4 --> Prop34 + Prop26 --> Prop34 + Prop29 --> Prop34 + Prop4 --> Prop35 + Prop29 --> Prop35 + Prop34 --> Prop35 + Prop33 --> Prop36 + Prop34 --> Prop36 + Prop35 --> Prop36 + Prop31 --> Prop37 + Prop34 --> Prop37 + Prop35 --> Prop37 + Prop31 --> Prop38 + Prop34 --> Prop38 + Prop36 --> Prop38 + Prop34 --> Prop41 + Prop37 --> Prop41 + Prop10 --> Prop42 + Prop23 --> Prop42 + Prop31 --> Prop42 + Prop38 --> Prop42 + Prop41 --> Prop42 + Prop34 --> Prop43 + Prop15 --> Prop44 + Prop29 --> Prop44 + Prop31 --> Prop44 + Prop42 --> Prop44 + Prop43 --> Prop44 + Prop14 --> Prop45 + Prop29 --> Prop45 + Prop30 --> Prop45 + Prop33 --> Prop45 + Prop34 --> Prop45 + Prop42 --> Prop45 + Prop44 --> Prop45 + Prop3 --> Prop46 + Prop11 --> Prop46 + Prop29 --> Prop46 + Prop31 --> Prop46 + Prop34 --> Prop46 + Prop4 --> Prop47 + Prop14 --> Prop47 + Prop31 --> Prop47 + Prop41 --> Prop47 + Prop46 --> Prop47 + Prop3 --> Prop48 + Prop8 --> Prop48 + Prop11 --> Prop48 + Prop47 --> Prop48 + classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b + classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class P1,P2,P3,P4,P5 postulate + class CN1,CN2,CN3,CN4,CN5 commonNotion + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop7,Prop8,Prop9,Prop10,Prop11,Prop13,Prop14,Prop15,Prop16,Prop18,Prop19,Prop20,Prop22,Prop23,Prop26,Prop27,Prop29,Prop30,Prop31,Prop33,Prop34,Prop35,Prop36,Prop37,Prop38,Prop41,Prop42,Prop43,Prop44,Prop45,Prop46,Prop47,Prop48 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-i.json b/data/euclid-elements-book-i.json new file mode 100644 index 0000000000000000000000000000000000000000..45d9a093b1e394b4c358067a2c00a1b649b601e4 --- /dev/null +++ b/data/euclid-elements-book-i.json @@ -0,0 +1,1167 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "euclid-elements-book-i", + "name": "Euclid's Elements, Book I", + "subject": "geometry", + "variant": "classical", + "description": "The 48 propositions of Book I with dependencies on postulates (P1–P5), common notions (CN1–CN5), and prior propositions. Source: David E. Joyce, Clark University.", + "structure": { + "books": 1, + "propositions": 48, + "foundationTypes": [ + "postulate", + "commonNotion" + ] + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book I Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book I", + "plane geometry", + "constructions", + "Pythagorean theorem" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book I", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI.html", + "notes": "Clark University; dependency table from Guide" + }, + { + "id": "euclid-heath", + "type": "primary", + "authors": "Heath, T.L.", + "title": "The Thirteen Books of Euclid's Elements", + "year": "1908", + "edition": "2nd", + "publisher": "Cambridge University Press", + "url": "https://archive.org/details/euclidheath00heatiala", + "notes": "Standard English translation" + } + ], + "nodes": [ + { + "id": "P1", + "type": "postulate", + "label": "Draw a straight line from any point to any point", + "shortLabel": "Post. 1", + "book": 1, + "number": 1, + "colorClass": "postulate" + }, + { + "id": "P2", + "type": "postulate", + "label": "Produce a finite straight line continuously in a straight line", + "shortLabel": "Post. 2", + "book": 1, + "number": 2, + "colorClass": "postulate" + }, + { + "id": "P3", + "type": "postulate", + "label": "Describe a circle with any center and radius", + "shortLabel": "Post. 3", + "book": 1, + "number": 3, + "colorClass": "postulate" + }, + { + "id": "P4", + "type": "postulate", + "label": "All right angles equal one another", + "shortLabel": "Post. 4", + "book": 1, + "number": 4, + "colorClass": "postulate" + }, + { + "id": "P5", + "type": "postulate", + "label": "Parallel postulate: if interior angles < two right, lines meet", + "shortLabel": "Post. 5", + "book": 1, + "number": 5, + "colorClass": "postulate" + }, + { + "id": "CN1", + "type": "commonNotion", + "label": "Things equal to the same thing are equal to each other", + "shortLabel": "CN 1", + "book": 1, + "number": 1, + "colorClass": "commonNotion" + }, + { + "id": "CN2", + "type": "commonNotion", + "label": "If equals are added to equals, the wholes are equal", + "shortLabel": "CN 2", + "book": 1, + "number": 2, + "colorClass": "commonNotion" + }, + { + "id": "CN3", + "type": "commonNotion", + "label": "If equals are subtracted from equals, the remainders are equal", + "shortLabel": "CN 3", + "book": 1, + "number": 3, + "colorClass": "commonNotion" + }, + { + "id": "CN4", + "type": "commonNotion", + "label": "Things coinciding with one another are equal", + "shortLabel": "CN 4", + "book": 1, + "number": 4, + "colorClass": "commonNotion" + }, + { + "id": "CN5", + "type": "commonNotion", + "label": "The whole is greater than the part", + "shortLabel": "CN 5", + "book": 1, + "number": 5, + "colorClass": "commonNotion" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "To construct an equilateral triangle on a given finite straight line", + "shortLabel": "Prop. I.1", + "short": "Equilateral triangle on given line", + "book": 1, + "number": 1, + "colorClass": "proposition" + }, + { + "id": "Prop2", + "type": "proposition", + "label": "To place a straight line equal to a given straight line with one end at a given point", + "shortLabel": "Prop. I.2", + "short": "Place line equal to given at point", + "book": 1, + "number": 2, + "colorClass": "proposition" + }, + { + "id": "Prop3", + "type": "proposition", + "label": "To cut off from the greater of two given unequal straight lines a straight line equal to the less", + "shortLabel": "Prop. I.3", + "short": "Cut off from greater segment equal to less", + "book": 1, + "number": 3, + "colorClass": "proposition" + }, + { + "id": "Prop4", + "type": "proposition", + "label": "If two triangles have two sides equal to two sides respectively, and the angles contained equal, then bases and remaining angles equal", + "shortLabel": "Prop. I.4", + "short": "SAS congruence", + "book": 1, + "number": 4, + "colorClass": "proposition" + }, + { + "id": "Prop5", + "type": "proposition", + "label": "In isosceles triangles the angles at the base equal one another", + "shortLabel": "Prop. I.5", + "short": "Base angles of isosceles equal", + "book": 1, + "number": 5, + "colorClass": "proposition" + }, + { + "id": "Prop6", + "type": "proposition", + "label": "If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another", + "shortLabel": "Prop. I.6", + "short": "Sides opposite equal angles equal", + "book": 1, + "number": 6, + "colorClass": "proposition" + }, + { + "id": "Prop7", + "type": "proposition", + "label": "Given two lines from ends of a line meeting at a point, no other such pair from same ends on same side", + "shortLabel": "Prop. I.7", + "short": "Uniqueness of triangle from ends", + "book": 1, + "number": 7, + "colorClass": "proposition" + }, + { + "id": "Prop8", + "type": "proposition", + "label": "If two triangles have two sides equal to two sides respectively, and the base equal to the base, then the angles contained are equal", + "shortLabel": "Prop. I.8", + "short": "SSS congruence", + "book": 1, + "number": 8, + "colorClass": "proposition" + }, + { + "id": "Prop9", + "type": "proposition", + "label": "To bisect a given rectilinear angle", + "shortLabel": "Prop. I.9", + "short": "Bisect angle", + "book": 1, + "number": 9, + "colorClass": "proposition" + }, + { + "id": "Prop10", + "type": "proposition", + "label": "To bisect a given finite straight line", + "shortLabel": "Prop. I.10", + "short": "Bisect line", + "book": 1, + "number": 10, + "colorClass": "proposition" + }, + { + "id": "Prop11", + "type": "proposition", + "label": "To draw a straight line at right angles to a given straight line from a given point on it", + "shortLabel": "Prop. I.11", + "short": "Perpendicular from point on line", + "book": 1, + "number": 11, + "colorClass": "proposition" + }, + { + "id": "Prop12", + "type": "proposition", + "label": "To draw a straight line perpendicular to a given infinite straight line from a given point not on it", + "shortLabel": "Prop. I.12", + "short": "Perpendicular from point not on line", + "book": 1, + "number": 12, + "colorClass": "proposition" + }, + { + "id": "Prop13", + "type": "proposition", + "label": "If a straight line stands on a straight line, it makes either two right angles or angles whose sum equals two right angles", + "shortLabel": "Prop. I.13", + "short": "Angles on line sum to two right", + "book": 1, + "number": 13, + "colorClass": "proposition" + }, + { + "id": "Prop14", + "type": "proposition", + "label": "If with any straight line, at a point, two lines not on same side make adjacent angles equal to two right, they are in a straight line", + "shortLabel": "Prop. I.14", + "short": "If angles sum to two right, straight line", + "book": 1, + "number": 14, + "colorClass": "proposition" + }, + { + "id": "Prop15", + "type": "proposition", + "label": "If two straight lines cut one another, they make the vertical angles equal to one another", + "shortLabel": "Prop. I.15", + "short": "Vertical angles equal", + "book": 1, + "number": 15, + "colorClass": "proposition" + }, + { + "id": "Prop16", + "type": "proposition", + "label": "In any triangle, if one side is produced, the exterior angle is greater than either interior opposite angle", + "shortLabel": "Prop. I.16", + "short": "Exterior angle > interior opposite", + "book": 1, + "number": 16, + "colorClass": "proposition" + }, + { + "id": "Prop17", + "type": "proposition", + "label": "In any triangle the sum of any two angles is less than two right angles", + "shortLabel": "Prop. I.17", + "short": "Sum of two angles < two right", + "book": 1, + "number": 17, + "colorClass": "proposition" + }, + { + "id": "Prop18", + "type": "proposition", + "label": "In any triangle the angle opposite the greater side is greater", + "shortLabel": "Prop. I.18", + "short": "Angle opposite greater side greater", + "book": 1, + "number": 18, + "colorClass": "proposition" + }, + { + "id": "Prop19", + "type": "proposition", + "label": "In any triangle the side opposite the greater angle is greater", + "shortLabel": "Prop. I.19", + "short": "Side opposite greater angle greater", + "book": 1, + "number": 19, + "colorClass": "proposition" + }, + { + "id": "Prop20", + "type": "proposition", + "label": "In any triangle the sum of any two sides is greater than the remaining one", + "shortLabel": "Prop. I.20", + "short": "Triangle inequality", + "book": 1, + "number": 20, + "colorClass": "proposition" + }, + { + "id": "Prop21", + "type": "proposition", + "label": "If from ends of one side two lines meet within the triangle, their sum < sum of other two sides", + "shortLabel": "Prop. I.21", + "short": "Lines from ends within triangle", + "book": 1, + "number": 21, + "colorClass": "proposition" + }, + { + "id": "Prop22", + "type": "proposition", + "label": "To construct a triangle out of three straight lines which equal three given straight lines", + "shortLabel": "Prop. I.22", + "short": "Construct triangle from three lines", + "book": 1, + "number": 22, + "colorClass": "proposition" + }, + { + "id": "Prop23", + "type": "proposition", + "label": "To construct a rectilinear angle equal to a given rectilinear angle on a given straight line", + "shortLabel": "Prop. I.23", + "short": "Construct angle equal to given", + "book": 1, + "number": 23, + "colorClass": "proposition" + }, + { + "id": "Prop24", + "type": "proposition", + "label": "If two triangles have two sides equal but one contained angle greater, the base is greater", + "shortLabel": "Prop. I.24", + "short": "SAS for greater angle => greater base", + "book": 1, + "number": 24, + "colorClass": "proposition" + }, + { + "id": "Prop25", + "type": "proposition", + "label": "If two triangles have two sides equal but base greater, the contained angle is greater", + "shortLabel": "Prop. I.25", + "short": "SAS for greater base => greater angle", + "book": 1, + "number": 25, + "colorClass": "proposition" + }, + { + "id": "Prop26", + "type": "proposition", + "label": "If two triangles have two angles equal and one side equal, the remaining sides and angle equal", + "shortLabel": "Prop. I.26", + "short": "AAS congruence", + "book": 1, + "number": 26, + "colorClass": "proposition" + }, + { + "id": "Prop27", + "type": "proposition", + "label": "If a line falling on two lines makes alternate angles equal, the lines are parallel", + "shortLabel": "Prop. I.27", + "short": "Alternate angles equal => parallel", + "book": 1, + "number": 27, + "colorClass": "proposition" + }, + { + "id": "Prop28", + "type": "proposition", + "label": "If exterior angle equals interior opposite, or interior same-side sum to two right, lines parallel", + "shortLabel": "Prop. I.28", + "short": "Exterior = interior opposite => parallel", + "book": 1, + "number": 28, + "colorClass": "proposition" + }, + { + "id": "Prop29", + "type": "proposition", + "label": "A line falling on parallel lines makes alternate angles equal, exterior = interior opposite", + "shortLabel": "Prop. I.29", + "short": "Parallel => alternate angles equal", + "book": 1, + "number": 29, + "colorClass": "proposition" + }, + { + "id": "Prop30", + "type": "proposition", + "label": "Straight lines parallel to the same straight line are also parallel to one another", + "shortLabel": "Prop. I.30", + "short": "Transitivity of parallel", + "book": 1, + "number": 30, + "colorClass": "proposition" + }, + { + "id": "Prop31", + "type": "proposition", + "label": "To draw a straight line through a given point parallel to a given straight line", + "shortLabel": "Prop. I.31", + "short": "Draw parallel through point", + "book": 1, + "number": 31, + "colorClass": "proposition" + }, + { + "id": "Prop32", + "type": "proposition", + "label": "In any triangle, exterior angle equals sum of two interior opposite; three angles = two right", + "shortLabel": "Prop. I.32", + "short": "Exterior angle = sum interior opposite", + "book": 1, + "number": 32, + "colorClass": "proposition" + }, + { + "id": "Prop33", + "type": "proposition", + "label": "Straight lines which join the ends of equal and parallel straight lines in same directions are equal and parallel", + "shortLabel": "Prop. I.33", + "short": "Joining ends of equal parallel lines", + "book": 1, + "number": 33, + "colorClass": "proposition" + }, + { + "id": "Prop34", + "type": "proposition", + "label": "In parallelogrammic areas the opposite sides and angles equal one another, diameter bisects", + "shortLabel": "Prop. I.34", + "short": "Parallelogram properties", + "book": 1, + "number": 34, + "colorClass": "proposition" + }, + { + "id": "Prop35", + "type": "proposition", + "label": "Parallelograms which are on the same base and in the same parallels equal one another", + "shortLabel": "Prop. I.35", + "short": "Parallelograms same base equal", + "book": 1, + "number": 35, + "colorClass": "proposition" + }, + { + "id": "Prop36", + "type": "proposition", + "label": "Parallelograms which are on equal bases and in the same parallels equal one another", + "shortLabel": "Prop. I.36", + "short": "Parallelograms equal bases equal", + "book": 1, + "number": 36, + "colorClass": "proposition" + }, + { + "id": "Prop37", + "type": "proposition", + "label": "Triangles which are on the same base and in the same parallels equal one another", + "shortLabel": "Prop. I.37", + "short": "Triangles same base equal", + "book": 1, + "number": 37, + "colorClass": "proposition" + }, + { + "id": "Prop38", + "type": "proposition", + "label": "Triangles which are on equal bases and in the same parallels equal one another", + "shortLabel": "Prop. I.38", + "short": "Triangles equal bases equal", + "book": 1, + "number": 38, + "colorClass": "proposition" + }, + { + "id": "Prop39", + "type": "proposition", + "label": "Equal triangles on same base and same side are in the same parallels", + "shortLabel": "Prop. I.39", + "short": "Equal triangles same base same side", + "book": 1, + "number": 39, + "colorClass": "proposition" + }, + { + "id": "Prop40", + "type": "proposition", + "label": "Equal triangles on equal bases and same side are in the same parallels", + "shortLabel": "Prop. I.40", + "short": "Equal triangles equal bases same side", + "book": 1, + "number": 40, + "colorClass": "proposition" + }, + { + "id": "Prop41", + "type": "proposition", + "label": "If a parallelogram has same base with triangle and same parallels, parallelogram is double the triangle", + "shortLabel": "Prop. I.41", + "short": "Parallelogram = 2× triangle", + "book": 1, + "number": 41, + "colorClass": "proposition" + }, + { + "id": "Prop42", + "type": "proposition", + "label": "To construct a parallelogram equal to a given triangle in a given rectilinear angle", + "shortLabel": "Prop. I.42", + "short": "Construct parallelogram = triangle", + "book": 1, + "number": 42, + "colorClass": "proposition" + }, + { + "id": "Prop43", + "type": "proposition", + "label": "In any parallelogram the complements of the parallelograms about the diameter equal one another", + "shortLabel": "Prop. I.43", + "short": "Complements of parallelogram", + "book": 1, + "number": 43, + "colorClass": "proposition" + }, + { + "id": "Prop44", + "type": "proposition", + "label": "To a given straight line in a given angle, to apply a parallelogram equal to a given triangle", + "shortLabel": "Prop. I.44", + "short": "Apply parallelogram to line", + "book": 1, + "number": 44, + "colorClass": "proposition" + }, + { + "id": "Prop45", + "type": "proposition", + "label": "To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle", + "shortLabel": "Prop. I.45", + "short": "Construct parallelogram = rectilinear figure", + "book": 1, + "number": 45, + "colorClass": "proposition" + }, + { + "id": "Prop46", + "type": "proposition", + "label": "To describe a square on a given straight line", + "shortLabel": "Prop. I.46", + "short": "Construct square on line", + "book": 1, + "number": 46, + "colorClass": "proposition" + }, + { + "id": "Prop47", + "type": "proposition", + "label": "In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle", + "shortLabel": "Prop. I.47", + "short": "Pythagorean theorem", + "book": 1, + "number": 47, + "colorClass": "proposition" + }, + { + "id": "Prop48", + "type": "proposition", + "label": "If in a triangle the square on one side equals the sum of squares on the other two, the angle contained by those sides is right", + "shortLabel": "Prop. I.48", + "short": "Converse Pythagorean", + "book": 1, + "number": 48, + "colorClass": "proposition" + } + ], + "edges": [ + { + "from": "P1", + "to": "Prop1" + }, + { + "from": "P3", + "to": "Prop1" + }, + { + "from": "Prop1", + "to": "Prop2" + }, + { + "from": "P1", + "to": "Prop2" + }, + { + "from": "P2", + "to": "Prop2" + }, + { + "from": "P3", + "to": "Prop2" + }, + { + "from": "Prop2", + "to": "Prop3" + }, + { + "from": "P3", + "to": "Prop3" + }, + { + "from": "CN4", + "to": "Prop4" + }, + { + "from": "CN5", + "to": "Prop4" + }, + { + "from": "Prop3", + "to": "Prop5" + }, + { + "from": "Prop4", + "to": "Prop5" + }, + { + "from": "Prop3", + "to": "Prop6" + }, + { + "from": "Prop4", + "to": "Prop6" + }, + { + "from": "Prop5", + "to": "Prop7" + }, + { + "from": "Prop7", + "to": "Prop8" + }, + { + "from": "Prop1", + "to": "Prop9" + }, + { + "from": "Prop3", + "to": "Prop9" + }, + { + "from": "Prop8", + "to": "Prop9" + }, + { + "from": "Prop1", + "to": "Prop10" + }, + { + "from": "Prop4", + "to": "Prop10" + }, + { + "from": "Prop9", + "to": "Prop10" + }, + { + "from": "Prop1", + "to": "Prop11" + }, + { + "from": "Prop3", + "to": "Prop11" + }, + { + "from": "Prop8", + "to": "Prop11" + }, + { + "from": "Prop8", + "to": "Prop12" + }, + { + "from": "Prop10", + "to": "Prop12" + }, + { + "from": "Prop11", + "to": "Prop13" + }, + { + "from": "Prop13", + "to": "Prop14" + }, + { + "from": "Prop13", + "to": "Prop15" + }, + { + "from": "Prop3", + "to": "Prop16" + }, + { + "from": "Prop4", + "to": "Prop16" + }, + { + "from": "Prop10", + "to": "Prop16" + }, + { + "from": "Prop15", + "to": "Prop16" + }, + { + "from": "Prop13", + "to": "Prop17" + }, + { + "from": "Prop16", + "to": "Prop17" + }, + { + "from": "Prop3", + "to": "Prop18" + }, + { + "from": "Prop5", + "to": "Prop18" + }, + { + "from": "Prop16", + "to": "Prop18" + }, + { + "from": "Prop5", + "to": "Prop19" + }, + { + "from": "Prop18", + "to": "Prop19" + }, + { + "from": "Prop3", + "to": "Prop20" + }, + { + "from": "Prop5", + "to": "Prop20" + }, + { + "from": "Prop19", + "to": "Prop20" + }, + { + "from": "Prop16", + "to": "Prop21" + }, + { + "from": "Prop20", + "to": "Prop21" + }, + { + "from": "Prop3", + "to": "Prop22" + }, + { + "from": "Prop20", + "to": "Prop22" + }, + { + "from": "Prop8", + "to": "Prop23" + }, + { + "from": "Prop22", + "to": "Prop23" + }, + { + "from": "Prop3", + "to": "Prop24" + }, + { + "from": "Prop4", + "to": "Prop24" + }, + { + "from": "Prop5", + "to": "Prop24" + }, + { + "from": "Prop19", + "to": "Prop24" + }, + { + "from": "Prop23", + "to": "Prop24" + }, + { + "from": "Prop4", + "to": "Prop25" + }, + { + "from": "Prop24", + "to": "Prop25" + }, + { + "from": "Prop3", + "to": "Prop26" + }, + { + "from": "Prop4", + "to": "Prop26" + }, + { + "from": "Prop16", + "to": "Prop26" + }, + { + "from": "Prop16", + "to": "Prop27" + }, + { + "from": "Prop13", + "to": "Prop28" + }, + { + "from": "Prop15", + "to": "Prop28" + }, + { + "from": "Prop27", + "to": "Prop28" + }, + { + "from": "Prop13", + "to": "Prop29" + }, + { + "from": "Prop15", + "to": "Prop29" + }, + { + "from": "Prop27", + "to": "Prop29" + }, + { + "from": "P5", + "to": "Prop29" + }, + { + "from": "Prop29", + "to": "Prop30" + }, + { + "from": "Prop23", + "to": "Prop31" + }, + { + "from": "Prop27", + "to": "Prop31" + }, + { + "from": "Prop13", + "to": "Prop32" + }, + { + "from": "Prop29", + "to": "Prop32" + }, + { + "from": "Prop31", + "to": "Prop32" + }, + { + "from": "Prop4", + "to": "Prop33" + }, + { + "from": "Prop27", + "to": "Prop33" + }, + { + "from": "Prop29", + "to": "Prop33" + }, + { + "from": "Prop4", + "to": "Prop34" + }, + { + "from": "Prop26", + "to": "Prop34" + }, + { + "from": "Prop29", + "to": "Prop34" + }, + { + "from": "Prop4", + "to": "Prop35" + }, + { + "from": "Prop29", + "to": "Prop35" + }, + { + "from": "Prop34", + "to": "Prop35" + }, + { + "from": "Prop33", + "to": "Prop36" + }, + { + "from": "Prop34", + "to": "Prop36" + }, + { + "from": "Prop35", + "to": "Prop36" + }, + { + "from": "Prop31", + "to": "Prop37" + }, + { + "from": "Prop34", + "to": "Prop37" + }, + { + "from": "Prop35", + "to": "Prop37" + }, + { + "from": "Prop31", + "to": "Prop38" + }, + { + "from": "Prop34", + "to": "Prop38" + }, + { + "from": "Prop36", + "to": "Prop38" + }, + { + "from": "Prop31", + "to": "Prop39" + }, + { + "from": "Prop37", + "to": "Prop39" + }, + { + "from": "Prop31", + "to": "Prop40" + }, + { + "from": "Prop38", + "to": "Prop40" + }, + { + "from": "Prop34", + "to": "Prop41" + }, + { + "from": "Prop37", + "to": "Prop41" + }, + { + "from": "Prop10", + "to": "Prop42" + }, + { + "from": "Prop23", + "to": "Prop42" + }, + { + "from": "Prop31", + "to": "Prop42" + }, + { + "from": "Prop38", + "to": "Prop42" + }, + { + "from": "Prop41", + "to": "Prop42" + }, + { + "from": "Prop34", + "to": "Prop43" + }, + { + "from": "Prop15", + "to": "Prop44" + }, + { + "from": "Prop29", + "to": "Prop44" + }, + { + "from": "Prop31", + "to": "Prop44" + }, + { + "from": "Prop42", + "to": "Prop44" + }, + { + "from": "Prop43", + "to": "Prop44" + }, + { + "from": "Prop14", + "to": "Prop45" + }, + { + "from": "Prop29", + "to": "Prop45" + }, + { + "from": "Prop30", + "to": "Prop45" + }, + { + "from": "Prop33", + "to": "Prop45" + }, + { + "from": "Prop34", + "to": "Prop45" + }, + { + "from": "Prop42", + "to": "Prop45" + }, + { + "from": "Prop44", + "to": "Prop45" + }, + { + "from": "Prop3", + "to": "Prop46" + }, + { + "from": "Prop11", + "to": "Prop46" + }, + { + "from": "Prop29", + "to": "Prop46" + }, + { + "from": "Prop31", + "to": "Prop46" + }, + { + "from": "Prop34", + "to": "Prop46" + }, + { + "from": "Prop4", + "to": "Prop47" + }, + { + "from": "Prop14", + "to": "Prop47" + }, + { + "from": "Prop31", + "to": "Prop47" + }, + { + "from": "Prop41", + "to": "Prop47" + }, + { + "from": "Prop46", + "to": "Prop47" + }, + { + "from": "Prop3", + "to": "Prop48" + }, + { + "from": "Prop8", + "to": "Prop48" + }, + { + "from": "Prop11", + "to": "Prop48" + }, + { + "from": "Prop47", + "to": "Prop48" + } + ], + "colorScheme": { + "postulate": { + "fill": "#e74c3c", + "stroke": "#c0392b" + }, + "commonNotion": { + "fill": "#9b59b6", + "stroke": "#8e44ad" + }, + "proposition": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/euclid-elements-book-i.mmd b/data/euclid-elements-book-i.mmd new file mode 100644 index 0000000000000000000000000000000000000000..51c423a56f6fe7ba6f2d88f7dcbee570974d4861 --- /dev/null +++ b/data/euclid-elements-book-i.mmd @@ -0,0 +1,195 @@ +graph TD + P1["Post. 1\nDraw a straight line from any po..."] + P2["Post. 2\nProduce a finite straight line c..."] + P3["Post. 3\nDescribe a circle with any cente..."] + P4["Post. 4\nAll right angles equal one another"] + P5["Post. 5\nParallel postulate: if interior ..."] + CN1["CN 1\nThings equal to the same thing a..."] + CN2["CN 2\nIf equals are added to equals, t..."] + CN3["CN 3\nIf equals are subtracted from eq..."] + CN4["CN 4\nThings coinciding with one anoth..."] + CN5["CN 5\nThe whole is greater than the part"] + Prop1["Prop. I.1\nEquilateral triangle on given line"] + Prop2["Prop. I.2\nPlace line equal to given at point"] + Prop3["Prop. I.3\nCut off from greater segment equal to less"] + Prop4["Prop. I.4\nSAS congruence"] + Prop5["Prop. I.5\nBase angles of isosceles equal"] + Prop6["Prop. I.6\nSides opposite equal angles equal"] + Prop7["Prop. I.7\nUniqueness of triangle from ends"] + Prop8["Prop. I.8\nSSS congruence"] + Prop9["Prop. I.9\nBisect angle"] + Prop10["Prop. I.10\nBisect line"] + Prop11["Prop. I.11\nPerpendicular from point on line"] + Prop12["Prop. I.12\nPerpendicular from point not on line"] + Prop13["Prop. I.13\nAngles on line sum to two right"] + Prop14["Prop. I.14\nIf angles sum to two right, straight line"] + Prop15["Prop. I.15\nVertical angles equal"] + Prop16["Prop. I.16\nExterior angle > interior opposite"] + Prop17["Prop. I.17\nSum of two angles < two right"] + Prop18["Prop. I.18\nAngle opposite greater side greater"] + Prop19["Prop. I.19\nSide opposite greater angle greater"] + Prop20["Prop. I.20\nTriangle inequality"] + Prop21["Prop. I.21\nLines from ends within triangle"] + Prop22["Prop. I.22\nConstruct triangle from three lines"] + Prop23["Prop. I.23\nConstruct angle equal to given"] + Prop24["Prop. I.24\nSAS for greater angle => greater base"] + Prop25["Prop. I.25\nSAS for greater base => greater angle"] + Prop26["Prop. I.26\nAAS congruence"] + Prop27["Prop. I.27\nAlternate angles equal => parallel"] + Prop28["Prop. I.28\nExterior = interior opposite => parallel"] + Prop29["Prop. I.29\nParallel => alternate angles equal"] + Prop30["Prop. I.30\nTransitivity of parallel"] + Prop31["Prop. I.31\nDraw parallel through point"] + Prop32["Prop. I.32\nExterior angle = sum interior opposite"] + Prop33["Prop. I.33\nJoining ends of equal parallel lines"] + Prop34["Prop. I.34\nParallelogram properties"] + Prop35["Prop. I.35\nParallelograms same base equal"] + Prop36["Prop. I.36\nParallelograms equal bases equal"] + Prop37["Prop. I.37\nTriangles same base equal"] + Prop38["Prop. I.38\nTriangles equal bases equal"] + Prop39["Prop. I.39\nEqual triangles same base same side"] + Prop40["Prop. I.40\nEqual triangles equal bases same side"] + Prop41["Prop. I.41\nParallelogram = 2× triangle"] + Prop42["Prop. I.42\nConstruct parallelogram = triangle"] + Prop43["Prop. I.43\nComplements of parallelogram"] + Prop44["Prop. I.44\nApply parallelogram to line"] + Prop45["Prop. I.45\nConstruct parallelogram = rectilinear figure"] + Prop46["Prop. I.46\nConstruct square on line"] + Prop47["Prop. I.47\nPythagorean theorem"] + Prop48["Prop. I.48\nConverse Pythagorean"] + P1 --> Prop1 + P3 --> Prop1 + Prop1 --> Prop2 + P1 --> Prop2 + P2 --> Prop2 + P3 --> Prop2 + Prop2 --> Prop3 + P3 --> Prop3 + CN4 --> Prop4 + CN5 --> Prop4 + Prop3 --> Prop5 + Prop4 --> Prop5 + Prop3 --> Prop6 + Prop4 --> Prop6 + Prop5 --> Prop7 + Prop7 --> Prop8 + Prop1 --> Prop9 + Prop3 --> Prop9 + Prop8 --> Prop9 + Prop1 --> Prop10 + Prop4 --> Prop10 + Prop9 --> Prop10 + Prop1 --> Prop11 + Prop3 --> Prop11 + Prop8 --> Prop11 + Prop8 --> Prop12 + Prop10 --> Prop12 + Prop11 --> Prop13 + Prop13 --> Prop14 + Prop13 --> Prop15 + Prop3 --> Prop16 + Prop4 --> Prop16 + Prop10 --> Prop16 + Prop15 --> Prop16 + Prop13 --> Prop17 + Prop16 --> Prop17 + Prop3 --> Prop18 + Prop5 --> Prop18 + Prop16 --> Prop18 + Prop5 --> Prop19 + Prop18 --> Prop19 + Prop3 --> Prop20 + Prop5 --> Prop20 + Prop19 --> Prop20 + Prop16 --> Prop21 + Prop20 --> Prop21 + Prop3 --> Prop22 + Prop20 --> Prop22 + Prop8 --> Prop23 + Prop22 --> Prop23 + Prop3 --> Prop24 + Prop4 --> Prop24 + Prop5 --> Prop24 + Prop19 --> Prop24 + Prop23 --> Prop24 + Prop4 --> Prop25 + Prop24 --> Prop25 + Prop3 --> Prop26 + Prop4 --> Prop26 + Prop16 --> Prop26 + Prop16 --> Prop27 + Prop13 --> Prop28 + Prop15 --> Prop28 + Prop27 --> Prop28 + Prop13 --> Prop29 + Prop15 --> Prop29 + Prop27 --> Prop29 + P5 --> Prop29 + Prop29 --> Prop30 + Prop23 --> Prop31 + Prop27 --> Prop31 + Prop13 --> Prop32 + Prop29 --> Prop32 + Prop31 --> Prop32 + Prop4 --> Prop33 + Prop27 --> Prop33 + Prop29 --> Prop33 + Prop4 --> Prop34 + Prop26 --> Prop34 + Prop29 --> Prop34 + Prop4 --> Prop35 + Prop29 --> Prop35 + Prop34 --> Prop35 + Prop33 --> Prop36 + Prop34 --> Prop36 + Prop35 --> Prop36 + Prop31 --> Prop37 + Prop34 --> Prop37 + Prop35 --> Prop37 + Prop31 --> Prop38 + Prop34 --> Prop38 + Prop36 --> Prop38 + Prop31 --> Prop39 + Prop37 --> Prop39 + Prop31 --> Prop40 + Prop38 --> Prop40 + Prop34 --> Prop41 + Prop37 --> Prop41 + Prop10 --> Prop42 + Prop23 --> Prop42 + Prop31 --> Prop42 + Prop38 --> Prop42 + Prop41 --> Prop42 + Prop34 --> Prop43 + Prop15 --> Prop44 + Prop29 --> Prop44 + Prop31 --> Prop44 + Prop42 --> Prop44 + Prop43 --> Prop44 + Prop14 --> Prop45 + Prop29 --> Prop45 + Prop30 --> Prop45 + Prop33 --> Prop45 + Prop34 --> Prop45 + Prop42 --> Prop45 + Prop44 --> Prop45 + Prop3 --> Prop46 + Prop11 --> Prop46 + Prop29 --> Prop46 + Prop31 --> Prop46 + Prop34 --> Prop46 + Prop4 --> Prop47 + Prop14 --> Prop47 + Prop31 --> Prop47 + Prop41 --> Prop47 + Prop46 --> Prop47 + Prop3 --> Prop48 + Prop8 --> Prop48 + Prop11 --> Prop48 + Prop47 --> Prop48 + classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b + classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class P1,P2,P3,P4,P5 postulate + class CN1,CN2,CN3,CN4,CN5 commonNotion + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14,Prop15,Prop16,Prop17,Prop18,Prop19,Prop20,Prop21,Prop22,Prop23,Prop24,Prop25,Prop26,Prop27,Prop28,Prop29,Prop30,Prop31,Prop32,Prop33,Prop34,Prop35,Prop36,Prop37,Prop38,Prop39,Prop40,Prop41,Prop42,Prop43,Prop44,Prop45,Prop46,Prop47,Prop48 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-ii.json b/data/euclid-elements-book-ii.json new file mode 100644 index 0000000000000000000000000000000000000000..34cf6714bb3744e0dad8d6389d25643b8a4c78eb --- /dev/null +++ b/data/euclid-elements-book-ii.json @@ -0,0 +1,365 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "euclid-elements-book-ii", + "name": "Euclid's Elements, Book II", + "subject": "geometry", + "variant": "classical", + "description": "The 14 propositions of Book II on geometric algebra (rectangles, squares). Props 1-10 are logically independent within Book II; 11-14 depend on 6, 4, 7, 5. All depend on Book I. Source: David E. Joyce, Clark University.", + "structure": { + "books": 2, + "propositions": 14, + "foundationTypes": [ + "definition" + ] + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book II Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book II", + "geometric algebra", + "rectangles", + "squares", + "golden section", + "quadrature" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book II", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookII/bookII.html", + "notes": "Clark University; dependency table from Logical structure" + }, + { + "id": "euclid-heath", + "type": "primary", + "authors": "Heath, T.L.", + "title": "The Thirteen Books of Euclid's Elements", + "year": "1908", + "edition": "2nd", + "publisher": "Cambridge University Press", + "url": "https://archive.org/details/euclidheath00heatiala", + "notes": "Standard English translation" + } + ], + "nodes": [ + { + "id": "BookI", + "type": "foundation", + "label": "Book I — Fundamentals of plane geometry", + "shortLabel": "Book I", + "short": "Foundation", + "book": 1, + "colorClass": "foundation" + }, + { + "id": "Def1", + "type": "definition", + "label": "Rectangle contained by two straight lines containing the right angle", + "shortLabel": "Def. II.1", + "book": 2, + "number": 1, + "colorClass": "definition" + }, + { + "id": "Def2", + "type": "definition", + "label": "Gnomon: parallelogram about diameter with two complements", + "shortLabel": "Def. II.2", + "book": 2, + "number": 2, + "colorClass": "definition" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "If one line is cut into segments, rectangle by whole equals sum of rectangles by each segment", + "shortLabel": "Prop. II.1", + "short": "Rectangle = sum of rectangles", + "book": 2, + "number": 1, + "colorClass": "proposition" + }, + { + "id": "Prop2", + "type": "proposition", + "label": "If a line is cut at random, sum of rectangles by whole and each segment equals square on whole", + "shortLabel": "Prop. II.2", + "short": "Sum of rectangles = square on whole", + "book": 2, + "number": 2, + "colorClass": "proposition" + }, + { + "id": "Prop3", + "type": "proposition", + "label": "If a line is cut at random, rectangle by whole and one segment equals rectangle by segments plus square on that segment", + "shortLabel": "Prop. II.3", + "short": "Rectangle = rectangle + square", + "book": 2, + "number": 3, + "colorClass": "proposition" + }, + { + "id": "Prop4", + "type": "proposition", + "label": "If a line is cut at random, square on whole equals squares on segments plus twice rectangle contained by segments", + "shortLabel": "Prop. II.4", + "short": "Square on whole = squares + 2×rectangle", + "book": 2, + "number": 4, + "colorClass": "proposition" + }, + { + "id": "Prop5", + "type": "proposition", + "label": "If a line cut into equal and unequal segments, rectangle by unequal segments plus square on difference equals square on half", + "shortLabel": "Prop. II.5", + "short": "Unequal segments: rectangle + square = square on half", + "book": 2, + "number": 5, + "colorClass": "proposition" + }, + { + "id": "Prop6", + "type": "proposition", + "label": "If a line bisected and added to, rectangle by whole-with-added and added plus square on half equals square on half-plus-added", + "shortLabel": "Prop. II.6", + "short": "Bisected + added: rectangle + square = square", + "book": 2, + "number": 6, + "colorClass": "proposition" + }, + { + "id": "Prop7", + "type": "proposition", + "label": "If a line cut at random, square on whole plus square on one segment equals twice rectangle by whole and segment plus square on remainder", + "shortLabel": "Prop. II.7", + "short": "Square on whole + square on segment", + "book": 2, + "number": 7, + "colorClass": "proposition" + }, + { + "id": "Prop8", + "type": "proposition", + "label": "If a line cut at random, four times rectangle by whole and one segment plus square on remainder equals square on whole-plus-segment", + "shortLabel": "Prop. II.8", + "short": "Four times rectangle + square", + "book": 2, + "number": 8, + "colorClass": "proposition" + }, + { + "id": "Prop9", + "type": "proposition", + "label": "If a line cut into equal and unequal segments, sum of squares on unequal segments is double sum of square on half and square on difference", + "shortLabel": "Prop. II.9", + "short": "Unequal segments: sum of squares", + "book": 2, + "number": 9, + "colorClass": "proposition" + }, + { + "id": "Prop10", + "type": "proposition", + "label": "If a line bisected and added to, square on whole-with-added plus square on added equals double sum of square on half and square on half-plus-added", + "shortLabel": "Prop. II.10", + "short": "Bisected + added: sum of squares", + "book": 2, + "number": 10, + "colorClass": "proposition" + }, + { + "id": "Prop11", + "type": "proposition", + "label": "To cut a given line so that rectangle by whole and one segment equals square on remaining segment", + "shortLabel": "Prop. II.11", + "short": "Cut line: rectangle = square (golden section)", + "book": 2, + "number": 11, + "colorClass": "proposition" + }, + { + "id": "Prop12", + "type": "proposition", + "label": "In obtuse-angled triangles, square on side opposite obtuse angle greater than sum of squares on sides containing it", + "shortLabel": "Prop. II.12", + "short": "Obtuse triangle: law of cosines", + "book": 2, + "number": 12, + "colorClass": "proposition" + }, + { + "id": "Prop13", + "type": "proposition", + "label": "In acute-angled triangles, square on side opposite acute angle less than sum of squares on sides containing it", + "shortLabel": "Prop. II.13", + "short": "Acute triangle: law of cosines", + "book": 2, + "number": 13, + "colorClass": "proposition" + }, + { + "id": "Prop14", + "type": "proposition", + "label": "To construct a square equal to a given rectilinear figure", + "shortLabel": "Prop. II.14", + "short": "Construct square = rectilinear figure", + "book": 2, + "number": 14, + "colorClass": "proposition" + } + ], + "edges": [ + { + "from": "BookI", + "to": "Prop1" + }, + { + "from": "Def1", + "to": "Prop1" + }, + { + "from": "BookI", + "to": "Prop2" + }, + { + "from": "Def1", + "to": "Prop2" + }, + { + "from": "BookI", + "to": "Prop3" + }, + { + "from": "Def1", + "to": "Prop3" + }, + { + "from": "BookI", + "to": "Prop4" + }, + { + "from": "Def1", + "to": "Prop4" + }, + { + "from": "BookI", + "to": "Prop5" + }, + { + "from": "Def1", + "to": "Prop5" + }, + { + "from": "Def2", + "to": "Prop5" + }, + { + "from": "BookI", + "to": "Prop6" + }, + { + "from": "Def1", + "to": "Prop6" + }, + { + "from": "Def2", + "to": "Prop6" + }, + { + "from": "BookI", + "to": "Prop7" + }, + { + "from": "Def1", + "to": "Prop7" + }, + { + "from": "BookI", + "to": "Prop8" + }, + { + "from": "Def1", + "to": "Prop8" + }, + { + "from": "BookI", + "to": "Prop9" + }, + { + "from": "Def1", + "to": "Prop9" + }, + { + "from": "BookI", + "to": "Prop10" + }, + { + "from": "Def1", + "to": "Prop10" + }, + { + "from": "BookI", + "to": "Prop11" + }, + { + "from": "Prop6", + "to": "Prop11" + }, + { + "from": "BookI", + "to": "Prop12" + }, + { + "from": "Prop4", + "to": "Prop12" + }, + { + "from": "BookI", + "to": "Prop13" + }, + { + "from": "Prop7", + "to": "Prop13" + }, + { + "from": "BookI", + "to": "Prop14" + }, + { + "from": "Prop5", + "to": "Prop14" + } + ], + "colorScheme": { + "foundation": { + "fill": "#95a5a6", + "stroke": "#7f8c8d" + }, + "definition": { + "fill": "#3498db", + "stroke": "#2980b9" + }, + "proposition": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/euclid-elements-book-ii.mmd b/data/euclid-elements-book-ii.mmd new file mode 100644 index 0000000000000000000000000000000000000000..500bc6377f72a880912a642808ab6120a4584e78 --- /dev/null +++ b/data/euclid-elements-book-ii.mmd @@ -0,0 +1,54 @@ +graph TD + BookI["Book I\nFoundation"] + Def1["Def. II.1\nRectangle contained by two strai..."] + Def2["Def. II.2\nGnomon: parallelogram about diam..."] + Prop1["Prop. II.1\nRectangle = sum of rectangles"] + Prop2["Prop. II.2\nSum of rectangles = square on whole"] + Prop3["Prop. II.3\nRectangle = rectangle + square"] + Prop4["Prop. II.4\nSquare on whole = squares + 2×rectangle"] + Prop5["Prop. II.5\nUnequal segments: rectangle + square = square on half"] + Prop6["Prop. II.6\nBisected + added: rectangle + square = square"] + Prop7["Prop. II.7\nSquare on whole + square on segment"] + Prop8["Prop. II.8\nFour times rectangle + square"] + Prop9["Prop. II.9\nUnequal segments: sum of squares"] + Prop10["Prop. II.10\nBisected + added: sum of squares"] + Prop11["Prop. II.11\nCut line: rectangle = square (golden section)"] + Prop12["Prop. II.12\nObtuse triangle: law of cosines"] + Prop13["Prop. II.13\nAcute triangle: law of cosines"] + Prop14["Prop. II.14\nConstruct square = rectilinear figure"] + BookI --> Prop1 + Def1 --> Prop1 + BookI --> Prop2 + Def1 --> Prop2 + BookI --> Prop3 + Def1 --> Prop3 + BookI --> Prop4 + Def1 --> Prop4 + BookI --> Prop5 + Def1 --> Prop5 + Def2 --> Prop5 + BookI --> Prop6 + Def1 --> Prop6 + Def2 --> Prop6 + BookI --> Prop7 + Def1 --> Prop7 + BookI --> Prop8 + Def1 --> Prop8 + BookI --> Prop9 + Def1 --> Prop9 + BookI --> Prop10 + Def1 --> Prop10 + BookI --> Prop11 + Prop6 --> Prop11 + BookI --> Prop12 + Prop4 --> Prop12 + BookI --> Prop13 + Prop7 --> Prop13 + BookI --> Prop14 + Prop5 --> Prop14 + classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085 + class BookI foundation + class Def1,Def2 definition + class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14 proposition \ No newline at end of file diff --git a/data/euclid-elements-book-iii.json b/data/euclid-elements-book-iii.json new file mode 100644 index 0000000000000000000000000000000000000000..de13968cebbb2331de37966710bd826c4b547ba7 --- /dev/null +++ b/data/euclid-elements-book-iii.json @@ -0,0 +1,885 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "euclid-elements-book-iii", + "name": "Euclid's Elements, Book III", + "subject": "geometry", + "variant": "classical", + "description": "Theory of circles: 11 definitions, 37 propositions. All depend on Book I. III.35 uses II.5. Source: David E. Joyce.", + "structure": { + "books": 3, + "definitions": 11, + "propositions": 37, + "foundationTypes": [ + "definition", + "foundation" + ] + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book III Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book III", + "circles", + "chords", + "tangents" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book III", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/bookIII.html", + "notes": "Clark University" + } + ], + "nodes": [ + { + "id": "BookI", + "type": "foundation", + "label": "Book I — Fundamentals of plane geometry", + "shortLabel": "Book I", + "short": "Foundation", + "book": 1, + "colorClass": "foundation" + }, + { + "id": "PropII5", + "type": "foundation", + "label": "Prop. II.5 — Rectangle + square = square on half", + "shortLabel": "Prop. II.5", + "short": "From Book II", + "book": 2, + "colorClass": "foundation" + }, + { + "id": "Def1", + "type": "definition", + "label": "Equal circles are those with equal radii", + "shortLabel": "Def. III.1", + "short": "Equal circles", + "book": 3, + "number": 1, + "colorClass": "definition" + }, + { + "id": "Def2", + "type": "definition", + "label": "A straight line touches a circle if it meets but does not cut it", + "shortLabel": "Def. III.2", + "short": "Tangent", + "book": 3, + "number": 2, + "colorClass": "definition" + }, + { + "id": "Def3", + "type": "definition", + "label": "Circles touch one another if they meet but do not cut", + "shortLabel": "Def. III.3", + "short": "Circles touching", + "book": 3, + "number": 3, + "colorClass": "definition" + }, + { + "id": "Def4", + "type": "definition", + "label": "Lines equally distant from center when perpendiculars from center equal", + "shortLabel": "Def. III.4", + "short": "Equally distant from center", + "book": 3, + "number": 4, + "colorClass": "definition" + }, + { + "id": "Def5", + "type": "definition", + "label": "Greater distance when greater perpendicular falls", + "shortLabel": "Def. III.5", + "short": "Greater distance", + "book": 3, + "number": 5, + "colorClass": "definition" + }, + { + "id": "Def6", + "type": "definition", + "label": "Segment of circle: figure contained by straight line and circumference", + "shortLabel": "Def. III.6", + "short": "Segment of circle", + "book": 3, + "number": 6, + "colorClass": "definition" + }, + { + "id": "Def7", + "type": "definition", + "label": "Angle of segment: contained by straight line and circumference", + "shortLabel": "Def. III.7", + "short": "Angle of segment", + "book": 3, + "number": 7, + "colorClass": "definition" + }, + { + "id": "Def8", + "type": "definition", + "label": "Angle in segment: contained by straight lines joining circumference", + "shortLabel": "Def. III.8", + "short": "Angle in segment", + "book": 3, + "number": 8, + "colorClass": "definition" + }, + { + "id": "Def9", + "type": "definition", + "label": "Angle stands on circumference when lines cut off that circumference", + "shortLabel": "Def. III.9", + "short": "Angle stands on circumference", + "book": 3, + "number": 9, + "colorClass": "definition" + }, + { + "id": "Def10", + "type": "definition", + "label": "Sector: figure contained by two radii and circumference between them", + "shortLabel": "Def. III.10", + "short": "Sector", + "book": 3, + "number": 10, + "colorClass": "definition" + }, + { + "id": "Def11", + "type": "definition", + "label": "Similar segments are those which admit equal angles", + "shortLabel": "Def. III.11", + "short": "Similar segments", + "book": 3, + "number": 11, + "colorClass": "definition" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "To find the center of a given circle", + "shortLabel": "Prop. III.1", + "short": "Find center of circle", + "book": 3, + "number": 1, + "colorClass": "proposition" + }, + { + "id": "Prop2", + "type": "proposition", + "label": "Straight line joining two points on circumference falls within circle", + "shortLabel": "Prop. III.2", + "short": "Chord falls within circle", + "book": 3, + "number": 2, + "colorClass": "proposition" + }, + { + "id": "Prop3", + "type": "proposition", + "label": "If diameter bisects chord not through center, it cuts at right angles", + "shortLabel": "Prop. III.3", + "short": "Diameter bisects chord at right angles", + "book": 3, + "number": 3, + "colorClass": "proposition" + }, + { + "id": "Prop4", + "type": "proposition", + "label": "Two non-diameters cutting one another do not bisect", + "shortLabel": "Prop. III.4", + "short": "Non-diameters do not bisect", + "book": 3, + "number": 4, + "colorClass": "proposition" + }, + { + "id": "Prop5", + "type": "proposition", + "label": "If two circles cut one another, they do not have same center", + "shortLabel": "Prop. III.5", + "short": "Cutting circles do not share center", + "book": 3, + "number": 5, + "colorClass": "proposition" + }, + { + "id": "Prop6", + "type": "proposition", + "label": "If two circles touch, they do not have same center", + "shortLabel": "Prop. III.6", + "short": "Touching circles do not share center", + "book": 3, + "number": 6, + "colorClass": "proposition" + }, + { + "id": "Prop7", + "type": "proposition", + "label": "From point on diameter: greatest through center, least is remainder", + "shortLabel": "Prop. III.7", + "short": "Greatest/shortest from point on diameter", + "book": 3, + "number": 7, + "colorClass": "proposition" + }, + { + "id": "Prop8", + "type": "proposition", + "label": "From point outside: through center greatest; between point and diameter least", + "shortLabel": "Prop. III.8", + "short": "Lines from point outside circle", + "book": 3, + "number": 8, + "colorClass": "proposition" + }, + { + "id": "Prop9", + "type": "proposition", + "label": "If more than two equal lines fall from point on circle, point is center", + "shortLabel": "Prop. III.9", + "short": "Three equal lines imply center", + "book": 3, + "number": 9, + "colorClass": "proposition" + }, + { + "id": "Prop10", + "type": "proposition", + "label": "A circle does not cut another at more than two points", + "shortLabel": "Prop. III.10", + "short": "Circles cut at most two points", + "book": 3, + "number": 10, + "colorClass": "proposition" + }, + { + "id": "Prop11", + "type": "proposition", + "label": "Line joining centers of internally touching circles passes through contact", + "shortLabel": "Prop. III.11", + "short": "Internally touching circles", + "book": 3, + "number": 11, + "colorClass": "proposition" + }, + { + "id": "Prop12", + "type": "proposition", + "label": "Line joining centers of externally touching circles passes through contact", + "shortLabel": "Prop. III.12", + "short": "Externally touching circles", + "book": 3, + "number": 12, + "colorClass": "proposition" + }, + { + "id": "Prop13", + "type": "proposition", + "label": "Circle does not touch another at more than one point", + "shortLabel": "Prop. III.13", + "short": "Circles touch at most one point", + "book": 3, + "number": 13, + "colorClass": "proposition" + }, + { + "id": "Prop14", + "type": "proposition", + "label": "Equal chords equally distant from center, and conversely", + "shortLabel": "Prop. III.14", + "short": "Equal chords equally distant", + "book": 3, + "number": 14, + "colorClass": "proposition" + }, + { + "id": "Prop15", + "type": "proposition", + "label": "Diameter greatest; nearer to center greater than more remote", + "shortLabel": "Prop. III.15", + "short": "Diameter greatest", + "book": 3, + "number": 15, + "colorClass": "proposition" + }, + { + "id": "Prop16", + "type": "proposition", + "label": "Perpendicular at end of diameter falls outside; horn angle", + "shortLabel": "Prop. III.16", + "short": "Tangent at end of diameter", + "book": 3, + "number": 16, + "colorClass": "proposition" + }, + { + "id": "Prop17", + "type": "proposition", + "label": "From given point to draw straight line touching given circle", + "shortLabel": "Prop. III.17", + "short": "Draw tangent from point", + "book": 3, + "number": 17, + "colorClass": "proposition" + }, + { + "id": "Prop18", + "type": "proposition", + "label": "Radius to point of contact perpendicular to tangent", + "shortLabel": "Prop. III.18", + "short": "Radius to tangent perpendicular", + "book": 3, + "number": 18, + "colorClass": "proposition" + }, + { + "id": "Prop19", + "type": "proposition", + "label": "Perpendicular from contact to tangent passes through center", + "shortLabel": "Prop. III.19", + "short": "Perpendicular from contact to center", + "book": 3, + "number": 19, + "colorClass": "proposition" + }, + { + "id": "Prop20", + "type": "proposition", + "label": "Angle at center double angle at circumference on same base", + "shortLabel": "Prop. III.20", + "short": "Angle at center double angle at circumference", + "book": 3, + "number": 20, + "colorClass": "proposition" + }, + { + "id": "Prop21", + "type": "proposition", + "label": "In a circle angles in same segment equal one another", + "shortLabel": "Prop. III.21", + "short": "Angles in same segment equal", + "book": 3, + "number": 21, + "colorClass": "proposition" + }, + { + "id": "Prop22", + "type": "proposition", + "label": "Sum of opposite angles of cyclic quadrilateral equals two right angles", + "shortLabel": "Prop. III.22", + "short": "Opposite angles of cyclic quadrilateral", + "book": 3, + "number": 22, + "colorClass": "proposition" + }, + { + "id": "Prop23", + "type": "proposition", + "label": "On same line cannot construct two similar unequal segments on same side", + "shortLabel": "Prop. III.23", + "short": "Same line, two similar unequal segments", + "book": 3, + "number": 23, + "colorClass": "proposition" + }, + { + "id": "Prop24", + "type": "proposition", + "label": "Similar segments on equal straight lines equal one another", + "shortLabel": "Prop. III.24", + "short": "Similar segments on equal lines equal", + "book": 3, + "number": 24, + "colorClass": "proposition" + }, + { + "id": "Prop25", + "type": "proposition", + "label": "Given segment of circle, describe complete circle", + "shortLabel": "Prop. III.25", + "short": "Complete circle from segment", + "book": 3, + "number": 25, + "colorClass": "proposition" + }, + { + "id": "Prop26", + "type": "proposition", + "label": "In equal circles equal angles stand on equal circumferences", + "shortLabel": "Prop. III.26", + "short": "Equal angles stand on equal arcs", + "book": 3, + "number": 26, + "colorClass": "proposition" + }, + { + "id": "Prop27", + "type": "proposition", + "label": "In equal circles angles on equal circumferences equal one another", + "shortLabel": "Prop. III.27", + "short": "Equal arcs imply equal angles", + "book": 3, + "number": 27, + "colorClass": "proposition" + }, + { + "id": "Prop28", + "type": "proposition", + "label": "In equal circles equal chords cut off equal circumferences", + "shortLabel": "Prop. III.28", + "short": "Equal chords cut off equal arcs", + "book": 3, + "number": 28, + "colorClass": "proposition" + }, + { + "id": "Prop29", + "type": "proposition", + "label": "In equal circles chords cutting equal circumferences are equal", + "shortLabel": "Prop. III.29", + "short": "Equal arcs imply equal chords", + "book": 3, + "number": 29, + "colorClass": "proposition" + }, + { + "id": "Prop30", + "type": "proposition", + "label": "To bisect a given circumference", + "shortLabel": "Prop. III.30", + "short": "Bisect given circumference", + "book": 3, + "number": 30, + "colorClass": "proposition" + }, + { + "id": "Prop31", + "type": "proposition", + "label": "Angle in semicircle right; in greater segment less; in less greater", + "shortLabel": "Prop. III.31", + "short": "Angle in semicircle is right", + "book": 3, + "number": 31, + "colorClass": "proposition" + }, + { + "id": "Prop32", + "type": "proposition", + "label": "Angle with tangent equals angle in alternate segment", + "shortLabel": "Prop. III.32", + "short": "Tangent-chord angle equals alternate segment", + "book": 3, + "number": 32, + "colorClass": "proposition" + }, + { + "id": "Prop33", + "type": "proposition", + "label": "On given line describe segment admitting angle equal to given", + "shortLabel": "Prop. III.33", + "short": "Segment admitting given angle", + "book": 3, + "number": 33, + "colorClass": "proposition" + }, + { + "id": "Prop34", + "type": "proposition", + "label": "From given circle cut off segment admitting given angle", + "shortLabel": "Prop. III.34", + "short": "Cut off segment admitting angle", + "book": 3, + "number": 34, + "colorClass": "proposition" + }, + { + "id": "Prop35", + "type": "proposition", + "label": "If chords cut one another, rectangle by segments of one equals other", + "shortLabel": "Prop. 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Does not depend on previous books. Source: David E. Joyce.", + "structure": { + "books": 5, + "definitions": 18, + "propositions": 25, + "foundationTypes": [ + "definition" + ] + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book V Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book V", + "proportion", + "ratio", + "Eudoxus" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book V", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookV/bookV.html", + "notes": "Clark University; Logical structure" + } + ], + "nodes": [ + { + "id": "Def1", + "type": "definition", + "label": "A magnitude is a part of a magnitude when it measures it", + "shortLabel": "Def. V.1", + "short": "Part", + "book": 5, + "number": 1, + "colorClass": "definition" + }, + { + "id": "Def2", + "type": "definition", + "label": "The greater is a multiple of the less when it is measured by the less", + "shortLabel": "Def. 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Depends on Book VII. Source: David E. Joyce.", + "structure": { + "books": 8, + "propositions": 27, + "foundationTypes": [ + "foundation" + ] + } + }, + "metadata": { + "created": "2026-03-18", + "lastUpdated": "2026-03-18", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book VIII Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book VIII", + "continued proportion", + "plane", + "solid" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book VIII", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookVIII/bookVIII.html", + "notes": "Clark University" + } + ], + "nodes": [ + { + "id": "BookVII", + "type": "foundation", + "label": "Book VII — Number theory", + "shortLabel": "Book VII", + "short": "Foundation", + "book": 7, + "colorClass": "foundation" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "Continued proportion, extremes relatively prime: least in ratio", + "shortLabel": "Prop. 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VIII.26", + "short": "Similar plane: square ratio", + "book": 8, + "number": 26, + "colorClass": "proposition" + }, + { + "id": "Prop27", + "type": "proposition", + "label": "Similar solid numbers have ratio of cube to cube", + "shortLabel": "Prop. 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Depends on Books I, V, VI. Source: David E. Joyce.", + "structure": { + "books": 10, + "definitions": 16, + "propositions": 115, + "foundationTypes": [ + "foundation" + ] + } + }, + "metadata": { + "created": "2026-03-18", + "lastUpdated": "2026-03-18", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book X Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book X", + "incommensurable", + "binomial", + "apotome", + "medial" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book X", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookX/bookX.html", + "notes": "Clark University" + } + ], + "nodes": [ + { + "id": "BookI", + "type": "foundation", + "label": "Book I — Plane geometry", + "shortLabel": "Book I", + "short": "Foundation", + "book": 1, + "colorClass": "foundation" + }, + { + "id": "BookV", + "type": "foundation", + "label": "Book V — Proportions", + "shortLabel": "Book V", + "short": "Foundation", + "book": 5, + "colorClass": "foundation" + }, + { + "id": "BookVI", + "type": "foundation", + "label": "Book VI — Similar figures", + "shortLabel": "Book VI", + "short": "Foundation", + "book": 6, + "colorClass": "foundation" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "Two unequal magnitudes: subtract more than half repeatedly; remainder less than lesser", + "shortLabel": "Prop. X.1", + "short": "Antenaresis for magnitudes", + "book": 10, + "number": 1, + "colorClass": "proposition" + }, + { + "id": "Prop2", + "type": "proposition", + "label": "If less subtracted from greater repeatedly and remainder never measures prior: incommensurable", + "shortLabel": "Prop. X.2", + "short": "Incommensurable criterion", + "book": 10, + "number": 2, + "colorClass": "proposition" + }, + { + "id": "Prop3", + "type": "proposition", + "label": "To find greatest common measure of two commensurable magnitudes", + "shortLabel": "Prop. X.3", + "short": "GCM of two commensurable", + "book": 10, + "number": 3, + "colorClass": "proposition" + }, + { + "id": "Prop4", + "type": "proposition", + "label": "To find greatest common measure of three commensurable magnitudes", + "shortLabel": "Prop. 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X.10", + "short": "Find incommensurable lines", + "book": 10, + "number": 10, + "colorClass": "proposition" + }, + { + "id": "Prop11", + "type": "proposition", + "label": "Four proportional: first commensurable with second iff third with fourth", + "shortLabel": "Prop. X.11", + "short": "Proportion preserves commensurability", + "book": 10, + "number": 11, + "colorClass": "proposition" + }, + { + "id": "Prop12", + "type": "proposition", + "label": "Magnitudes commensurable with same magnitude are commensurable", + "shortLabel": "Prop. X.12", + "short": "Commensurable with same", + "book": 10, + "number": 12, + "colorClass": "proposition" + }, + { + "id": "Prop13", + "type": "proposition", + "label": "If two commensurable, one incommensurable with third, so is the other", + "shortLabel": "Prop. 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X.16", + "short": "Incommensurable sum", + "book": 10, + "number": 16, + "colorClass": "proposition" + }, + { + "id": "Prop17", + "type": "proposition", + "label": "Applied parallelogram falling short by square: parts commensurable iff square difference commensurable", + "shortLabel": "Prop. X.17", + "short": "Parallelogram falling short", + "book": 10, + "number": 17, + "colorClass": "proposition" + }, + { + "id": "Prop18", + "type": "proposition", + "label": "Applied parallelogram: parts incommensurable iff square difference incommensurable", + "shortLabel": "Prop. X.18", + "short": "Parallelogram: incommensurable parts", + "book": 10, + "number": 18, + "colorClass": "proposition" + }, + { + "id": "Prop19", + "type": "proposition", + "label": "Rectangle by rational lines commensurable in length is rational", + "shortLabel": "Prop. X.19", + "short": "Rational rectangle from rational", + "book": 10, + "number": 19, + "colorClass": "proposition" + }, + { + "id": "Prop20", + "type": "proposition", + "label": "Rational area applied to rational line: breadth rational and commensurable", + "shortLabel": "Prop. X.20", + "short": "Rational area on rational", + "book": 10, + "number": 20, + "colorClass": "proposition" + }, + { + "id": "Prop21", + "type": "proposition", + "label": "Rectangle by rational in square only is irrational; side called medial", + "shortLabel": "Prop. X.21", + "short": "Medial: rational in square only", + "book": 10, + "number": 21, + "colorClass": "proposition" + }, + { + "id": "Prop22", + "type": "proposition", + "label": "Square on medial applied to rational: breadth rational, incommensurable in length", + "shortLabel": "Prop. 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X.29", + "short": "Find rational in square only, commensurable diff", + "book": 10, + "number": 29, + "colorClass": "proposition" + }, + { + "id": "Prop30", + "type": "proposition", + "label": "To find two rational in square only: square diff incommensurable with greater", + "shortLabel": "Prop. X.30", + "short": "Find rational in square only, incommensurable diff", + "book": 10, + "number": 30, + "colorClass": "proposition" + }, + { + "id": "Prop31", + "type": "proposition", + "label": "To find two medial in square only, rational rect: diff commensurable with greater", + "shortLabel": "Prop. X.31", + "short": "Find medial, rational rect, commensurable diff", + "book": 10, + "number": 31, + "colorClass": "proposition" + }, + { + "id": "Prop32", + "type": "proposition", + "label": "To find two medial in square only, medial rect: diff commensurable with greater", + "shortLabel": "Prop. X.32", + "short": "Find medial, medial rect, commensurable diff", + "book": 10, + "number": 32, + "colorClass": "proposition" + }, + { + "id": "Prop33", + "type": "proposition", + "label": "To find two incommensurable in square: sum of squares rational, rectangle medial", + "shortLabel": "Prop. X.33", + "short": "Find incommensurable: rational sum, medial rect", + "book": 10, + "number": 33, + "colorClass": "proposition" + }, + { + "id": "Prop34", + "type": "proposition", + "label": "To find two incommensurable in square: sum medial, rectangle rational", + "shortLabel": "Prop. X.34", + "short": "Find incommensurable: medial sum, rational rect", + "book": 10, + "number": 34, + "colorClass": "proposition" + }, + { + "id": "Prop35", + "type": "proposition", + "label": "To find two incommensurable in square: sum and rect medial, incommensurable", + "shortLabel": "Prop. X.35", + "short": "Find incommensurable: both medial", + "book": 10, + "number": 35, + "colorClass": "proposition" + }, + { + "id": "Prop36", + "type": "proposition", + "label": "Two rational in square only added: whole irrational, called binomial", + "shortLabel": "Prop. X.36", + "short": "Binomial defined", + "book": 10, + "number": 36, + "colorClass": "proposition" + }, + { + "id": "Prop37", + "type": "proposition", + "label": "Two medial in square only, rational rect added: first bimedial", + "shortLabel": "Prop. X.37", + "short": "First bimedial defined", + "book": 10, + "number": 37, + "colorClass": "proposition" + }, + { + "id": "Prop38", + "type": "proposition", + "label": "Two medial in square only, medial rect added: second bimedial", + "shortLabel": "Prop. X.38", + "short": "Second bimedial defined", + "book": 10, + "number": 38, + "colorClass": "proposition" + }, + { + "id": "Prop39", + "type": "proposition", + "label": "Two incommensurable in square, rational sum, medial rect added: major", + "shortLabel": "Prop. X.39", + "short": "Major defined", + "book": 10, + "number": 39, + "colorClass": "proposition" + }, + { + "id": "Prop40", + "type": "proposition", + "label": "Two incommensurable in square, medial sum, rational rect added: side of rational plus medial", + "shortLabel": "Prop. X.40", + "short": "Side of rational plus medial", + "book": 10, + "number": 40, + "colorClass": "proposition" + }, + { + "id": "Prop41", + "type": "proposition", + "label": "Two incommensurable in square, both medial added: side of sum of two medial", + "shortLabel": "Prop. X.41", + "short": "Side of sum of two medial", + "book": 10, + "number": 41, + "colorClass": "proposition" + }, + { + "id": "Prop42", + "type": "proposition", + "label": "Binomial divided into terms at one point only", + "shortLabel": "Prop. X.42", + "short": "Binomial: unique division", + "book": 10, + "number": 42, + "colorClass": "proposition" + }, + { + "id": "Prop43", + "type": "proposition", + "label": "First bimedial divided at one point only", + "shortLabel": "Prop. X.43", + "short": "First bimedial: unique division", + "book": 10, + "number": 43, + "colorClass": "proposition" + }, + { + "id": "Prop44", + "type": "proposition", + "label": "Second bimedial divided at one point only", + "shortLabel": "Prop. X.44", + "short": "Second bimedial: unique division", + "book": 10, + "number": 44, + "colorClass": "proposition" + }, + { + "id": "Prop45", + "type": "proposition", + "label": "Major divided at one point only", + "shortLabel": "Prop. X.45", + "short": "Major: unique division", + "book": 10, + "number": 45, + "colorClass": "proposition" + }, + { + "id": "Prop46", + "type": "proposition", + "label": "Side of rational plus medial divided at one point only", + "shortLabel": "Prop. X.46", + "short": "Side rational+medial: unique division", + "book": 10, + "number": 46, + "colorClass": "proposition" + }, + { + "id": "Prop47", + "type": "proposition", + "label": "Side of sum of two medial divided at one point only", + "shortLabel": "Prop. X.47", + "short": "Side two medial: unique division", + "book": 10, + "number": 47, + "colorClass": "proposition" + }, + { + "id": "Prop48", + "type": "proposition", + "label": "To find the first binomial line", + "shortLabel": "Prop. X.48", + "short": "Find first binomial", + "book": 10, + "number": 48, + "colorClass": "proposition" + }, + { + "id": "Prop49", + "type": "proposition", + "label": "To find the second binomial line", + "shortLabel": "Prop. X.49", + "short": "Find second binomial", + "book": 10, + "number": 49, + "colorClass": "proposition" + }, + { + "id": "Prop50", + "type": "proposition", + "label": "To find the third binomial line", + "shortLabel": "Prop. X.50", + "short": "Find third binomial", + "book": 10, + "number": 50, + "colorClass": "proposition" + }, + { + "id": "Prop51", + "type": "proposition", + "label": "To find the fourth binomial line", + "shortLabel": "Prop. X.51", + "short": "Find fourth binomial", + "book": 10, + "number": 51, + "colorClass": "proposition" + }, + { + "id": "Prop52", + "type": "proposition", + "label": "To find the fifth binomial line", + "shortLabel": "Prop. X.52", + "short": "Find fifth binomial", + "book": 10, + "number": 52, + "colorClass": "proposition" + }, + { + "id": "Prop53", + "type": "proposition", + "label": "To find the sixth binomial line", + "shortLabel": "Prop. X.53", + "short": "Find sixth binomial", + "book": 10, + "number": 53, + "colorClass": "proposition" + }, + { + "id": "Prop54", + "type": "proposition", + "label": "Area by rational and first binomial: side is binomial", + "shortLabel": "Prop. X.54", + "short": "Rational × first binomial", + "book": 10, + "number": 54, + "colorClass": "proposition" + }, + { + "id": "Prop55", + "type": "proposition", + "label": "Area by rational and second binomial: side is first bimedial", + "shortLabel": "Prop. X.55", + "short": "Rational × second binomial", + "book": 10, + "number": 55, + "colorClass": "proposition" + }, + { + "id": "Prop56", + "type": "proposition", + "label": "Area by rational and third binomial: side is second bimedial", + "shortLabel": "Prop. X.56", + "short": "Rational × third binomial", + "book": 10, + "number": 56, + "colorClass": "proposition" + }, + { + "id": "Prop57", + "type": "proposition", + "label": "Area by rational and fourth binomial: side is major", + "shortLabel": "Prop. X.57", + "short": "Rational × fourth binomial", + "book": 10, + "number": 57, + "colorClass": "proposition" + }, + { + "id": "Prop58", + "type": "proposition", + "label": "Area by rational and fifth binomial: side is rational plus medial", + "shortLabel": "Prop. X.58", + "short": "Rational × fifth binomial", + "book": 10, + "number": 58, + "colorClass": "proposition" + }, + { + "id": "Prop59", + "type": "proposition", + "label": "Area by rational and sixth binomial: side is sum of two medial", + "shortLabel": "Prop. 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newline at end of file diff --git a/data/euclid-elements-book-xi.json b/data/euclid-elements-book-xi.json new file mode 100644 index 0000000000000000000000000000000000000000..44ad6c94b87a26b702b12bcb5f07f9081205ed43 --- /dev/null +++ b/data/euclid-elements-book-xi.json @@ -0,0 +1,783 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "euclid-elements-book-xi", + "name": "Euclid's Elements, Book XI", + "subject": "solid_geometry", + "variant": "classical", + "description": "Solid geometry: planes, perpendiculars, parallelepipeds, prisms. 28 definitions, 39 propositions. Depends on Books I and VI. Source: David E. Joyce.", + "structure": { + "books": 11, + "definitions": 28, + "propositions": 39, + "foundationTypes": [ + "foundation" + ] + } + }, + "metadata": { + "created": "2026-03-18", + "lastUpdated": "2026-03-18", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Euclid's Elements Book XI Dependency Graph. Programming Framework.", + "keywords": [ + "Euclid", + "Elements", + "Book XI", + "solid geometry", + "plane", + "parallelepiped", + "prism" + ] + }, + "sources": [ + { + "id": "joyce", + "type": "digital", + "authors": "Joyce, David E.", + "title": "Euclid's Elements, Book XI", + "year": "1996", + "url": "https://mathcs.clarku.edu/~djoyce/java/elements/bookXI/bookXI.html", + "notes": "Clark University" + } + ], + "nodes": [ + { + "id": "BookI", + "type": "foundation", + "label": "Book I — Plane geometry", + "shortLabel": "Book I", + "short": "Foundation", + "book": 1, + "colorClass": "foundation" + }, + { + "id": "BookVI", + "type": "foundation", + "label": "Book VI — Similar figures", + "shortLabel": "Book VI", + "short": "Foundation", + "book": 6, + "colorClass": "foundation" + }, + { + "id": "Prop1", + "type": "proposition", + "label": "A part of a straight line cannot be in one plane and part in another elevated", + "shortLabel": "Prop. XI.1", + "short": "Line part in plane", + "book": 11, + "number": 1, + "colorClass": "proposition" + }, + { + "id": "Prop2", + "type": "proposition", + "label": "If two straight lines cut one another, they lie in one plane; every triangle in one plane", + "shortLabel": "Prop. XI.2", + "short": "Two lines cut: one plane", + "book": 11, + "number": 2, + "colorClass": "proposition" + }, + { + "id": "Prop3", + "type": "proposition", + "label": "If two planes cut one another, their intersection is a straight line", + "shortLabel": "Prop. XI.3", + "short": "Planes cut: line", + "book": 11, + "number": 3, + "colorClass": "proposition" + }, + { + "id": "Prop4", + "type": "proposition", + "label": "If line at right angles to two lines cutting at point, also perpendicular to plane through them", + "shortLabel": "Prop. XI.4", + "short": "Line perpendicular to plane", + "book": 11, + "number": 4, + "colorClass": "proposition" + }, + { + "id": "Prop5", + "type": "proposition", + "label": "If line at right angles to three lines meeting at point, the three lie in one plane", + "shortLabel": "Prop. XI.5", + "short": "Three lines from point", + "book": 11, + "number": 5, + "colorClass": "proposition" + }, + { + "id": "Prop6", + "type": "proposition", + "label": "If two lines at right angles to same plane, they are parallel", + "shortLabel": "Prop. XI.6", + "short": "Perpendicular to same plane: parallel", + "book": 11, + "number": 6, + "colorClass": "proposition" + }, + { + "id": "Prop7", + "type": "proposition", + "label": "If two lines parallel, line joining points on each is in same plane", + "shortLabel": "Prop. 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"to": "Prop18" + }, + { + "from": "BookIV", + "to": "Prop18" + }, + { + "from": "BookVI", + "to": "Prop18" + }, + { + "from": "BookX", + "to": "Prop18" + }, + { + "from": "BookXI", + "to": "Prop18" + } + ], + "colorScheme": { + "foundation": { + "fill": "#95a5a6", + "stroke": "#7f8c8d" + }, + "proposition": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/peano-arithmetic-addition-multiplication.mmd b/data/peano-arithmetic-addition-multiplication.mmd new file mode 100644 index 0000000000000000000000000000000000000000..c7b15fc92f1b439abafe644294b8ed8d41d02c27 --- /dev/null +++ b/data/peano-arithmetic-addition-multiplication.mmd @@ -0,0 +1,65 @@ +graph TD + A5["A5\nInduction"] + DefAdd["DefAdd\nDefinition of +"] + T5["T5\nAssociativity of +"] + T6["T6\nLeft identity"] + T7["T7\nSuccessor and add"] + T8["T8\nCommutativity of +"] + T9["T9\nCancellation for +"] + DefMul["DefMul\nDefinition of ·"] + T10["T10\nMul well-defined"] + T11["T11\nZero times"] + T12["T12\nZero from left"] + T13["T13\nSuccessor and mul"] + T14["T14\nCommutativity of ·"] + T15["T15\nAssociativity of ·"] + T16["T16\nDistributivity"] + T17["T17\nDistributivity (right)"] + A5 --> DefAdd + DefAdd --> T5 + A5 --> T5 + DefAdd --> T6 + A5 --> T6 + DefAdd --> T7 + T6 --> T7 + A5 --> T7 + DefAdd --> T8 + T5 --> T8 + T6 --> T8 + T7 --> T8 + A5 --> T8 + DefAdd --> T9 + T8 --> T9 + A5 --> T9 + DefAdd --> DefMul + A5 --> DefMul + DefMul --> T10 + A5 --> T10 + DefMul --> T11 + DefMul --> T12 + T6 --> T12 + A5 --> T12 + DefMul --> T13 + T8 --> T13 + A5 --> T13 + DefMul --> T14 + T12 --> T14 + T13 --> T14 + A5 --> T14 + DefMul --> T15 + T5 --> T15 + T8 --> T15 + A5 --> T15 + DefMul --> T16 + T5 --> T16 + T8 --> T16 + T15 --> T16 + A5 --> T16 + T16 --> T17 + T8 --> T17 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A5 axiom + class DefAdd,DefMul definition + class T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,T15,T16,T17 theorem \ No newline at end of file diff --git a/data/peano-arithmetic-axioms-foundations.mmd b/data/peano-arithmetic-axioms-foundations.mmd new file mode 100644 index 0000000000000000000000000000000000000000..a7c75d037fbfe82ae9fe1047012f88c611bf07f2 --- /dev/null +++ b/data/peano-arithmetic-axioms-foundations.mmd @@ -0,0 +1,33 @@ +graph TD + A1["A1\n0 ∈ N"] + A2["A2\n0 not a successor"] + A3["A3\nS injective"] + A4["A4\nN closed under S"] + A5["A5\nInduction"] + T1["T1\nContrapositive of A3"] + T2["T2\nSuccessor ≠ identity"] + T3["T3\nEvery nonzero is successor"] + DefAdd["DefAdd\nDefinition of +"] + T4["T4\nAdd well-defined"] + T5["T5\nAssociativity of +"] + T6["T6\nLeft identity"] + A3 --> T1 + A1 --> T2 + A2 --> T2 + A3 --> T2 + T1 --> T2 + A5 --> T2 + A5 --> T3 + A5 --> DefAdd + DefAdd --> T4 + A5 --> T4 + DefAdd --> T5 + A5 --> T5 + DefAdd --> T6 + A5 --> T6 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A1,A2,A3,A4,A5 axiom + class DefAdd definition + class T1,T2,T3,T4,T5,T6 theorem \ No newline at end of file diff --git a/data/peano-arithmetic-order-induction.mmd b/data/peano-arithmetic-order-induction.mmd new file mode 100644 index 0000000000000000000000000000000000000000..cb69bea46270225b431c587eb2e7252813ae5ca4 --- /dev/null +++ b/data/peano-arithmetic-order-induction.mmd @@ -0,0 +1,86 @@ +graph TD + A5["A5\nInduction"] + DefAdd["DefAdd\nDefinition of +"] + T5["T5\nAssociativity of +"] + T6["T6\nLeft identity"] + T7["T7\nSuccessor and add"] + T8["T8\nCommutativity of +"] + T9["T9\nCancellation for +"] + DefMul["DefMul\nDefinition of ·"] + T12["T12\nZero from left"] + T13["T13\nSuccessor and mul"] + T14["T14\nCommutativity of ·"] + T15["T15\nAssociativity of ·"] + T16["T16\nDistributivity"] + T18["T18\nOrder definition"] + T19["T19\nTrichotomy"] + T20["T20\nOrder + add"] + T21["T21\nOrder + mul"] + T22["T22\nMultiplicative identity"] + T23["T23\nRight identity"] + T24["T24\nWell-ordering"] + T25["T25\nStrong induction"] + A5 --> DefAdd + DefAdd --> T5 + A5 --> T5 + DefAdd --> T6 + A5 --> T6 + DefAdd --> T7 + T6 --> T7 + A5 --> T7 + DefAdd --> T8 + T5 --> T8 + T6 --> T8 + T7 --> T8 + A5 --> T8 + DefAdd --> T9 + T8 --> T9 + A5 --> T9 + DefAdd --> DefMul + A5 --> DefMul + DefMul --> T12 + T6 --> T12 + A5 --> T12 + DefMul --> T13 + T8 --> T13 + A5 --> T13 + DefMul --> T14 + T12 --> T14 + T13 --> T14 + A5 --> T14 + DefMul --> T15 + T5 --> T15 + T8 --> T15 + A5 --> T15 + DefMul --> T16 + T5 --> T16 + T8 --> T16 + T15 --> T16 + A5 --> T16 + DefAdd --> T18 + T8 --> T18 + T9 --> T18 + T18 --> T19 + T9 --> T19 + T18 --> T20 + T8 --> T20 + T18 --> T21 + T16 --> T21 + T14 --> T21 + DefMul --> T22 + T6 --> T22 + A5 --> T22 + T14 --> T23 + T22 --> T23 + T18 --> T24 + T19 --> T24 + A5 --> T24 + T18 --> T25 + T24 --> T25 + A5 --> T25 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A5 axiom + class DefAdd,DefMul definition + class T5,T6,T7,T8,T9,T12,T13,T14,T15,T16,T18,T19,T20,T21,T22,T23,T24,T25 theorem \ No newline at end of file diff --git a/data/peano-arithmetic.json b/data/peano-arithmetic.json new file mode 100644 index 0000000000000000000000000000000000000000..47b74516536d3eecf7a0339d1842bb541217fbd3 --- /dev/null +++ b/data/peano-arithmetic.json @@ -0,0 +1,614 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "peano-arithmetic", + "name": "Peano Arithmetic", + "subject": "arithmetic", + "variant": "classical", + "description": "Axiomatic development of natural number arithmetic. Five axioms, definitions of addition and multiplication, and key theorems (associativity, commutativity, distributivity, order). Based on Landau, Foundations of Analysis.", + "structure": { + "axioms": 5, + "definitions": 2, + "theorems": 25 + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Peano Arithmetic Dependency Graph. Programming Framework.", + "keywords": [ + "Peano", + "arithmetic", + "natural numbers", + "induction", + "foundations" + ] + }, + "sources": [ + { + "id": "landau", + "type": "primary", + "authors": "Landau, E.", + "title": "Foundations of Analysis", + "year": "1930", + "publisher": "Chelsea", + "edition": "1951", + "notes": "Canonical development" + }, + { + "id": "wikipedia", + "type": "digital", + "title": "Peano axioms", + "url": "https://en.wikipedia.org/wiki/Peano_axioms", + "notes": "Overview and definitions" + } + ], + "nodes": [ + { + "id": "A1", + "type": "axiom", + "label": "0 is a natural number", + "shortLabel": "A1", + "short": "0 ∈ N", + "colorClass": "axiom" + }, + { + "id": "A2", + "type": "axiom", + "label": "No predecessor of 0: S(x) ≠ 0", + "shortLabel": "A2", + "short": "0 not a successor", + "colorClass": "axiom" + }, + { + "id": "A3", + "type": "axiom", + "label": "Successor injective: S(x)=S(y) ⇒ x=y", + "shortLabel": "A3", + "short": "S injective", + "colorClass": "axiom" + }, + { + "id": "A4", + "type": "axiom", + "label": "Closure: S(x) ∈ N for all x ∈ N", + "shortLabel": "A4", + "short": "N closed under S", + "colorClass": "axiom" + }, + { + "id": "A5", + "type": "axiom", + "label": "Induction: if 0∈K and (x∈K⇒S(x)∈K) then K=N", + "shortLabel": "A5", + "short": "Induction", + "colorClass": "axiom" + }, + { + "id": "T1", + "type": "theorem", + "label": "x≠y ⇒ S(x)≠S(y)", + "shortLabel": "T1", + "short": "Contrapositive of A3", + "colorClass": "theorem" + }, + { + "id": "T2", + "type": "theorem", + "label": "S(x)≠x for all x", + "shortLabel": "T2", + "short": "Successor ≠ identity", + "colorClass": "theorem" + }, + { + "id": "T3", + "type": "theorem", + "label": "If x≠0 then x=S(u) for some u", + "shortLabel": "T3", + "short": "Every nonzero is successor", + "colorClass": "theorem" + }, + { + "id": "DefAdd", + "type": "definition", + "label": "Addition: x+0=x, x+S(y)=S(x+y)", + "shortLabel": "DefAdd", + "short": "Definition of +", + "colorClass": "definition" + }, + { + "id": "T4", + "type": "theorem", + "label": "Addition is well-defined for all x,y", + "shortLabel": "T4", + "short": "Add well-defined", + "colorClass": "theorem" + }, + { + "id": "T5", + "type": "theorem", + "label": "(x+y)+z = x+(y+z)", + "shortLabel": "T5", + "short": "Associativity of +", + "colorClass": "theorem" + }, + { + "id": "T6", + "type": "theorem", + "label": "0+x = x", + "shortLabel": "T6", + "short": "Left identity", + "colorClass": "theorem" + }, + { + "id": "T7", + "type": "theorem", + "label": "S(x)+y = S(x+y)", + "shortLabel": "T7", + "short": "Successor and add", + "colorClass": "theorem" + }, + { + "id": "T8", + "type": "theorem", + "label": "x+y = y+x", + "shortLabel": "T8", + "short": "Commutativity of +", + "colorClass": "theorem" + }, + { + "id": "T9", + "type": "theorem", + "label": "x+y=x+z ⇒ y=z", + "shortLabel": "T9", + "short": "Cancellation for +", + "colorClass": "theorem" + }, + { + "id": "DefMul", + "type": "definition", + "label": "Multiplication: x·0=0, x·S(y)=x·y+x", + "shortLabel": "DefMul", + "short": "Definition of ·", + "colorClass": "definition" + }, + { + "id": "T10", + "type": "theorem", + "label": "Multiplication is well-defined for all x,y", + "shortLabel": "T10", + "short": "Mul well-defined", + "colorClass": "theorem" + }, + { + "id": "T11", + "type": "theorem", + "label": "x·0 = 0", + "shortLabel": "T11", + "short": "Zero times", + "colorClass": "theorem" + }, + { + "id": "T12", + "type": "theorem", + "label": "0·x = 0", + "shortLabel": "T12", + "short": "Zero from left", + "colorClass": "theorem" + }, + { + "id": "T13", + "type": "theorem", + "label": "S(x)·y = x·y + y", + "shortLabel": "T13", + "short": "Successor and mul", + "colorClass": "theorem" + }, + { + "id": "T14", + "type": "theorem", + "label": "x·y = y·x", + "shortLabel": "T14", + "short": "Commutativity of ·", + "colorClass": "theorem" + }, + { + "id": "T15", + "type": "theorem", + "label": "(x·y)·z = x·(y·z)", + "shortLabel": "T15", + "short": "Associativity of ·", + "colorClass": "theorem" + }, + { + "id": "T16", + "type": "theorem", + "label": "x·(y+z) = x·y + x·z", + "shortLabel": "T16", + "short": "Distributivity", + "colorClass": "theorem" + }, + { + "id": "T17", + "type": "theorem", + "label": "(x+y)·z = x·z + y·z", + "shortLabel": "T17", + "short": "Distributivity (right)", + "colorClass": "theorem" + }, + { + "id": "T18", + "type": "theorem", + "label": "x≤y iff ∃z x+z=y", + "shortLabel": "T18", + "short": "Order definition", + "colorClass": "theorem" + }, + { + "id": "T19", + "type": "theorem", + "label": "Trichotomy: exactly one of x0 ⇒ x·z≤y·z", + "shortLabel": "T21", + "short": "Order + mul", + "colorClass": "theorem" + }, + { + "id": "T22", + "type": "theorem", + "label": "1·x = x (where 1=S(0))", + "shortLabel": "T22", + "short": "Multiplicative identity", + "colorClass": "theorem" + }, + { + "id": "T23", + "type": "theorem", + "label": "x·1 = x", + "shortLabel": "T23", + "short": "Right identity", + "colorClass": "theorem" + }, + { + "id": "T24", + "type": "theorem", + "label": "Well-ordering: every nonempty subset has least element", + "shortLabel": "T24", + "short": "Well-ordering", + "colorClass": "theorem" + }, + { + "id": "T25", + "type": "theorem", + "label": "Strong induction principle", + "shortLabel": "T25", + "short": "Strong induction", + "colorClass": "theorem" + } + ], + "edges": [ + { + "from": "A3", + "to": "T1" + }, + { + "from": "A1", + "to": "T2" + }, + { + "from": "A2", + "to": "T2" + }, + { + "from": "A3", + "to": "T2" + }, + { + "from": "T1", + "to": "T2" + }, + { + "from": "A5", + "to": "T2" + }, + { + "from": "A5", + "to": "T3" + }, + { + "from": "A5", + "to": "DefAdd" + }, + { + "from": "DefAdd", + "to": "T4" + }, + { + "from": "A5", + "to": "T4" + }, + { + "from": "DefAdd", + "to": "T5" + }, + { + "from": "A5", + "to": "T5" + }, + { + "from": "DefAdd", + "to": "T6" + }, + { + "from": "A5", + "to": "T6" + }, + { + "from": "DefAdd", + "to": "T7" + }, + { + "from": "T6", + "to": "T7" + }, + { + "from": "A5", + "to": "T7" + }, + { + "from": "DefAdd", + "to": "T8" + }, + { + "from": "T5", + "to": "T8" + }, + { + "from": "T6", + "to": "T8" + }, + { + "from": "T7", + "to": "T8" + }, + { + "from": "A5", + "to": "T8" + }, + { + "from": "DefAdd", + "to": "T9" + }, + { + "from": "T8", + "to": "T9" + }, + { + "from": "A5", + "to": "T9" + }, + { + "from": "DefAdd", + "to": "DefMul" + }, + { + "from": "A5", + "to": "DefMul" + }, + { + "from": "DefMul", + "to": "T10" + }, + { + "from": "A5", + "to": "T10" + }, + { + "from": "DefMul", + "to": "T11" + }, + { + "from": "DefMul", + "to": "T12" + }, + { + "from": "T6", + "to": "T12" + }, + { + "from": "A5", + "to": "T12" + }, + { + "from": "DefMul", + "to": "T13" + }, + { + "from": "T8", + "to": "T13" + }, + { + "from": "A5", + "to": "T13" + }, + { + "from": "DefMul", + "to": "T14" + }, + { + "from": "T12", + "to": "T14" + }, + { + "from": "T13", + "to": "T14" + }, + { + "from": "A5", + "to": "T14" + }, + { + "from": "DefMul", + "to": "T15" + }, + { + "from": "T5", + "to": "T15" + }, + { + "from": "T8", + "to": "T15" + }, + { + "from": "A5", + "to": "T15" + }, + { + "from": "DefMul", + "to": "T16" + }, + { + "from": "T5", + "to": "T16" + }, + { + "from": "T8", + "to": "T16" + }, + { + "from": "T15", + "to": "T16" + }, + { + "from": "A5", + "to": "T16" + }, + { + "from": "T16", + "to": "T17" + }, + { + "from": "T8", + "to": "T17" + }, + { + "from": "DefAdd", + "to": "T18" + }, + { + "from": "T8", + "to": "T18" + }, + { + "from": "T9", + "to": "T18" + }, + { + "from": "T18", + "to": "T19" + }, + { + "from": "T9", + "to": "T19" + }, + { + "from": "T18", + "to": "T20" + }, + { + "from": "T8", + "to": "T20" + }, + { + "from": "T18", + "to": "T21" + }, + { + "from": "T16", + "to": "T21" + }, + { + "from": "T14", + "to": "T21" + }, + { + "from": "DefMul", + "to": "T22" + }, + { + "from": "T6", + "to": "T22" + }, + { + "from": "A5", + "to": "T22" + }, + { + "from": "T14", + "to": "T23" + }, + { + "from": "T22", + "to": "T23" + }, + { + "from": "T18", + "to": "T24" + }, + { + "from": "T19", + "to": "T24" + }, + { + "from": "A5", + "to": "T24" + }, + { + "from": "T18", + "to": "T25" + }, + { + "from": "T24", + "to": "T25" + }, + { + "from": "A5", + "to": "T25" + } + ], + "colorScheme": { + "axiom": { + "fill": "#e74c3c", + "stroke": "#c0392b" + }, + "definition": { + "fill": "#3498db", + "stroke": "#2980b9" + }, + "theorem": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/peano-arithmetic.mmd b/data/peano-arithmetic.mmd new file mode 100644 index 0000000000000000000000000000000000000000..89105eff1d6888d1ff9f85c5c220434dbf6ba401 --- /dev/null +++ b/data/peano-arithmetic.mmd @@ -0,0 +1,111 @@ +graph TD + A1["A1\n0 ∈ N"] + A2["A2\n0 not a successor"] + A3["A3\nS injective"] + A4["A4\nN closed under S"] + A5["A5\nInduction"] + T1["T1\nContrapositive of A3"] + T2["T2\nSuccessor ≠ identity"] + T3["T3\nEvery nonzero is successor"] + DefAdd["DefAdd\nDefinition of +"] + T4["T4\nAdd well-defined"] + T5["T5\nAssociativity of +"] + T6["T6\nLeft identity"] + T7["T7\nSuccessor and add"] + T8["T8\nCommutativity of +"] + T9["T9\nCancellation for +"] + DefMul["DefMul\nDefinition of ·"] + T10["T10\nMul well-defined"] + T11["T11\nZero times"] + T12["T12\nZero from left"] + T13["T13\nSuccessor and mul"] + T14["T14\nCommutativity of ·"] + T15["T15\nAssociativity of ·"] + T16["T16\nDistributivity"] + T17["T17\nDistributivity (right)"] + T18["T18\nOrder definition"] + T19["T19\nTrichotomy"] + T20["T20\nOrder + add"] + T21["T21\nOrder + mul"] + T22["T22\nMultiplicative identity"] + T23["T23\nRight identity"] + T24["T24\nWell-ordering"] + T25["T25\nStrong induction"] + A3 --> T1 + A1 --> T2 + A2 --> T2 + A3 --> T2 + T1 --> T2 + A5 --> T2 + A5 --> T3 + A5 --> DefAdd + DefAdd --> T4 + A5 --> T4 + DefAdd --> T5 + A5 --> T5 + DefAdd --> T6 + A5 --> T6 + DefAdd --> T7 + T6 --> T7 + A5 --> T7 + DefAdd --> T8 + T5 --> T8 + T6 --> T8 + T7 --> T8 + A5 --> T8 + DefAdd --> T9 + T8 --> T9 + A5 --> T9 + DefAdd --> DefMul + A5 --> DefMul + DefMul --> T10 + A5 --> T10 + DefMul --> T11 + DefMul --> T12 + T6 --> T12 + A5 --> T12 + DefMul --> T13 + T8 --> T13 + A5 --> T13 + DefMul --> T14 + T12 --> T14 + T13 --> T14 + A5 --> T14 + DefMul --> T15 + T5 --> T15 + T8 --> T15 + A5 --> T15 + DefMul --> T16 + T5 --> T16 + T8 --> T16 + T15 --> T16 + A5 --> T16 + T16 --> T17 + T8 --> T17 + DefAdd --> T18 + T8 --> T18 + T9 --> T18 + T18 --> T19 + T9 --> T19 + T18 --> T20 + T8 --> T20 + T18 --> T21 + T16 --> T21 + T14 --> T21 + DefMul --> T22 + T6 --> T22 + A5 --> T22 + T14 --> T23 + T22 --> T23 + T18 --> T24 + T19 --> T24 + A5 --> T24 + T18 --> T25 + T24 --> T25 + A5 --> T25 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A1,A2,A3,A4,A5 axiom + class DefAdd,DefMul definition + class T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,T15,T16,T17,T18,T19,T20,T21,T22,T23,T24,T25 theorem \ No newline at end of file diff --git a/data/propositional-logic-axioms-implication.mmd b/data/propositional-logic-axioms-implication.mmd new file mode 100644 index 0000000000000000000000000000000000000000..3bdf2d938eefabc8edfb07a47df7659c130f4034 --- /dev/null +++ b/data/propositional-logic-axioms-implication.mmd @@ -0,0 +1,31 @@ +graph TD + A1("A1 Weakening") + A2("A2 Distrib. of impl.") + A3("A3 Contraposition") + MP("MP MP") + T1("T1 Self-implication") + T2("T2 Double neg. elim") + T3("T3 Double neg. intro") + T4("T4 Transposition") + T5("T5 Hyp. syllogism") + A1 --> T1 + A2 --> T1 + MP --> T1 + A3 --> T2 + T1 --> T2 + MP --> T2 + A1 --> T3 + A3 --> T3 + MP --> T3 + A3 --> T4 + T2 --> T4 + T3 --> T4 + MP --> T4 + A2 --> T5 + T1 --> T5 + MP --> T5 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A1,A2,A3,MP axiom + class T1,T2,T3,T4,T5 theorem \ No newline at end of file diff --git a/data/propositional-logic-definitions-connectives.mmd b/data/propositional-logic-definitions-connectives.mmd new file mode 100644 index 0000000000000000000000000000000000000000..f05e7115c76575c70e47523c1467294eb1ef204f --- /dev/null +++ b/data/propositional-logic-definitions-connectives.mmd @@ -0,0 +1,74 @@ +graph TD + A1("A1 Weakening") + A2("A2 Distrib. of impl.") + A3("A3 Contraposition") + MP("MP MP") + T1("T1 Self-implication") + T2("T2 Double neg. elim") + T3("T3 Double neg. intro") + T4("T4 Transposition") + DefOr("DefOr Def. disjunction") + DefAnd("DefAnd Def. conjunction") + DefIff("DefIff Def. biconditional") + T6("T6 Addition (orI)") + T7("T7 Simplification (andE)") + T8("T8 Simplification (andE)") + T9("T9 Conjunction (andI)") + T10("T10 Material impl.") + T11("T11 De Morgan (1)") + T12("T12 De Morgan (2)") + A1 --> T1 + A2 --> T1 + MP --> T1 + A3 --> T2 + T1 --> T2 + MP --> T2 + A1 --> T3 + A3 --> T3 + MP --> T3 + A3 --> T4 + T2 --> T4 + T3 --> T4 + MP --> T4 + A1 --> DefOr + A2 --> DefOr + A3 --> DefOr + MP --> DefOr + DefOr --> DefAnd + A3 --> DefAnd + MP --> DefAnd + DefAnd --> DefIff + T9 --> DefIff + MP --> DefIff + DefOr --> T6 + A1 --> T6 + MP --> T6 + DefAnd --> T7 + A1 --> T7 + A3 --> T7 + MP --> T7 + DefAnd --> T8 + A1 --> T8 + A3 --> T8 + MP --> T8 + A1 --> T9 + A2 --> T9 + MP --> T9 + DefOr --> T10 + T4 --> T10 + MP --> T10 + DefAnd --> T11 + DefOr --> T11 + T4 --> T11 + T6 --> T11 + MP --> T11 + DefAnd --> T12 + DefOr --> T12 + T4 --> T12 + MP --> T12 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A1,A2,A3,MP axiom + class DefOr,DefAnd,DefIff definition + class T1,T2,T3,T4,T6,T7,T8,T9,T10,T11,T12 theorem \ No newline at end of file diff --git a/data/propositional-logic-tautologies-metalogic.mmd b/data/propositional-logic-tautologies-metalogic.mmd new file mode 100644 index 0000000000000000000000000000000000000000..8149a976d6d0efe07491f230d42406370794dffd --- /dev/null +++ b/data/propositional-logic-tautologies-metalogic.mmd @@ -0,0 +1,89 @@ +graph TD + A1("A1 Weakening") + A2("A2 Distrib. of impl.") + A3("A3 Contraposition") + MP("MP MP") + T1("T1 Self-implication") + T2("T2 Double neg. elim") + T3("T3 Double neg. intro") + T4("T4 Transposition") + DefOr("DefOr Def. disjunction") + DefAnd("DefAnd Def. conjunction") + T6("T6 Addition (orI)") + T7("T7 Simplification (andE)") + T8("T8 Simplification (andE)") + T9("T9 Conjunction (andI)") + T13("T13 Excluded middle") + T14("T14 Non-contradiction") + T15("T15 Explosion") + T16("T16 Commutation (or)") + T17("T17 Commutation (and)") + T18("T18 Distribution") + T19("T19 Deduction thm") + A1 --> T1 + A2 --> T1 + MP --> T1 + A3 --> T2 + T1 --> T2 + MP --> T2 + A1 --> T3 + A3 --> T3 + MP --> T3 + A3 --> T4 + T2 --> T4 + T3 --> T4 + MP --> T4 + A1 --> DefOr + A2 --> DefOr + A3 --> DefOr + MP --> DefOr + DefOr --> DefAnd + A3 --> DefAnd + MP --> DefAnd + DefOr --> T6 + A1 --> T6 + MP --> T6 + DefAnd --> T7 + A1 --> T7 + A3 --> T7 + MP --> T7 + DefAnd --> T8 + A1 --> T8 + A3 --> T8 + MP --> T8 + A1 --> T9 + A2 --> T9 + MP --> T9 + DefOr --> T13 + T2 --> T13 + T3 --> T13 + MP --> T13 + DefAnd --> T14 + T4 --> T14 + MP --> T14 + DefAnd --> T15 + A1 --> T15 + A2 --> T15 + MP --> T15 + DefOr --> T16 + T4 --> T16 + MP --> T16 + DefAnd --> T17 + T9 --> T17 + MP --> T17 + DefAnd --> T18 + DefOr --> T18 + T6 --> T18 + T7 --> T18 + T8 --> T18 + T9 --> T18 + MP --> T18 + A1 --> T19 + A2 --> T19 + MP --> T19 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A1,A2,A3,MP axiom + class DefOr,DefAnd definition + class T1,T2,T3,T4,T6,T7,T8,T9,T13,T14,T15,T16,T17,T18,T19 theorem \ No newline at end of file diff --git a/data/propositional-logic.json b/data/propositional-logic.json new file mode 100644 index 0000000000000000000000000000000000000000..7d25b5083410a250ae81624903c41ab9c96d1f00 --- /dev/null +++ b/data/propositional-logic.json @@ -0,0 +1,600 @@ +{ + "schemaVersion": "1.0", + "discourse": { + "id": "propositional-logic", + "name": "Propositional Logic", + "subject": "logic", + "variant": "classical", + "description": "Hilbert-style axiomatic development of classical propositional logic. Three axioms (Łukasiewicz P2), modus ponens, definitions of disjunction, conjunction, biconditional, and key theorems (double negation, De Morgan, excluded middle, deduction theorem).", + "structure": { + "axioms": 4, + "definitions": 3, + "theorems": 19 + } + }, + "metadata": { + "created": "2026-03-15", + "lastUpdated": "2026-03-15", + "version": "1.0.0", + "license": "CC BY 4.0", + "authors": [ + "Welz, G." + ], + "methodology": "Programming Framework", + "citation": "Welz, G. (2026). Propositional Logic Dependency Graph. Programming Framework.", + "keywords": [ + "propositional logic", + "Hilbert", + "Łukasiewicz", + "tautology", + "modus ponens" + ] + }, + "sources": [ + { + "id": "frege", + "type": "primary", + "authors": "Frege, G.", + "title": "Begriffsschrift", + "year": "1879", + "notes": "First axiomatic propositional logic" + }, + { + "id": "lukasiewicz", + "type": "primary", + "authors": "Łukasiewicz, J.", + "title": "Elements of Mathematical Logic", + "year": "1929", + "notes": "P2: 3 axioms" + }, + { + "id": "wikipedia", + "type": "digital", + "title": "Propositional calculus", + "url": "https://en.wikipedia.org/wiki/Propositional_calculus", + "notes": "Axioms and theorems" + } + ], + "nodes": [ + { + "id": "A1", + "type": "axiom", + "label": "φ → (ψ → φ)", + "shortLabel": "A1", + "short": "Weakening", + "colorClass": "axiom" + }, + { + "id": "A2", + "type": "axiom", + "label": "(φ→(ψ→χ)) → ((φ→ψ)→(φ→χ))", + "shortLabel": "A2", + "short": "Distrib. of impl.", + "colorClass": "axiom" + }, + { + "id": "A3", + "type": "axiom", + "label": "(¬φ→¬ψ) → (ψ→φ)", + "shortLabel": "A3", + "short": "Contraposition", + "colorClass": "axiom" + }, + { + "id": "MP", + "type": "axiom", + "label": "Modus Ponens: φ, (φ→ψ) ⊢ ψ", + "shortLabel": "MP", + "short": "MP", + "colorClass": "axiom" + }, + { + "id": "T1", + "type": "theorem", + "label": "φ → φ", + "shortLabel": "T1", + "short": "Self-implication", + "colorClass": "theorem" + }, + { + "id": "T2", + "type": "theorem", + "label": "¬¬φ → φ", + "shortLabel": "T2", + "short": "Double neg. elim", + "colorClass": "theorem" + }, + { + "id": "T3", + "type": "theorem", + "label": "φ → ¬¬φ", + "shortLabel": "T3", + "short": "Double neg. intro", + "colorClass": "theorem" + }, + { + "id": "T4", + "type": "theorem", + "label": "(φ→ψ) → (¬ψ→¬φ)", + "shortLabel": "T4", + "short": "Transposition", + "colorClass": "theorem" + }, + { + "id": "T5", + "type": "theorem", + "label": "(φ→ψ)∧(ψ→χ) ⇒ (φ→χ)", + "shortLabel": "T5", + "short": "Hyp. syllogism", + "colorClass": "theorem" + }, + { + "id": "DefOr", + "type": "definition", + "label": "φ ∨ ψ := ¬φ → ψ", + "shortLabel": "DefOr", + "short": "Def. disjunction", + "colorClass": "definition" + }, + { + "id": "DefAnd", + "type": "definition", + "label": "φ ∧ ψ := ¬(φ → ¬ψ)", + "shortLabel": "DefAnd", + "short": "Def. conjunction", + "colorClass": "definition" + }, + { + "id": "DefIff", + "type": "definition", + "label": "φ ↔ ψ := (φ→ψ)∧(ψ→φ)", + "shortLabel": "DefIff", + "short": "Def. biconditional", + "colorClass": "definition" + }, + { + "id": "T6", + "type": "theorem", + "label": "φ → (φ ∨ ψ)", + "shortLabel": "T6", + "short": "Addition (∨I)", + "colorClass": "theorem" + }, + { + "id": "T7", + "type": "theorem", + "label": "(φ∧ψ) → φ", + "shortLabel": "T7", + "short": "Simplification (∧E)", + "colorClass": "theorem" + }, + { + "id": "T8", + "type": "theorem", + "label": "(φ∧ψ) → ψ", + "shortLabel": "T8", + "short": "Simplification (∧E)", + "colorClass": "theorem" + }, + { + "id": "T9", + "type": "theorem", + "label": "φ → (ψ → (φ∧ψ))", + "shortLabel": "T9", + "short": "Conjunction (∧I)", + "colorClass": "theorem" + }, + { + "id": "T10", + "type": "theorem", + "label": "(φ→ψ) ↔ (¬φ∨ψ)", + "shortLabel": "T10", + "short": "Material impl.", + "colorClass": "theorem" + }, + { + "id": "T11", + "type": "theorem", + "label": "¬(φ∧ψ) ↔ (¬φ∨¬ψ)", + "shortLabel": "T11", + "short": "De Morgan (1)", + "colorClass": "theorem" + }, + { + "id": "T12", + "type": "theorem", + "label": "¬(φ∨ψ) ↔ (¬φ∧¬ψ)", + "shortLabel": "T12", + "short": "De Morgan (2)", + "colorClass": "theorem" + }, + { + "id": "T13", + "type": "theorem", + "label": "φ ∨ ¬φ", + "shortLabel": "T13", + "short": "Excluded middle", + "colorClass": "theorem" + }, + { + "id": "T14", + "type": "theorem", + "label": "¬(φ ∧ ¬φ)", + "shortLabel": "T14", + "short": "Non-contradiction", + "colorClass": "theorem" + }, + { + "id": "T15", + "type": "theorem", + "label": "(φ∧¬φ) → ψ", + "shortLabel": "T15", + "short": "Explosion", + "colorClass": "theorem" + }, + { + "id": "T16", + "type": "theorem", + "label": "(φ∨ψ) ↔ (ψ∨φ)", + "shortLabel": "T16", + "short": "Commutation (∨)", + "colorClass": "theorem" + }, + { + "id": "T17", + "type": "theorem", + "label": "(φ∧ψ) ↔ (ψ∧φ)", + "shortLabel": "T17", + "short": "Commutation (∧)", + "colorClass": "theorem" + }, + { + "id": "T18", + "type": "theorem", + "label": "(φ∧(ψ∨χ)) ↔ ((φ∧ψ)∨(φ∧χ))", + "shortLabel": "T18", + "short": "Distribution", + "colorClass": "theorem" + }, + { + "id": "T19", + "type": "theorem", + "label": "Deduction theorem", + "shortLabel": "T19", + "short": "Deduction thm", + "colorClass": "theorem" + } + ], + "edges": [ + { + "from": "A1", + "to": "T1" + }, + { + "from": "A2", + "to": "T1" + }, + { + "from": "MP", + "to": "T1" + }, + { + "from": "A3", + "to": "T2" + }, + { + "from": "T1", + "to": "T2" + }, + { + "from": "MP", + "to": "T2" + }, + { + "from": "A1", + "to": "T3" + }, + { + "from": "A3", + "to": "T3" + }, + { + "from": "MP", + "to": "T3" + }, + { + "from": "A3", + "to": "T4" + }, + { + "from": "T2", + "to": "T4" + }, + { + "from": "T3", + "to": "T4" + }, + { + "from": "MP", + "to": "T4" + }, + { + "from": "A2", + "to": "T5" + }, + { + "from": "T1", + "to": "T5" + }, + { + "from": "MP", + "to": "T5" + }, + { + "from": "A1", + "to": "DefOr" + }, + { + "from": "A2", + "to": "DefOr" + }, + { + "from": "A3", + "to": "DefOr" + }, + { + "from": "MP", + "to": "DefOr" + }, + { + "from": "DefOr", + "to": "DefAnd" + }, + { + "from": "A3", + "to": "DefAnd" + }, + { + "from": "MP", + "to": "DefAnd" + }, + { + "from": "DefAnd", + "to": "DefIff" + }, + { + "from": "T9", + "to": "DefIff" + }, + { + "from": "MP", + "to": "DefIff" + }, + { + "from": "DefOr", + "to": "T6" + }, + { + "from": "A1", + "to": "T6" + }, + { + "from": "MP", + "to": "T6" + }, + { + "from": "DefAnd", + "to": "T7" + }, + { + "from": "A1", + "to": "T7" + }, + { + "from": "A3", + "to": "T7" + }, + { + "from": "MP", + "to": "T7" + }, + { + "from": "DefAnd", + "to": "T8" + }, + { + "from": "A1", + "to": "T8" + }, + { + "from": "A3", + "to": "T8" + }, + { + "from": "MP", + "to": "T8" + }, + { + "from": "A1", + "to": "T9" + }, + { + "from": "A2", + "to": "T9" + }, + { + "from": "MP", + "to": "T9" + }, + { + "from": "DefOr", + "to": "T10" + }, + { + "from": "T4", + "to": "T10" + }, + { + "from": "MP", + "to": "T10" + }, + { + "from": "DefAnd", + "to": "T11" + }, + { + "from": "DefOr", + "to": "T11" + }, + { + "from": "T4", + "to": "T11" + }, + { + "from": "T6", + "to": "T11" + }, + { + "from": "MP", + "to": "T11" + }, + { + "from": "DefAnd", + "to": "T12" + }, + { + "from": "DefOr", + "to": "T12" + }, + { + "from": "T4", + "to": "T12" + }, + { + "from": "MP", + "to": "T12" + }, + { + "from": "DefOr", + "to": "T13" + }, + { + "from": "T2", + "to": "T13" + }, + { + "from": "T3", + "to": "T13" + }, + { + "from": "MP", + "to": "T13" + }, + { + "from": "DefAnd", + "to": "T14" + }, + { + "from": "T4", + "to": "T14" + }, + { + "from": "MP", + "to": "T14" + }, + { + "from": "DefAnd", + "to": "T15" + }, + { + "from": "A1", + "to": "T15" + }, + { + "from": "A2", + "to": "T15" + }, + { + "from": "MP", + "to": "T15" + }, + { + "from": "DefOr", + "to": "T16" + }, + { + "from": "T4", + "to": "T16" + }, + { + "from": "MP", + "to": "T16" + }, + { + "from": "DefAnd", + "to": "T17" + }, + { + "from": "T9", + "to": "T17" + }, + { + "from": "MP", + "to": "T17" + }, + { + "from": "DefAnd", + "to": "T18" + }, + { + "from": "DefOr", + "to": "T18" + }, + { + "from": "T6", + "to": "T18" + }, + { + "from": "T7", + "to": "T18" + }, + { + "from": "T8", + "to": "T18" + }, + { + "from": "T9", + "to": "T18" + }, + { + "from": "MP", + "to": "T18" + }, + { + "from": "A1", + "to": "T19" + }, + { + "from": "A2", + "to": "T19" + }, + { + "from": "MP", + "to": "T19" + } + ], + "colorScheme": { + "axiom": { + "fill": "#e74c3c", + "stroke": "#c0392b" + }, + "definition": { + "fill": "#3498db", + "stroke": "#2980b9" + }, + "theorem": { + "fill": "#1abc9c", + "stroke": "#16a085" + } + } +} \ No newline at end of file diff --git a/data/propositional-logic.mmd b/data/propositional-logic.mmd new file mode 100644 index 0000000000000000000000000000000000000000..32bbaeb2c109c160e2d30e5d200304391054676b --- /dev/null +++ b/data/propositional-logic.mmd @@ -0,0 +1,112 @@ +graph TD + A1("A1 Weakening") + A2("A2 Distrib. of impl.") + A3("A3 Contraposition") + MP("MP MP") + T1("T1 Self-implication") + T2("T2 Double neg. elim") + T3("T3 Double neg. intro") + T4("T4 Transposition") + T5("T5 Hyp. syllogism") + DefOr("DefOr Def. disjunction") + DefAnd("DefAnd Def. conjunction") + DefIff("DefIff Def. biconditional") + T6("T6 Addition (orI)") + T7("T7 Simplification (andE)") + T8("T8 Simplification (andE)") + T9("T9 Conjunction (andI)") + T10("T10 Material impl.") + T11("T11 De Morgan (1)") + T12("T12 De Morgan (2)") + T13("T13 Excluded middle") + T14("T14 Non-contradiction") + T15("T15 Explosion") + T16("T16 Commutation (or)") + T17("T17 Commutation (and)") + T18("T18 Distribution") + T19("T19 Deduction thm") + A1 --> T1 + A2 --> T1 + MP --> T1 + A3 --> T2 + T1 --> T2 + MP --> T2 + A1 --> T3 + A3 --> T3 + MP --> T3 + A3 --> T4 + T2 --> T4 + T3 --> T4 + MP --> T4 + A2 --> T5 + T1 --> T5 + MP --> T5 + A1 --> DefOr + A2 --> DefOr + A3 --> DefOr + MP --> DefOr + DefOr --> DefAnd + A3 --> DefAnd + MP --> DefAnd + DefAnd --> DefIff + T9 --> DefIff + MP --> DefIff + DefOr --> T6 + A1 --> T6 + MP --> T6 + DefAnd --> T7 + A1 --> T7 + A3 --> T7 + MP --> T7 + DefAnd --> T8 + A1 --> T8 + A3 --> T8 + MP --> T8 + A1 --> T9 + A2 --> T9 + MP --> T9 + DefOr --> T10 + T4 --> T10 + MP --> T10 + DefAnd --> T11 + DefOr --> T11 + T4 --> T11 + T6 --> T11 + MP --> T11 + DefAnd --> T12 + DefOr --> T12 + T4 --> T12 + MP --> T12 + DefOr --> T13 + T2 --> T13 + T3 --> T13 + MP --> T13 + DefAnd --> T14 + T4 --> T14 + MP --> T14 + DefAnd --> T15 + A1 --> T15 + A2 --> T15 + MP --> T15 + DefOr --> T16 + T4 --> T16 + MP --> T16 + DefAnd --> T17 + T9 --> T17 + MP --> T17 + DefAnd --> T18 + DefOr --> T18 + T6 --> T18 + T7 --> T18 + T8 --> T18 + T9 --> T18 + MP --> T18 + A1 --> T19 + A2 --> T19 + MP --> T19 + classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class A1,A2,A3,MP axiom + class DefOr,DefAnd,DefIff definition + class T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T11,T12,T13,T14,T15,T16,T17,T18,T19 theorem \ No newline at end of file diff --git a/dependency-graphs-design.html b/dependency-graphs-design.html new file mode 100644 index 0000000000000000000000000000000000000000..313e65b009e3c2edfcc196aa6a4c5a0b7606e8e0 --- /dev/null +++ b/dependency-graphs-design.html @@ -0,0 +1,80 @@ + + + + + + Mathematical Dependency Graphs — Design Document + + + +
+ ← Mathematics Database + Schema (JSON) + Design (Markdown) +
+ +

Mathematical Dependency Graphs — Design Document

+ +

Overview

+

A hybrid architecture for representing and visualizing axiomatic dependency structures across multiple mathematical subjects. Supports both static Mermaid subgraphs and interactive full-graph exploration.

+ +

Scope: Target Subjects

+ + + + + + + + + + +
SubjectFoundationsDerived ItemsNotes
Euclid's ElementsPostulates, Common Notions, Definitions464 Propositions (13 books)Geometric constructions
Peano Arithmetic5 axioms, definitionsTheoremsSuccessor, induction
Other number systemsAxioms (integers, rationals, reals)TheoremsConstruction sequences
Number theoryDefinitions, lemmasTheoremsDivisibility, primes
AlgebraGroup/ring/field axiomsTheoremsAbstract structures
Hilbert's geometry5 groups of axiomsTheoremsGrundlagen der Geometrie
Tarski's geometryBetweenness, congruence relationsTheoremsFirst-order, decidable
AnalysisCompleteness, continuity axiomsTheoremsReal analysis, limits
+ +

Metadata & Sources

+

Each discourse includes metadata (created, lastUpdated, version, license, authors, methodology, citation) and sources (primary texts, digital editions, commentaries). Nodes can reference sources via sourceRef.

+ +

Hybrid Architecture

+
    +
  1. Canonical JSON — One file per discourse, source of truth
    2. +
  2. Mermaid generator — Filter by book/chapter, output subgraph
    3. +
  3. Interactive viewer — Full graph with zoom, search, highlight
    4. +
  4. Index/Registry — Catalog of all discourses with metadata
    5. +
+ +

Implementation Phases

+ + + + + + + + +
PhaseDeliverable
1Schema + Euclid Props 1–6 JSON; Mermaid generator script
2Euclid Book I full JSON; static pages for Books I–IV
3Interactive viewer (single discourse)
4Peano Arithmetic, Hilbert Geometry JSON
5Multi-discourse index; cross-discourse navigation
6Tarski, Analysis, other subjects
+ +

References

+
    +
  • Euclid's Elements: Perseus Digital Library
    • +
  • Heath, T.L. The Thirteen Books of Euclid's Elements (1908, 2nd ed.)
    • +
  • Hilbert: Grundlagen der Geometrie (1899)
    • +
  • Tarski: What is Elementary Geometry? (1959)
    • +
  • Peano: Arithmetices principia (1889)
    • +
+ +

Programming Framework · Mathematical Dependency Graphs Design · 2026

+ + diff --git a/discourse-schema.json b/discourse-schema.json new file mode 100644 index 0000000000000000000000000000000000000000..0e359735b6cd812383f91fd84a79cbc57d521850 --- /dev/null +++ b/discourse-schema.json @@ -0,0 +1,102 @@ +{ + "$schema": "http://json-schema.org/draft-07/schema#", + "title": "Mathematical Discourse Dependency Graph", + "description": "Schema for axiomatic dependency structures across mathematical subjects", + "type": "object", + "required": ["schemaVersion", "discourse", "nodes", "edges"], + "properties": { + "schemaVersion": { "type": "string", "const": "1.0" }, + "discourse": { + "type": "object", + "required": ["id", "name", "subject"], + "properties": { + "id": { "type": "string", "pattern": "^[a-z0-9-]+$" }, + "name": { "type": "string" }, + "subject": { + "type": "string", + "enum": ["geometry", "arithmetic", "algebra", "analysis", "number_theory", "foundations", "other"] + }, + "variant": { "type": "string" }, + "description": { "type": "string" }, + "structure": { "type": "object" } + } + }, + "metadata": { + "type": "object", + "properties": { + "created": { "type": "string", "format": "date" }, + "lastUpdated": { "type": "string", "format": "date" }, + "version": { "type": "string" }, + "license": { "type": "string" }, + "authors": { "type": "array", "items": { "type": "string" } }, + "methodology": { "type": "string" }, + "citation": { "type": "string" }, + "keywords": { "type": "array", "items": { "type": "string" } } + } + }, + "sources": { + "type": "array", + "items": { + "type": "object", + "required": ["id"], + "properties": { + "id": { "type": "string" }, + "type": { "type": "string", "enum": ["primary", "secondary", "digital", "commentary"] }, + "authors": { "type": "string" }, + "title": { "type": "string" }, + "year": { "type": ["string", "integer"] }, + "edition": { "type": "string" }, + "publisher": { "type": "string" }, + "url": { "type": "string", "format": "uri" }, + "doi": { "type": "string" }, + "notes": { "type": "string" } + } + } + }, + "nodes": { + "type": "array", + "items": { + "type": "object", + "required": ["id", "type", "label"], + "properties": { + "id": { "type": "string" }, + "type": { + "type": "string", + "enum": ["axiom", "postulate", "commonNotion", "definition", "proposition", "theorem", "lemma", "corollary"] + }, + "label": { "type": "string" }, + "shortLabel": { "type": "string" }, + "book": { "type": "integer" }, + "chapter": { "type": "integer" }, + "number": { "type": "integer" }, + "colorClass": { "type": "string" }, + "sourceRef": { "type": "string", "description": "Reference to sources[].id + location (e.g., 'euclid-heath, Book I, Prop 1')" }, + "notes": { "type": "string" }, + "keywords": { "type": "array", "items": { "type": "string" } }, + "relatedNodes": { "type": "array", "items": { "type": "string" }, "description": "IDs of conceptually related nodes" } + } + } + }, + "edges": { + "type": "array", + "items": { + "type": "object", + "required": ["from", "to"], + "properties": { + "from": { "type": "string" }, + "to": { "type": "string" } + } + } + }, + "colorScheme": { + "type": "object", + "additionalProperties": { + "type": "object", + "properties": { + "fill": { "type": "string" }, + "stroke": { "type": "string" } + } + } + } + } +} diff --git a/generator/build-aristotle-syllogistic.js b/generator/build-aristotle-syllogistic.js new file mode 100644 index 0000000000000000000000000000000000000000..ffdb5d4689ea6929a2fbe6d4e2ce4ce3b5e4c1f4 --- /dev/null +++ b/generator/build-aristotle-syllogistic.js @@ -0,0 +1,355 @@ +#!/usr/bin/env node +/** + * Build Aristotle Syllogistic Logic discourse JSON and Mermaid. + * Based on Prior Analytics: 4 perfect syllogisms, 3 conversion rules, 10 imperfect syllogisms. + * Source: Stanford Encyclopedia of Philosophy, Aristotle's Logic. + */ + +const fs = require('fs'); +const path = require('path'); + +const NODES = [ + { id: "DefAEIO", type: "definition", label: "A, E, I, O: All/No/Some/Some-not", short: "Categorical forms", colorClass: "definition" }, + { id: "DefFig", type: "definition", label: "Three figures: middle term position", short: "Figures 1,2,3", colorClass: "definition" }, + { id: "Econv", type: "axiom", label: "Eab implies Eba (No M is P implies No P is M)", short: "E-conversion", colorClass: "axiom" }, + { id: "Iconv", type: "axiom", label: "Iab implies Iba (Some M is P implies Some P is M)", short: "I-conversion", colorClass: "axiom" }, + { id: "Aconv", type: "axiom", label: "Aab implies Iba (All M is P implies Some P is M)", short: "A-conversion", colorClass: "axiom" }, + { id: "Barbara", type: "axiom", label: "AAA-1: All M is P, All S is M therefore All S is P", short: "Barbara", colorClass: "axiom" }, + { id: "Celarent", type: "axiom", label: "EAE-1: No M is P, All S is M therefore No S is P", short: "Celarent", colorClass: "axiom" }, + { id: "Darii", type: "axiom", label: "AII-1: All M is P, Some S is M therefore Some S is P", short: "Darii", colorClass: "axiom" }, + { id: "Ferio", type: "axiom", label: "EIO-1: No M is P, Some S is M therefore Some S is not P", short: "Ferio", colorClass: "axiom" }, + { id: "Cesare", type: "theorem", label: "EAE-2: No P is M, All S is M therefore No S is P", short: "Cesare", colorClass: "theorem" }, + { id: "Camestres", type: "theorem", label: "AEE-2: All P is M, No S is M therefore No S is P", short: "Camestres", colorClass: "theorem" }, + { id: "Festino", type: "theorem", label: "EIO-2: No P is M, Some S is M therefore Some S is not P", short: "Festino", colorClass: "theorem" }, + { id: "Baroco", type: "theorem", label: "AOO-2: All P is M, Some S is not M therefore Some S is not P", short: "Baroco", colorClass: "theorem" }, + { id: "Darapti", type: "theorem", label: "AAI-3: All M is P, All M is S therefore Some S is P", short: "Darapti", colorClass: "theorem" }, + { id: "Felapton", type: "theorem", label: "EAO-3: No M is P, All M is S therefore Some S is not P", short: "Felapton", colorClass: "theorem" }, + { id: "Disamis", type: "theorem", label: "IAI-3: Some M is P, All M is S therefore Some S is P", short: "Disamis", colorClass: "theorem" }, + { id: "Datisi", type: "theorem", label: "AII-3: All M is P, Some M is S therefore Some S is P", short: "Datisi", colorClass: "theorem" }, + { id: "Bocardo", type: "theorem", label: "OAO-3: Some M is not P, All M is S therefore Some S is not P", short: "Bocardo", colorClass: "theorem" }, + { id: "Ferison", type: "theorem", label: "EIO-3: No M is P, Some M is S therefore Some S is not P", short: "Ferison", colorClass: "theorem" } +]; + +// Dependencies (from → to). Based on Prior Analytics reduction proofs. +const DEPS = { + Barbara: ["DefAEIO", "DefFig"], + Celarent: ["DefAEIO", "DefFig"], + Darii: ["DefAEIO", "DefFig"], + Ferio: ["DefAEIO", "DefFig"], + Cesare: ["Econv", "Celarent"], + Camestres: ["Econv", "Celarent"], + Festino: ["Econv", "Ferio"], + Baroco: ["Barbara"], + Darapti: ["Aconv", "Darii"], + Felapton: ["Aconv", "Ferio"], + Disamis: ["Iconv", "Darii"], + Datisi: ["Aconv", "Darii"], + Bocardo: ["Barbara"], + Ferison: ["Aconv", "Ferio"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "aristotle-syllogistic", + name: "Aristotle Syllogistic Logic", + subject: "logic", + variant: "classical", + description: "Aristotelian categorical syllogistic. Four perfect syllogisms (Barbara, Celarent, Darii, Ferio), three conversion rules, and ten imperfect syllogisms reduced to the perfect ones. Based on Prior Analytics.", + structure: { axioms: 7, definitions: 2, theorems: 10 } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Aristotle Syllogistic Dependency Graph. Programming Framework.", + keywords: ["Aristotle", "syllogism", "categorical logic", "Prior Analytics", "Barbara", "Celarent"] + }, + sources: [ + { id: "aristotle", type: "primary", authors: "Aristotle", title: "Prior Analytics", year: "c. 350 BCE", notes: "Syllogistic theory" }, + { id: "stanford", type: "secondary", authors: "Smith, R.", title: "Aristotle's Logic", url: "https://plato.stanford.edu/entries/aristotle-logic/", notes: "Stanford Encyclopedia" } + ], + nodes: [], + edges: [], + colorScheme: { + axiom: { fill: "#e74c3c", stroke: "#c0392b" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + theorem: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Add nodes +for (const n of NODES) { + discourse.nodes.push({ + id: n.id, + type: n.type, + label: n.label, + shortLabel: n.id, + short: n.short, + colorClass: n.colorClass + }); + for (const dep of DEPS[n.id] || []) { + discourse.edges.push({ from: dep, to: n.id }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +const outPath = path.join(dataDir, "aristotle-syllogistic.json"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote", outPath); + +// Sanitize label for Mermaid +function sanitizeMermaidLabel(s) { + return String(s) + .replace(/→/g, "impl") + .replace(/⊢/g, "|-") + .replace(/∨/g, "or") + .replace(/∧/g, "and") + .replace(/↔/g, "iff") + .replace(/\n/g, " "); +} + +// Generate Mermaid +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || n.label; + const raw = (n.shortLabel || n.id) + " " + (desc.length > 30 ? desc.slice(0, 27) + "..." : desc); + const lbl = sanitizeMermaidLabel(raw).replace(/"/g, '\\"'); + lines.push(` ${n.id}("${lbl}")`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085"); + const axiomIds = nodes.filter(n => n.type === "axiom").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const thmIds = nodes.filter(n => n.type === "theorem").map(n => n.id).join(","); + if (axiomIds) lines.push(` class ${axiomIds} axiom`); + if (defIds) lines.push(` class ${defIds} definition`); + if (thmIds) lines.push(` class ${thmIds} theorem`); + return lines.join("\n"); +} + +function closure(ids) { + const needed = new Set(ids); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +function toMermaidWithCounts(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; +} + +// 3 sections +const sections = [ + { name: "foundations-perfect", ids: ["DefAEIO", "DefFig", "Econv", "Iconv", "Aconv", "Barbara", "Celarent", "Darii", "Ferio"], title: "Foundations and Perfect Syllogisms", desc: "Categorical forms, figures, conversion rules, and the four perfect syllogisms (Barbara, Celarent, Darii, Ferio)" }, + { name: "figure-2", ids: ["Cesare", "Camestres", "Festino", "Baroco"], title: "Figure 2 Syllogisms", desc: "Cesare, Camestres, Festino, Baroco reduced to perfect syllogisms via conversion" }, + { name: "figure-3", ids: ["Darapti", "Felapton", "Disamis", "Datisi", "Bocardo", "Ferison"], title: "Figure 3 Syllogisms", desc: "Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison reduced to perfect syllogisms" } +]; + +const subgraphData = []; +for (const s of sections) { + const filter = closure(s.ids); + const { mermaid: sub, nodes: n, edges: e } = toMermaidWithCounts(filter); + subgraphData.push({ ...s, mermaid: sub, nodes: n, edges: e }); + fs.writeFileSync(path.join(dataDir, `aristotle-syllogistic-${s.name}.mmd`), sub, "utf8"); + console.log("Wrote", path.join(dataDir, `aristotle-syllogistic-${s.name}.mmd`)); +} + +fs.writeFileSync(path.join(dataDir, "aristotle-syllogistic.mmd"), toMermaid(), "utf8"); + +// Generate HTML +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const DISC_DIR = path.join(MATH_DB, "processes", "discrete_mathematics"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Discrete Mathematics / Logic + Source: Aristotle, Prior Analytics +
+
+
+ ← Back to Mathematics Database + Aristotle Syllogistic Index + Aristotle's Logic (Stanford) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Aristotle, Prior Analytics (c. 350 BCE); Stanford Encyclopedia of Philosophy

+
+
+

Dependency Flowchart

+

Note: Arrows mean "depends on" (tail to head).

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Red
Axioms
+
Blue
Definitions
+
Teal
Theorems
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Aristotle
  • syllogism
  • Barbara
  • Celarent
  • Prior Analytics
  • categorical logic
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(path.join(MATH_DB, "processes"))) { + for (const d of subgraphData) { + const html = htmlTemplate( + `Aristotle Syllogistic — ${d.title}`, + d.desc + ". Shows how imperfect syllogisms reduce to perfect ones via conversion.", + d.mermaid, + d.nodes, + d.edges + ); + const fileName = "discrete_mathematics-aristotle-syllogistic-" + d.name; + fs.writeFileSync(path.join(DISC_DIR, fileName + ".html"), html, "utf8"); + console.log("Wrote", path.join(DISC_DIR, fileName + ".html")); + } + const indexHtml = ` + + + + + Aristotle Syllogistic - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Aristotle's Logic (Stanford) +
+ +

Aristotle Syllogistic Logic

+

Categorical syllogistic from Prior Analytics. Four perfect syllogisms (Barbara, Celarent, Darii, Ferio), three conversion rules, and ten imperfect syllogisms reduced to the perfect ones. Split into three views.

+
+ Chart 1 — Foundations and Perfect Syllogisms + Chart 2 — Figure 2 Syllogisms + Chart 3 — Figure 3 Syllogisms +
+
+ +`; + fs.writeFileSync(path.join(DISC_DIR, "discrete_mathematics-aristotle-syllogistic.html"), indexHtml, "utf8"); + console.log("Wrote", path.join(DISC_DIR, "discrete_mathematics-aristotle-syllogistic.html")); +} else { + console.log("MATH_DB not found - skipping HTML generation."); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-combinatorics.js b/generator/build-combinatorics.js new file mode 100644 index 0000000000000000000000000000000000000000..25e319bc91ce552e86dcf686476bd4639fbcac40 --- /dev/null +++ b/generator/build-combinatorics.js @@ -0,0 +1,340 @@ +#!/usr/bin/env node +/** + * Build Combinatorics discourse JSON and Mermaid. + * Counting principles, permutations, combinations, binomial theorem, pigeonhole. + * Based on standard discrete math texts. + */ + +const fs = require('fs'); +const path = require('path'); + +const NODES = [ + { id: "DefFact", type: "definition", label: "Factorial: n! = n(n-1)...1, 0!=1", short: "Factorial", colorClass: "definition" }, + { id: "DefSum", type: "definition", label: "Sum principle: disjoint choices add (OR)", short: "Sum principle", colorClass: "definition" }, + { id: "DefProd", type: "definition", label: "Product principle: sequential choices multiply (AND)", short: "Product principle", colorClass: "definition" }, + { id: "PermNoRep", type: "theorem", label: "P(n,r) = n!/(n-r)! arrangements of r from n", short: "Permutations no rep", colorClass: "theorem" }, + { id: "PermRep", type: "theorem", label: "n^r arrangements of r from n with repetition", short: "Permutations with rep", colorClass: "theorem" }, + { id: "CombNoRep", type: "theorem", label: "C(n,r) = n!/(r!(n-r)!) = P(n,r)/r!", short: "Combinations", colorClass: "theorem" }, + { id: "CombRep", type: "theorem", label: "C(n+r-1,r) ways to choose r from n with rep", short: "Combinations with rep", colorClass: "theorem" }, + { id: "BinomThm", type: "theorem", label: "(a+b)^n = sum C(n,k) a^k b^(n-k)", short: "Binomial theorem", colorClass: "theorem" }, + { id: "Pascal", type: "theorem", label: "C(n,k) = C(n-1,k-1) + C(n-1,k)", short: "Pascal identity", colorClass: "theorem" }, + { id: "Pigeonhole", type: "theorem", label: "n+1 objects in n boxes implies one box has 2+", short: "Pigeonhole principle", colorClass: "theorem" }, + { id: "InclExcl", type: "theorem", label: "|A union B| = |A| + |B| - |A intersect B|", short: "Inclusion-exclusion", colorClass: "theorem" }, + { id: "InclExcl3", type: "theorem", label: "Inclusion-exclusion for 3 sets", short: "Incl-excl 3 sets", colorClass: "theorem" }, + { id: "Derange", type: "theorem", label: "D(n) = n! sum (-1)^k/k! derangements", short: "Derangements", colorClass: "theorem" }, + { id: "Stirling2", type: "theorem", label: "S(n,k) = partitions of n into k nonempty sets", short: "Stirling numbers", colorClass: "theorem" } +]; + +const DEPS = { + PermNoRep: ["DefFact", "DefProd"], + PermRep: ["DefProd"], + CombNoRep: ["PermNoRep", "DefFact"], + CombRep: ["CombNoRep"], + BinomThm: ["CombNoRep"], + Pascal: ["CombNoRep"], + Pigeonhole: ["DefSum"], + InclExcl: ["DefSum"], + InclExcl3: ["InclExcl"], + Derange: ["InclExcl", "PermNoRep"], + Stirling2: ["DefSum", "DefProd"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "combinatorics", + name: "Combinatorics", + subject: "discrete_mathematics", + variant: "classical", + description: "Counting principles: sum and product rules, permutations (with/without repetition), combinations, binomial theorem, pigeonhole principle, inclusion-exclusion, derangements.", + structure: { axioms: 0, definitions: 3, theorems: 11 } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Combinatorics Dependency Graph. Programming Framework.", + keywords: ["combinatorics", "permutations", "combinations", "counting", "binomial theorem"] + }, + sources: [ + { id: "dmoi", type: "primary", title: "Discrete Mathematics: An Open Introduction", url: "https://discrete.openmathbooks.org/dmoi4/sec_counting-combperm.html", notes: "Counting principles" }, + { id: "mathisfun", type: "digital", title: "Combinations and Permutations", url: "https://www.mathsisfun.com/combinatorics/combinations-permutations.html", notes: "Formulas" } + ], + nodes: [], + edges: [], + colorScheme: { + axiom: { fill: "#e74c3c", stroke: "#c0392b" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + theorem: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +for (const n of NODES) { + discourse.nodes.push({ + id: n.id, + type: n.type, + label: n.label, + shortLabel: n.id, + short: n.short, + colorClass: n.colorClass + }); + for (const dep of DEPS[n.id] || []) { + discourse.edges.push({ from: dep, to: n.id }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +const outPath = path.join(dataDir, "combinatorics.json"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote", outPath); + +function sanitizeMermaidLabel(s) { + return String(s) + .replace(/→/g, "impl") + .replace(/⊢/g, "|-") + .replace(/∨/g, "or") + .replace(/∧/g, "and") + .replace(/↔/g, "iff") + .replace(/\n/g, " "); +} + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || n.label; + const raw = (n.shortLabel || n.id) + " " + (desc.length > 30 ? desc.slice(0, 27) + "..." : desc); + const lbl = sanitizeMermaidLabel(raw).replace(/"/g, '\\"'); + lines.push(` ${n.id}("${lbl}")`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085"); + const axiomIds = nodes.filter(n => n.type === "axiom").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const thmIds = nodes.filter(n => n.type === "theorem").map(n => n.id).join(","); + if (axiomIds) lines.push(` class ${axiomIds} axiom`); + if (defIds) lines.push(` class ${defIds} definition`); + if (thmIds) lines.push(` class ${thmIds} theorem`); + return lines.join("\n"); +} + +function closure(ids) { + const needed = new Set(ids); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +function toMermaidWithCounts(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; +} + +const sections = [ + { name: "principles-permutations", ids: ["DefFact", "DefSum", "DefProd", "PermNoRep", "PermRep", "CombNoRep"], title: "Principles and Permutations", desc: "Factorial, sum and product principles, permutations with and without repetition, combinations" }, + { name: "combinations-binomial", ids: ["CombRep", "BinomThm", "Pascal"], title: "Combinations and Binomial Theorem", desc: "Combinations with repetition, binomial theorem, Pascal identity" }, + { name: "advanced-counting", ids: ["Pigeonhole", "InclExcl", "InclExcl3", "Derange", "Stirling2"], title: "Pigeonhole and Inclusion-Exclusion", desc: "Pigeonhole principle, inclusion-exclusion, derangements, Stirling numbers" } +]; + +const subgraphData = []; +for (const s of sections) { + const filter = closure(s.ids); + const { mermaid: sub, nodes: n, edges: e } = toMermaidWithCounts(filter); + subgraphData.push({ ...s, mermaid: sub, nodes: n, edges: e }); + fs.writeFileSync(path.join(dataDir, `combinatorics-${s.name}.mmd`), sub, "utf8"); + console.log("Wrote", path.join(dataDir, `combinatorics-${s.name}.mmd`)); +} + +fs.writeFileSync(path.join(dataDir, "combinatorics.mmd"), toMermaid(), "utf8"); + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEO_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology / Discrete + Source: Standard discrete math texts +
+
+
+ ← Back to Mathematics Database + Combinatorics Index + Counting (Open Math) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Discrete Mathematics: An Open Introduction; standard combinatorics texts

+
+
+

Dependency Flowchart

+

Note: Arrows mean "depends on" (tail to head).

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Red
Axioms
+
Blue
Definitions
+
Teal
Theorems
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • combinatorics
  • permutations
  • combinations
  • binomial theorem
  • counting
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(path.join(MATH_DB, "processes"))) { + for (const d of subgraphData) { + const html = htmlTemplate( + `Combinatorics — ${d.title}`, + d.desc + ". Shows how counting formulas depend on principles and prior results.", + d.mermaid, + d.nodes, + d.edges + ); + const fileName = "geometry_topology-combinatorics-" + d.name; + fs.writeFileSync(path.join(GEO_DIR, fileName + ".html"), html, "utf8"); + console.log("Wrote", path.join(GEO_DIR, fileName + ".html")); + } + const indexHtml = ` + + + + + Combinatorics - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Counting (Open Math) +
+ +

Combinatorics

+

Counting principles: sum and product rules, permutations, combinations, binomial theorem, pigeonhole principle, inclusion-exclusion, derangements. Split into three views.

+
+ Chart 1 — Principles and Permutations + Chart 2 — Combinations and Binomial Theorem + Chart 3 — Pigeonhole and Inclusion-Exclusion +
+
+ +`; + fs.writeFileSync(path.join(GEO_DIR, "geometry_topology-combinatorics.html"), indexHtml, "utf8"); + console.log("Wrote", path.join(GEO_DIR, "geometry_topology-combinatorics.html")); +} else { + console.log("MATH_DB not found - skipping HTML generation."); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-i.js b/generator/build-euclid-book-i.js new file mode 100644 index 0000000000000000000000000000000000000000..66cd2bc180065e0aee43f7be0bb1e829233f3265 --- /dev/null +++ b/generator/build-euclid-book-i.js @@ -0,0 +1,441 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book I discourse JSON and Mermaid. + * Dependencies from David E. Joyce, Clark University: + * https://mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI.html + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPOSITIONS = [ + { n: 1, short: "Equilateral triangle on given line", full: "To construct an equilateral triangle on a given finite straight line" }, + { n: 2, short: "Place line equal to given at point", full: "To place a straight line equal to a given straight line with one end at a given point" }, + { n: 3, short: "Cut off from greater segment equal to less", full: "To cut off from the greater of two given unequal straight lines a straight line equal to the less" }, + { n: 4, short: "SAS congruence", full: "If two triangles have two sides equal to two sides respectively, and the angles contained equal, then bases and remaining angles equal" }, + { n: 5, short: "Base angles of isosceles equal", full: "In isosceles triangles the angles at the base equal one another" }, + { n: 6, short: "Sides opposite equal angles equal", full: "If in a triangle two angles equal one another, then the sides opposite the equal angles also equal one another" }, + { n: 7, short: "Uniqueness of triangle from ends", full: "Given two lines from ends of a line meeting at a point, no other such pair from same ends on same side" }, + { n: 8, short: "SSS congruence", full: "If two triangles have two sides equal to two sides respectively, and the base equal to the base, then the angles contained are equal" }, + { n: 9, short: "Bisect angle", full: "To bisect a given rectilinear angle" }, + { n: 10, short: "Bisect line", full: "To bisect a given finite straight line" }, + { n: 11, short: "Perpendicular from point on line", full: "To draw a straight line at right angles to a given straight line from a given point on it" }, + { n: 12, short: "Perpendicular from point not on line", full: "To draw a straight line perpendicular to a given infinite straight line from a given point not on it" }, + { n: 13, short: "Angles on line sum to two right", full: "If a straight line stands on a straight line, it makes either two right angles or angles whose sum equals two right angles" }, + { n: 14, short: "If angles sum to two right, straight line", full: "If with any straight line, at a point, two lines not on same side make adjacent angles equal to two right, they are in a straight line" }, + { n: 15, short: "Vertical angles equal", full: "If two straight lines cut one another, they make the vertical angles equal to one another" }, + { n: 16, short: "Exterior angle > interior opposite", full: "In any triangle, if one side is produced, the exterior angle is greater than either interior opposite angle" }, + { n: 17, short: "Sum of two angles < two right", full: "In any triangle the sum of any two angles is less than two right angles" }, + { n: 18, short: "Angle opposite greater side greater", full: "In any triangle the angle opposite the greater side is greater" }, + { n: 19, short: "Side opposite greater angle greater", full: "In any triangle the side opposite the greater angle is greater" }, + { n: 20, short: "Triangle inequality", full: "In any triangle the sum of any two sides is greater than the remaining one" }, + { n: 21, short: "Lines from ends within triangle", full: "If from ends of one side two lines meet within the triangle, their sum < sum of other two sides" }, + { n: 22, short: "Construct triangle from three lines", full: "To construct a triangle out of three straight lines which equal three given straight lines" }, + { n: 23, short: "Construct angle equal to given", full: "To construct a rectilinear angle equal to a given rectilinear angle on a given straight line" }, + { n: 24, short: "SAS for greater angle => greater base", full: "If two triangles have two sides equal but one contained angle greater, the base is greater" }, + { n: 25, short: "SAS for greater base => greater angle", full: "If two triangles have two sides equal but base greater, the contained angle is greater" }, + { n: 26, short: "AAS congruence", full: "If two triangles have two angles equal and one side equal, the remaining sides and angle equal" }, + { n: 27, short: "Alternate angles equal => parallel", full: "If a line falling on two lines makes alternate angles equal, the lines are parallel" }, + { n: 28, short: "Exterior = interior opposite => parallel", full: "If exterior angle equals interior opposite, or interior same-side sum to two right, lines parallel" }, + { n: 29, short: "Parallel => alternate angles equal", full: "A line falling on parallel lines makes alternate angles equal, exterior = interior opposite" }, + { n: 30, short: "Transitivity of parallel", full: "Straight lines parallel to the same straight line are also parallel to one another" }, + { n: 31, short: "Draw parallel through point", full: "To draw a straight line through a given point parallel to a given straight line" }, + { n: 32, short: "Exterior angle = sum interior opposite", full: "In any triangle, exterior angle equals sum of two interior opposite; three angles = two right" }, + { n: 33, short: "Joining ends of equal parallel lines", full: "Straight lines which join the ends of equal and parallel straight lines in same directions are equal and parallel" }, + { n: 34, short: "Parallelogram properties", full: "In parallelogrammic areas the opposite sides and angles equal one another, diameter bisects" }, + { n: 35, short: "Parallelograms same base equal", full: "Parallelograms which are on the same base and in the same parallels equal one another" }, + { n: 36, short: "Parallelograms equal bases equal", full: "Parallelograms which are on equal bases and in the same parallels equal one another" }, + { n: 37, short: "Triangles same base equal", full: "Triangles which are on the same base and in the same parallels equal one another" }, + { n: 38, short: "Triangles equal bases equal", full: "Triangles which are on equal bases and in the same parallels equal one another" }, + { n: 39, short: "Equal triangles same base same side", full: "Equal triangles on same base and same side are in the same parallels" }, + { n: 40, short: "Equal triangles equal bases same side", full: "Equal triangles on equal bases and same side are in the same parallels" }, + { n: 41, short: "Parallelogram = 2× triangle", full: "If a parallelogram has same base with triangle and same parallels, parallelogram is double the triangle" }, + { n: 42, short: "Construct parallelogram = triangle", full: "To construct a parallelogram equal to a given triangle in a given rectilinear angle" }, + { n: 43, short: "Complements of parallelogram", full: "In any parallelogram the complements of the parallelograms about the diameter equal one another" }, + { n: 44, short: "Apply parallelogram to line", full: "To a given straight line in a given angle, to apply a parallelogram equal to a given triangle" }, + { n: 45, short: "Construct parallelogram = rectilinear figure", full: "To construct a parallelogram equal to a given rectilinear figure in a given rectilinear angle" }, + { n: 46, short: "Construct square on line", full: "To describe a square on a given straight line" }, + { n: 47, short: "Pythagorean theorem", full: "In right-angled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle" }, + { n: 48, short: "Converse Pythagorean", full: "If in a triangle the square on one side equals the sum of squares on the other two, the angle contained by those sides is right" } +]; + +// Joyce dependency table: { prop: [deps] } +const DEPS = { + 1: ["P1", "P3"], + 2: ["Prop1", "P1", "P2", "P3"], + 3: ["Prop2", "P3"], + 4: ["CN4", "CN5"], + 5: ["Prop3", "Prop4"], + 6: ["Prop3", "Prop4"], + 7: ["Prop5"], + 8: ["Prop7"], + 9: ["Prop1", "Prop3", "Prop8"], + 10: ["Prop1", "Prop4", "Prop9"], + 11: ["Prop1", "Prop3", "Prop8"], + 12: ["Prop8", "Prop10"], + 13: ["Prop11"], + 14: ["Prop13"], + 15: ["Prop13"], + 16: ["Prop3", "Prop4", "Prop10", "Prop15"], + 17: ["Prop13", "Prop16"], + 18: ["Prop3", "Prop5", "Prop16"], + 19: ["Prop5", "Prop18"], + 20: ["Prop3", "Prop5", "Prop19"], + 21: ["Prop16", "Prop20"], + 22: ["Prop3", "Prop20"], + 23: ["Prop8", "Prop22"], + 24: ["Prop3", "Prop4", "Prop5", "Prop19", "Prop23"], + 25: ["Prop4", "Prop24"], + 26: ["Prop3", "Prop4", "Prop16"], + 27: ["Prop16"], + 28: ["Prop13", "Prop15", "Prop27"], + 29: ["Prop13", "Prop15", "Prop27", "P5"], + 30: ["Prop29"], + 31: ["Prop23", "Prop27"], + 32: ["Prop13", "Prop29", "Prop31"], + 33: ["Prop4", "Prop27", "Prop29"], + 34: ["Prop4", "Prop26", "Prop29"], + 35: ["Prop4", "Prop29", "Prop34"], + 36: ["Prop33", "Prop34", "Prop35"], + 37: ["Prop31", "Prop34", "Prop35"], + 38: ["Prop31", "Prop34", "Prop36"], + 39: ["Prop31", "Prop37"], + 40: ["Prop31", "Prop38"], + 41: ["Prop34", "Prop37"], + 42: ["Prop10", "Prop23", "Prop31", "Prop38", "Prop41"], + 43: ["Prop34"], + 44: ["Prop15", "Prop29", "Prop31", "Prop42", "Prop43"], + 45: ["Prop14", "Prop29", "Prop30", "Prop33", "Prop34", "Prop42", "Prop44"], + 46: ["Prop3", "Prop11", "Prop29", "Prop31", "Prop34"], + 47: ["Prop4", "Prop14", "Prop31", "Prop41", "Prop46"], + 48: ["Prop3", "Prop8", "Prop11", "Prop47"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-i", + name: "Euclid's Elements, Book I", + subject: "geometry", + variant: "classical", + description: "The 48 propositions of Book I with dependencies on postulates (P1–P5), common notions (CN1–CN5), and prior propositions. Source: David E. Joyce, Clark University.", + structure: { books: 1, propositions: 48, foundationTypes: ["postulate", "commonNotion"] } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book I Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book I", "plane geometry", "constructions", "Pythagorean theorem"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book I", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookI/bookI.html", notes: "Clark University; dependency table from Guide" }, + { id: "euclid-heath", type: "primary", authors: "Heath, T.L.", title: "The Thirteen Books of Euclid's Elements", year: "1908", edition: "2nd", publisher: "Cambridge University Press", url: "https://archive.org/details/euclidheath00heatiala", notes: "Standard English translation" } + ], + nodes: [], + edges: [], + colorScheme: { + postulate: { fill: "#e74c3c", stroke: "#c0392b" }, + commonNotion: { fill: "#9b59b6", stroke: "#8e44ad" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Add postulates and common notions +const postulates = [ + { id: "P1", label: "Draw a straight line from any point to any point", shortLabel: "Post. 1" }, + { id: "P2", label: "Produce a finite straight line continuously in a straight line", shortLabel: "Post. 2" }, + { id: "P3", label: "Describe a circle with any center and radius", shortLabel: "Post. 3" }, + { id: "P4", label: "All right angles equal one another", shortLabel: "Post. 4" }, + { id: "P5", label: "Parallel postulate: if interior angles < two right, lines meet", shortLabel: "Post. 5" } +]; +const commonNotions = [ + { id: "CN1", label: "Things equal to the same thing are equal to each other", shortLabel: "CN 1" }, + { id: "CN2", label: "If equals are added to equals, the wholes are equal", shortLabel: "CN 2" }, + { id: "CN3", label: "If equals are subtracted from equals, the remainders are equal", shortLabel: "CN 3" }, + { id: "CN4", label: "Things coinciding with one another are equal", shortLabel: "CN 4" }, + { id: "CN5", label: "The whole is greater than the part", shortLabel: "CN 5" } +]; + +for (const p of postulates) { + discourse.nodes.push({ id: p.id, type: "postulate", label: p.label, shortLabel: p.shortLabel, book: 1, number: parseInt(p.id.slice(1)), colorClass: "postulate" }); +} +for (const c of commonNotions) { + discourse.nodes.push({ id: c.id, type: "commonNotion", label: c.label, shortLabel: c.shortLabel, book: 1, number: parseInt(c.id.slice(2)), colorClass: "commonNotion" }); +} + +// Add propositions +for (const prop of PROPOSITIONS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. I.${prop.n}`, + short: prop.short, + book: 1, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n] || []) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +const outPath = path.join(dataDir, "euclid-elements-book-i.json"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote", outPath); + +// Generate Mermaid (full graph - may be large) +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label); + const lbl = (n.shortLabel || n.id) + "\\n" + desc; + lines.push(` ${n.id}["${lbl.replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b"); + lines.push(" classDef commonNotion fill:#9b59b6,color:#fff,stroke:#8e44ad"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const postIds = nodes.filter(n => n.type === "postulate").map(n => n.id).join(","); + const cnIds = nodes.filter(n => n.type === "commonNotion").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + lines.push(` class ${postIds} postulate`); + lines.push(` class ${cnIds} commonNotion`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +// Full graph +const fullMermaid = toMermaid(); +const mermaidPath = path.join(dataDir, "euclid-elements-book-i.mmd"); +fs.writeFileSync(mermaidPath, fullMermaid, "utf8"); +console.log("Wrote", mermaidPath); + +// Subgraphs: include foundations + props in range + all their dependencies (transitive) +function closure(propMin, propMax) { + const needed = new Set(); + for (let i = propMin; i <= propMax; i++) needed.add(`Prop${i}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => n.type !== "proposition" || needed.has(n.id); +} +function toMermaidWithCounts(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; +} +const subgraphData = []; +const sections = [ + { name: "props-1-10", min: 1, max: 10, title: "Propositions 1–10", desc: "Foundations, SAS, SSS, bisections, perpendiculars" }, + { name: "props-11-20", min: 11, max: 20, title: "Propositions 11–20", desc: "Right angles, straight lines, vertical angles, triangle exterior, triangle inequality" }, + { name: "props-21-30", min: 21, max: 30, title: "Propositions 21–30", desc: "Lines within triangle, construct triangle/angle, parallel lines" }, + { name: "props-31-41", min: 31, max: 41, title: "Propositions 31–41", desc: "Parallelograms, triangles, areas" }, + { name: "props-42-48", min: 42, max: 48, title: "Propositions 42–48", desc: "Constructions, Pythagorean theorem" } +]; +for (const s of sections) { + const { mermaid: sub, nodes: n, edges: e } = toMermaidWithCounts(closure(s.min, s.max)); + subgraphData.push({ ...s, mermaid: sub, nodes: n, edges: e }); + const subPath = path.join(dataDir, `euclid-elements-book-i-${s.name}.mmd`); + fs.writeFileSync(subPath, sub, "utf8"); + console.log("Wrote", subPath); +} + +// Generate HTML pages for Mathematics Processes Database +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid Book I Index + Euclid's Elements Book I (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book I (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+

Note: Arrows mean "depends on" (tail → head). Edge crossing can create illusions of connections between adjacent nodes—e.g., I.47 and I.40 have no direct dependency; both depend on I.31 among others.

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Red
Postulates
+
Purple
Common Notions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book I
  • axioms
  • postulates
  • propositions
  • geometry
  • Pythagorean theorem
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + for (const d of subgraphData) { + const html = htmlTemplate( + `Euclid's Elements Book I — ${d.title}`, + `Dependency graph for ${d.title} of Euclid's Elements Book I. ${d.desc}. Shows how propositions depend on postulates (P1–P5), common notions (CN1–CN5), and prior propositions.`, + d.mermaid, + d.nodes, + d.edges + ); + const fileName = "geometry_topology-euclid-elements-book-i-" + d.name; + fs.writeFileSync(path.join(GEOM_DIR, fileName + ".html"), html, "utf8"); + console.log("Wrote", path.join(GEOM_DIR, fileName + ".html")); + } + // Index page + const indexHtml = ` + + + + + Euclid's Elements Book I - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements Book I (Joyce) +
+ +

Euclid's Elements, Book I

+

Full dependency graph of all 48 propositions. Dependencies from David E. Joyce, Clark University. Split into five views for clarity.

+
+ Propositions 1–10 — Foundations, SAS, SSS, bisections, perpendiculars + Propositions 11–20 — Right angles, straight lines, vertical angles, triangle exterior, triangle inequality + Propositions 21–30 — Lines within triangle, construct triangle/angle, parallel lines + Propositions 31–41 — Parallelograms, triangles, areas + Propositions 42–48 — Constructions, Pythagorean theorem +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-i.html"), indexHtml, "utf8"); + console.log("Wrote", path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-i.html")); +} else { + console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation. Set MATH_DB or ensure copernicus-web-public is available."); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-ii.js b/generator/build-euclid-book-ii.js new file mode 100644 index 0000000000000000000000000000000000000000..702898b841037123fc1e95bbdc9d947692e426d3 --- /dev/null +++ b/generator/build-euclid-book-ii.js @@ -0,0 +1,298 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book II discourse JSON and Mermaid. + * Dependencies from David E. Joyce, Clark University: + * https://mathcs.clarku.edu/~djoyce/java/elements/bookII/bookII.html + * + * Book II: 14 propositions on geometric algebra (rectangles, squares). + * Props 1-10 logically independent within Book II; 11-14 depend on 6, 4, 7, 5. + * All depend on Book I (right angles, parallels, areas). + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPOSITIONS = [ + { n: 1, short: "Rectangle = sum of rectangles", full: "If one line is cut into segments, rectangle by whole equals sum of rectangles by each segment" }, + { n: 2, short: "Sum of rectangles = square on whole", full: "If a line is cut at random, sum of rectangles by whole and each segment equals square on whole" }, + { n: 3, short: "Rectangle = rectangle + square", full: "If a line is cut at random, rectangle by whole and one segment equals rectangle by segments plus square on that segment" }, + { n: 4, short: "Square on whole = squares + 2×rectangle", full: "If a line is cut at random, square on whole equals squares on segments plus twice rectangle contained by segments" }, + { n: 5, short: "Unequal segments: rectangle + square = square on half", full: "If a line cut into equal and unequal segments, rectangle by unequal segments plus square on difference equals square on half" }, + { n: 6, short: "Bisected + added: rectangle + square = square", full: "If a line bisected and added to, rectangle by whole-with-added and added plus square on half equals square on half-plus-added" }, + { n: 7, short: "Square on whole + square on segment", full: "If a line cut at random, square on whole plus square on one segment equals twice rectangle by whole and segment plus square on remainder" }, + { n: 8, short: "Four times rectangle + square", full: "If a line cut at random, four times rectangle by whole and one segment plus square on remainder equals square on whole-plus-segment" }, + { n: 9, short: "Unequal segments: sum of squares", full: "If a line cut into equal and unequal segments, sum of squares on unequal segments is double sum of square on half and square on difference" }, + { n: 10, short: "Bisected + added: sum of squares", full: "If a line bisected and added to, square on whole-with-added plus square on added equals double sum of square on half and square on half-plus-added" }, + { n: 11, short: "Cut line: rectangle = square (golden section)", full: "To cut a given line so that rectangle by whole and one segment equals square on remaining segment" }, + { n: 12, short: "Obtuse triangle: law of cosines", full: "In obtuse-angled triangles, square on side opposite obtuse angle greater than sum of squares on sides containing it" }, + { n: 13, short: "Acute triangle: law of cosines", full: "In acute-angled triangles, square on side opposite acute angle less than sum of squares on sides containing it" }, + { n: 14, short: "Construct square = rectilinear figure", full: "To construct a square equal to a given rectilinear figure" } +]; + +// Joyce: within Book II only. 6→11, 4→12, 7→13, 5→14. All depend on Book I. +const DEPS = { + 1: ["Def1"], + 2: ["Def1"], + 3: ["Def1"], + 4: ["Def1"], + 5: ["Def1", "Def2"], + 6: ["Def1", "Def2"], + 7: ["Def1"], + 8: ["Def1"], + 9: ["Def1"], + 10: ["Def1"], + 11: ["Prop6"], + 12: ["Prop4"], + 13: ["Prop7"], + 14: ["Prop5"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-ii", + name: "Euclid's Elements, Book II", + subject: "geometry", + variant: "classical", + description: "The 14 propositions of Book II on geometric algebra (rectangles, squares). Props 1-10 are logically independent within Book II; 11-14 depend on 6, 4, 7, 5. All depend on Book I. Source: David E. Joyce, Clark University.", + structure: { books: 2, propositions: 14, foundationTypes: ["definition"] } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book II Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book II", "geometric algebra", "rectangles", "squares", "golden section", "quadrature"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book II", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookII/bookII.html", notes: "Clark University; dependency table from Logical structure" }, + { id: "euclid-heath", type: "primary", authors: "Heath, T.L.", title: "The Thirteen Books of Euclid's Elements", year: "1908", edition: "2nd", publisher: "Cambridge University Press", url: "https://archive.org/details/euclidheath00heatiala", notes: "Standard English translation" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Add Book I foundation (cross-book reference) +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" } +); + +// Add definitions +discourse.nodes.push( + { id: "Def1", type: "definition", label: "Rectangle contained by two straight lines containing the right angle", shortLabel: "Def. II.1", book: 2, number: 1, colorClass: "definition" }, + { id: "Def2", type: "definition", label: "Gnomon: parallelogram about diameter with two complements", shortLabel: "Def. II.2", book: 2, number: 2, colorClass: "definition" } +); + +// Add propositions +for (const prop of PROPOSITIONS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. II.${prop.n}`, + short: prop.short, + book: 2, + number: prop.n, + colorClass: "proposition" + }); + discourse.edges.push({ from: "BookI", to: `Prop${prop.n}` }); + for (const dep of DEPS[prop.n] || []) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +const outPath = path.join(dataDir, "euclid-elements-book-ii.json"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote", outPath); + +// Generate Mermaid +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${defIds} definition`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => n.type !== "proposition" || needed.has(n.id); +} + +function toMermaidWithCounts(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; +} + +// Full graph (Book II is small - 16 nodes) +const fullMermaid = toMermaid(); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-ii.mmd"), fullMermaid, "utf8"); +console.log("Wrote", path.join(dataDir, "euclid-elements-book-ii.mmd")); + +// Single HTML page (Book II fits in one view) +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book II (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book II (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I (foundation)
+
Blue
Definitions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book II
  • geometric algebra
  • rectangles
  • squares
  • golden section
  • quadrature
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + const { mermaid, nodes, edges } = toMermaidWithCounts(() => true); + const html = htmlTemplate( + "Euclid's Elements Book II", + "Dependency graph for all 14 propositions of Euclid's Elements Book II. Geometric algebra: rectangles, squares, distributive law. Props 1-10 independent within Book II; 11-14 depend on 6, 4, 7, 5. All depend on Book I.", + mermaid, + nodes, + edges + ); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-ii.html"), html, "utf8"); + console.log("Wrote", path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-ii.html")); +} else { + console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation."); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-iii.js b/generator/build-euclid-book-iii.js new file mode 100644 index 0000000000000000000000000000000000000000..6ade2471e9371adf216bfa7a6a6b33a3ad6725fd --- /dev/null +++ b/generator/build-euclid-book-iii.js @@ -0,0 +1,442 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book III discourse JSON and Mermaid charts. + * 11 definitions, 37 propositions. All depend on Book I. III.35 uses II.5, I.47. + * Source: David E. Joyce, Clark University. + * + * Charts: ~16 nodes each. Chart 1: Defs + Props 1-5. Chart 2: Props 6-20. Chart 3: Props 21-37. + */ + +const fs = require('fs'); +const path = require('path'); + +const DEFS = [ + { n: 1, short: "Equal circles", full: "Equal circles are those with equal radii" }, + { n: 2, short: "Tangent", full: "A straight line touches a circle if it meets but does not cut it" }, + { n: 3, short: "Circles touching", full: "Circles touch one another if they meet but do not cut" }, + { n: 4, short: "Equally distant from center", full: "Lines equally distant from center when perpendiculars from center equal" }, + { n: 5, short: "Greater distance", full: "Greater distance when greater perpendicular falls" }, + { n: 6, short: "Segment of circle", full: "Segment of circle: figure contained by straight line and circumference" }, + { n: 7, short: "Angle of segment", full: "Angle of segment: contained by straight line and circumference" }, + { n: 8, short: "Angle in segment", full: "Angle in segment: contained by straight lines joining circumference" }, + { n: 9, short: "Angle stands on circumference", full: "Angle stands on circumference when lines cut off that circumference" }, + { n: 10, short: "Sector", full: "Sector: figure contained by two radii and circumference between them" }, + { n: 11, short: "Similar segments", full: "Similar segments are those which admit equal angles" } +]; + +const PROPS = [ + { n: 1, short: "Find center of circle", full: "To find the center of a given circle" }, + { n: 2, short: "Chord falls within circle", full: "Straight line joining two points on circumference falls within circle" }, + { n: 3, short: "Diameter bisects chord at right angles", full: "If diameter bisects chord not through center, it cuts at right angles" }, + { n: 4, short: "Non-diameters do not bisect", full: "Two non-diameters cutting one another do not bisect" }, + { n: 5, short: "Cutting circles do not share center", full: "If two circles cut one another, they do not have same center" }, + { n: 6, short: "Touching circles do not share center", full: "If two circles touch, they do not have same center" }, + { n: 7, short: "Greatest/shortest from point on diameter", full: "From point on diameter: greatest through center, least is remainder" }, + { n: 8, short: "Lines from point outside circle", full: "From point outside: through center greatest; between point and diameter least" }, + { n: 9, short: "Three equal lines imply center", full: "If more than two equal lines fall from point on circle, point is center" }, + { n: 10, short: "Circles cut at most two points", full: "A circle does not cut another at more than two points" }, + { n: 11, short: "Internally touching circles", full: "Line joining centers of internally touching circles passes through contact" }, + { n: 12, short: "Externally touching circles", full: "Line joining centers of externally touching circles passes through contact" }, + { n: 13, short: "Circles touch at most one point", full: "Circle does not touch another at more than one point" }, + { n: 14, short: "Equal chords equally distant", full: "Equal chords equally distant from center, and conversely" }, + { n: 15, short: "Diameter greatest", full: "Diameter greatest; nearer to center greater than more remote" }, + { n: 16, short: "Tangent at end of diameter", full: "Perpendicular at end of diameter falls outside; horn angle" }, + { n: 17, short: "Draw tangent from point", full: "From given point to draw straight line touching given circle" }, + { n: 18, short: "Radius to tangent perpendicular", full: "Radius to point of contact perpendicular to tangent" }, + { n: 19, short: "Perpendicular from contact to center", full: "Perpendicular from contact to tangent passes through center" }, + { n: 20, short: "Angle at center double angle at circumference", full: "Angle at center double angle at circumference on same base" }, + { n: 21, short: "Angles in same segment equal", full: "In a circle angles in same segment equal one another" }, + { n: 22, short: "Opposite angles of cyclic quadrilateral", full: "Sum of opposite angles of cyclic quadrilateral equals two right angles" }, + { n: 23, short: "Same line, two similar unequal segments", full: "On same line cannot construct two similar unequal segments on same side" }, + { n: 24, short: "Similar segments on equal lines equal", full: "Similar segments on equal straight lines equal one another" }, + { n: 25, short: "Complete circle from segment", full: "Given segment of circle, describe complete circle" }, + { n: 26, short: "Equal angles stand on equal arcs", full: "In equal circles equal angles stand on equal circumferences" }, + { n: 27, short: "Equal arcs imply equal angles", full: "In equal circles angles on equal circumferences equal one another" }, + { n: 28, short: "Equal chords cut off equal arcs", full: "In equal circles equal chords cut off equal circumferences" }, + { n: 29, short: "Equal arcs imply equal chords", full: "In equal circles chords cutting equal circumferences are equal" }, + { n: 30, short: "Bisect given circumference", full: "To bisect a given circumference" }, + { n: 31, short: "Angle in semicircle is right", full: "Angle in semicircle right; in greater segment less; in less greater" }, + { n: 32, short: "Tangent-chord angle equals alternate segment", full: "Angle with tangent equals angle in alternate segment" }, + { n: 33, short: "Segment admitting given angle", full: "On given line describe segment admitting angle equal to given" }, + { n: 34, short: "Cut off segment admitting angle", full: "From given circle cut off segment admitting given angle" }, + { n: 35, short: "Rectangle from chord segments equal", full: "If chords cut one another, rectangle by segments of one equals other" }, + { n: 36, short: "Tangent squared = secant × external", full: "From point outside: tangent squared = secant × external part" }, + { n: 37, short: "Converse: tangent if rectangle = square", full: "If rectangle equals square on line, that line touches circle" } +]; + +// Joyce: III.1 uses I.10, I.11, I.Def.15, I.8, I.Def.10. III.9, III.10 use III.1 cor. III.16 cor → III.17, III.33, III.37. III.35 uses III.1, I.12, III.3, II.5, I.47. +// Simplified: all depend on Book I. Key within-Book: 1→2,3; 3→4,14,15,35; 16→17,33,37; 20→21,31; 21→22; 31→32; 32→33,34; 35→36; 36→37. +const DEPS = { + 1: ["BookI"], + 2: ["BookI", "Prop1"], + 3: ["BookI", "Prop1"], + 4: ["BookI", "Prop3"], + 5: ["BookI"], + 6: ["BookI"], + 7: ["BookI"], + 8: ["BookI"], + 9: ["BookI", "Prop1"], + 10: ["BookI", "Prop1"], + 11: ["BookI"], + 12: ["BookI"], + 13: ["BookI"], + 14: ["BookI", "Prop3"], + 15: ["BookI", "Prop3"], + 16: ["BookI"], + 17: ["BookI", "Prop16"], + 18: ["BookI", "Prop1"], + 19: ["BookI", "Prop18"], + 20: ["BookI", "Prop1"], + 21: ["BookI", "Prop20"], + 22: ["BookI", "Prop21"], + 23: ["BookI"], + 24: ["BookI", "Prop23"], + 25: ["BookI"], + 26: ["BookI"], + 27: ["BookI", "Prop26"], + 28: ["BookI", "Prop27"], + 29: ["BookI", "Prop28"], + 30: ["BookI"], + 31: ["BookI", "Prop20"], + 32: ["BookI", "Prop31"], + 33: ["BookI", "Prop16", "Prop32"], + 34: ["BookI", "Prop32"], + 35: ["BookI", "Prop1", "Prop3", "PropII5"], + 36: ["BookI", "Prop1", "Prop18", "Prop35"], + 37: ["BookI", "Prop1", "Prop16", "Prop32", "Prop36"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-iii", + name: "Euclid's Elements, Book III", + subject: "geometry", + variant: "classical", + description: "Theory of circles: 11 definitions, 37 propositions. All depend on Book I. III.35 uses II.5. Source: David E. Joyce.", + structure: { books: 3, definitions: 11, propositions: 37, foundationTypes: ["definition", "foundation"] } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book III Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book III", "circles", "chords", "tangents"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book III", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookIII/bookIII.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Cross-book foundations +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "PropII5", type: "foundation", label: "Prop. II.5 — Rectangle + square = square on half", shortLabel: "Prop. II.5", short: "From Book II", book: 2, colorClass: "foundation" } +); + +// Definitions +for (const d of DEFS) { + discourse.nodes.push({ + id: `Def${d.n}`, + type: "definition", + label: d.full, + shortLabel: `Def. III.${d.n}`, + short: d.short, + book: 3, + number: d.n, + colorClass: "definition" + }); + discourse.edges.push({ from: "BookI", to: `Def${d.n}` }); +} + +// Propositions +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. III.${prop.n}`, + short: prop.short, + book: 3, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n] || ["BookI"]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-iii.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-iii.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${defIds} definition`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + needed.add("BookI"); + needed.add("PropII5"); + for (const d of DEFS) needed.add(`Def${d.n}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book III Index + Euclid's Elements Book III (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book III (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, Prop II.5 (foundation)
+
Blue
Definitions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book III
  • circles
  • chords
  • tangents
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + // Chart 1: Book I + Prop II.5 + Defs 1-11 + Props 1-5 = 2+11+5 = 18 (slightly over) + const filter1 = closure(5); + const nodes1 = discourse.nodes.filter(filter1); + const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); + const m1 = toMermaid(filter1); + const html1 = htmlTemplate( + "Euclid's Elements Book III — Propositions 1–5", + "Dependency graph for definitions and propositions 1–5 of Book III. Theory of circles: center, chords, diameters. All depend on Book I.", + m1, + nodes1.length, + edges1.length + ); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii-props-1-5.html"), html1, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iii-props-1-5.html"); + + // Chart 2: Props 6-20 + const filter2 = closure(20); + const nodes2 = discourse.nodes.filter(filter2); + const edges2 = discourse.edges.filter(e => filter2({ id: e.from }) && filter2({ id: e.to })); + const m2 = toMermaid(filter2); + const html2 = htmlTemplate( + "Euclid's Elements Book III — Propositions 6–20", + "Dependency graph for propositions 6–20. Touching circles, distances, tangent at diameter, angles at center and circumference.", + m2, + nodes2.length, + edges2.length + ); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii-props-6-20.html"), html2, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iii-props-6-20.html"); + + // Chart 3: Props 21-37 + const filter3 = () => true; + const m3 = toMermaid(filter3); + const nodes3 = discourse.nodes; + const edges3 = discourse.edges; + const html3 = htmlTemplate( + "Euclid's Elements Book III — Propositions 21–37", + "Dependency graph for propositions 21–37. Cyclic quadrilaterals, segments, chord rectangle theorem (III.35 uses Prop II.5), tangent-secant.", + m3, + nodes3.length, + edges3.length + ); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii-props-21-37.html"), html3, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iii-props-21-37.html"); +} else { + console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation."); +} + +// Book III index page +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book III - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book III (Joyce) +
+ +

Euclid's Elements Book III

+

Theory of circles: 11 definitions, 37 propositions. Chords, tangents, angles at center and circumference. All depend on Book I. Prop III.35 uses Prop II.5. Dependency charts split into three views (~16 nodes each).

+
+ Propositions 1–5 Defs + center, chords, diameters + Propositions 6–20 Touching circles, tangent, angles + Propositions 21–37 Cyclic quadrilaterals, chord rectangle, tangent-secant +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iii.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iii.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-iv.js b/generator/build-euclid-book-iv.js new file mode 100644 index 0000000000000000000000000000000000000000..9cf565c815dd5deba5adbf6fb810cb8fdae4d6d7 --- /dev/null +++ b/generator/build-euclid-book-iv.js @@ -0,0 +1,381 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book IV discourse JSON and Mermaid charts. + * 7 definitions, 16 propositions. Inscribed/circumscribed figures. + * Joyce: IV.10←IV.1,IV.5,II.11; IV.11←IV.2,IV.10; IV.12←IV.11; IV.16←IV.1,IV.2,IV.11. + * All rely on Books I and III. + * + * Charts: 2. Chart 1: Defs + Props 1-5. Chart 2: Props 6-16. + */ + +const fs = require('fs'); +const path = require('path'); + +const DEFS = [ + { n: 1, short: "Inscribe in circle", full: "Rectilinear figure inscribed in circle when each vertex on circumference" }, + { n: 2, short: "Circumscribe about circle", full: "Figure circumscribed about circle when each side touches circle" }, + { n: 3, short: "Inscribe circle in figure", full: "Circle inscribed in figure when each side touches circle" }, + { n: 4, short: "Circumscribe circle about figure", full: "Circle circumscribed about figure when each vertex on circumference" }, + { n: 5, short: "Inscribe in figure", full: "Figure inscribed in figure when each vertex of inner on sides of outer" }, + { n: 6, short: "Circumscribe about figure", full: "Figure circumscribed about figure when each side of outer touches inner" }, + { n: 7, short: "Inscribe line in circle", full: "Straight line inscribed in circle when its ends on circumference" } +]; + +const PROPS = [ + { n: 1, short: "Fit line in circle", full: "To fit into given circle a straight line equal to given, not greater than diameter" }, + { n: 2, short: "Inscribe triangle in circle", full: "To inscribe in given circle a triangle equiangular with given triangle" }, + { n: 3, short: "Circumscribe triangle about circle", full: "To circumscribe about given circle a triangle equiangular with given" }, + { n: 4, short: "Inscribe circle in triangle", full: "To inscribe a circle in a given triangle" }, + { n: 5, short: "Circumscribe circle about triangle", full: "To circumscribe a circle about a given triangle" }, + { n: 6, short: "Inscribe square in circle", full: "To inscribe a square in a given circle" }, + { n: 7, short: "Circumscribe square about circle", full: "To circumscribe a square about a given circle" }, + { n: 8, short: "Inscribe circle in square", full: "To inscribe a circle in a given square" }, + { n: 9, short: "Circumscribe circle about square", full: "To circumscribe a circle about a given square" }, + { n: 10, short: "Isosceles triangle, base angles double", full: "To construct isosceles triangle with each base angle double the remaining" }, + { n: 11, short: "Inscribe pentagon in circle", full: "To inscribe an equilateral equiangular pentagon in a given circle" }, + { n: 12, short: "Circumscribe pentagon about circle", full: "To circumscribe an equilateral equiangular pentagon about a given circle" }, + { n: 13, short: "Inscribe circle in pentagon", full: "To inscribe a circle in a given equilateral equiangular pentagon" }, + { n: 14, short: "Circumscribe circle about pentagon", full: "To circumscribe a circle about a given equilateral equiangular pentagon" }, + { n: 15, short: "Inscribe hexagon in circle", full: "To inscribe an equilateral equiangular hexagon in a given circle" }, + { n: 16, short: "Inscribe 15-gon in circle", full: "To inscribe an equilateral equiangular fifteen-angled figure in a given circle" } +]; + +// Joyce: IV.10←IV.1,IV.5,II.11; IV.11←IV.2,IV.10; IV.12←IV.11; IV.16←IV.1,IV.2,IV.11. All use Book I, Book III. +const DEPS = { + 1: ["BookI", "BookIII"], + 2: ["BookI", "BookIII"], + 3: ["BookI", "BookIII"], + 4: ["BookI", "BookIII"], + 5: ["BookI", "BookIII"], + 6: ["BookI", "BookIII", "Prop1"], // inscribe square uses IV.1 + 7: ["BookI", "BookIII", "Prop6"], + 8: ["BookI", "BookIII", "Prop7"], + 9: ["BookI", "BookIII", "Prop8"], + 10: ["BookI", "BookIII", "Prop1", "Prop5", "PropII11"], + 11: ["BookI", "BookIII", "Prop2", "Prop10"], + 12: ["BookI", "BookIII", "Prop11"], + 13: ["BookI", "BookIII", "Prop11"], + 14: ["BookI", "BookIII", "Prop11"], + 15: ["BookI", "BookIII", "Prop1"], + 16: ["BookI", "BookIII", "Prop1", "Prop2", "Prop11"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-iv", + name: "Euclid's Elements, Book IV", + subject: "geometry", + variant: "classical", + description: "Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. IV.10 uses II.11. Source: David E. Joyce.", + structure: { books: 4, definitions: 7, propositions: 16, foundationTypes: ["definition", "foundation"] } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book IV Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book IV", "inscribed", "circumscribed", "pentagon", "hexagon"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book IV", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookIV/bookIV.html", notes: "Clark University; Logical structure" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Cross-book foundations +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "BookIII", type: "foundation", label: "Book III — Theory of circles", shortLabel: "Book III", short: "Foundation", book: 3, colorClass: "foundation" }, + { id: "PropII11", type: "foundation", label: "Prop. II.11 — Golden section", shortLabel: "Prop. II.11", short: "From Book II", book: 2, colorClass: "foundation" } +); + +// Definitions +for (const d of DEFS) { + discourse.nodes.push({ + id: `Def${d.n}`, + type: "definition", + label: d.full, + shortLabel: `Def. IV.${d.n}`, + short: d.short, + book: 4, + number: d.n, + colorClass: "definition" + }); + discourse.edges.push({ from: "BookI", to: `Def${d.n}` }); + discourse.edges.push({ from: "BookIII", to: `Def${d.n}` }); +} + +// Propositions +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. IV.${prop.n}`, + short: prop.short, + book: 4, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-iv.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-iv.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${defIds} definition`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + needed.add("BookI"); + needed.add("BookIII"); + needed.add("PropII11"); + for (const d of DEFS) needed.add(`Def${d.n}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book IV Index + Euclid's Elements Book IV (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book IV (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, Book III, Prop II.11 (foundation)
+
Blue
Definitions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book IV
  • inscribed
  • circumscribed
  • pentagon
  • hexagon
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + // Chart 1: Defs + Props 1-5 (triangle constructions) + const filter1 = closure(5); + const nodes1 = discourse.nodes.filter(filter1); + const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); + const m1 = toMermaid(filter1); + const html1 = htmlTemplate( + "Euclid's Elements Book IV — Propositions 1–5", + "Dependency graph for definitions and propositions 1–5. Inscribe/circumscribe triangle and circle. All depend on Book I and Book III.", + m1, + nodes1.length, + edges1.length + ); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iv-props-1-5.html"), html1, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iv-props-1-5.html"); + + // Chart 2: Props 6-16 (square, pentagon, hexagon, 15-gon) + const filter2 = () => true; + const m2 = toMermaid(filter2); + const html2 = htmlTemplate( + "Euclid's Elements Book IV — Propositions 6–16", + "Dependency graph for propositions 6–16. Square, pentagon (IV.10 uses Prop II.11), hexagon, 15-gon. IV.11←IV.2,IV.10; IV.16←IV.1,IV.2,IV.11.", + m2, + discourse.nodes.length, + discourse.edges.length + ); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iv-props-6-16.html"), html2, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iv-props-6-16.html"); +} else { + console.log("MATH_DB not found at", GEOM_DIR, "- skipping HTML generation."); +} + +// Book IV index page +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book IV - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book IV (Joyce) +
+ +

Euclid's Elements Book IV

+

Inscribed and circumscribed figures: triangle, square, pentagon, hexagon, 15-gon. All depend on Books I and III. Prop IV.10 uses Prop II.11 (golden section). Dependency charts split into two views.

+
+ Propositions 1–5 Defs + triangle, circle + Propositions 6–16 Square, pentagon, hexagon, 15-gon +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-iv.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-iv.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-ix.js b/generator/build-euclid-book-ix.js new file mode 100644 index 0000000000000000000000000000000000000000..65594e39be22b9978c2c6c6182670a2f8e9b51e1 --- /dev/null +++ b/generator/build-euclid-book-ix.js @@ -0,0 +1,314 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book IX discourse JSON and Mermaid charts. + * 36 propositions. Primes, perfect numbers, odd/even. Depends on Books VII and VIII. Source: David E. Joyce. + * + * Charts: 3. Chart 1: Props 1-12. Chart 2: Props 13-24. Chart 3: Props 25-36. + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPS = [ + { n: 1, short: "Similar plane product square", full: "Two similar plane numbers multiplied: product is square" }, + { n: 2, short: "Product square: similar plane", full: "Two numbers product square: they are similar plane" }, + { n: 3, short: "Cube times itself", full: "Cubic number multiplied by itself: product is cube" }, + { n: 4, short: "Cube times cube", full: "Cubic times cubic: product is cube" }, + { n: 5, short: "Cube times any makes cube", full: "If cube times any makes cube, the multiplied is cubic" }, + { n: 6, short: "Number times itself cubic", full: "If number times itself makes cubic, it is cubic" }, + { n: 7, short: "Composite times any: solid", full: "Composite times any: product is solid" }, + { n: 8, short: "Continued proportion from unit", full: "Numbers from unit in continued proportion: 3rd square, 4th cube, 7th both" }, + { n: 9, short: "Second square: all square", full: "If second from unit square, all square; if cubic, all cubic" }, + { n: 10, short: "Second not square", full: "If second not square, only 3rd and every other square; similar for cube" }, + { n: 11, short: "Less measures greater", full: "Continued proportion from unit: less measures greater" }, + { n: 12, short: "Prime measures last", full: "If prime measures last, it measures second from unit" }, + { n: 13, short: "Second prime: only those measure", full: "Continued proportion, second prime: only proportional numbers measure last" }, + { n: 14, short: "Least measured by primes", full: "Least measured by given primes: not measured by any other prime" }, + { n: 15, short: "Three in proportion", full: "Three least in ratio: sum of any two prime to remainder" }, + { n: 16, short: "Relatively prime: no third", full: "Two relatively prime: no third as first to second" }, + { n: 17, short: "Extremes prime: no extension", full: "Continued proportion, extremes prime: last not to any as first to second" }, + { n: 18, short: "Third proportional", full: "Given two numbers, investigate if third proportional exists" }, + { n: 19, short: "Fourth proportional", full: "Given three numbers, investigate when fourth proportional exists" }, + { n: 20, short: "Infinitude of primes", full: "Prime numbers are more than any assigned multitude" }, + { n: 21, short: "Sum of evens even", full: "Sum of even numbers is even" }, + { n: 22, short: "Sum of odds (even count) even", full: "Sum of odd numbers, even multitude: sum even" }, + { n: 23, short: "Sum of odds (odd count) odd", full: "Sum of odd numbers, odd multitude: sum odd" }, + { n: 24, short: "Even minus even", full: "Even minus even: remainder even" }, + { n: 25, short: "Even minus odd", full: "Even minus odd: remainder odd" }, + { n: 26, short: "Odd minus odd", full: "Odd minus odd: remainder even" }, + { n: 27, short: "Odd minus even", full: "Odd minus even: remainder odd" }, + { n: 28, short: "Odd times even", full: "Odd times even: product even" }, + { n: 29, short: "Odd times odd", full: "Odd times odd: product odd" }, + { n: 30, short: "Odd measures even", full: "Odd measuring even: measures half" }, + { n: 31, short: "Odd prime to double", full: "Odd relatively prime to any: also prime to its double" }, + { n: 32, short: "Powers of 2", full: "Numbers doubled from 2: even-times even only" }, + { n: 33, short: "Half odd", full: "Number with half odd: even-times odd only" }, + { n: 34, short: "Neither", full: "Number neither: both even-times even and even-times odd" }, + { n: 35, short: "Geometric series", full: "Continued proportion: (second−first):first = (last−first):sum of rest" }, + { n: 36, short: "Perfect numbers", full: "If sum of powers of 2 is prime, product with last is perfect" } +]; + +const DEPS = {}; +for (let i = 1; i <= 36; i++) DEPS[i] = ["BookVII", "BookVIII"]; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-ix", + name: "Euclid's Elements, Book IX", + subject: "number_theory", + variant: "classical", + description: "Primes, perfect numbers, odd/even. 36 propositions. Depends on Books VII and VIII. Source: David E. Joyce.", + structure: { books: 9, propositions: 36, foundationTypes: ["foundation"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book IX Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book IX", "prime", "perfect", "odd", "even"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book IX", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookIX/bookIX.html", notes: "Clark University; IX.20 infinitude of primes" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookVII", type: "foundation", label: "Book VII — Number theory", shortLabel: "Book VII", short: "Foundation", book: 7, colorClass: "foundation" }, + { id: "BookVIII", type: "foundation", label: "Book VIII — Continued proportions", shortLabel: "Book VIII", short: "Foundation", book: 8, colorClass: "foundation" } +); + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. IX.${prop.n}`, + short: prop.short, + book: 9, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-ix.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-ix.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(["BookVII", "BookVIII"]); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Number Theory + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book IX Index + Euclid's Elements Book IX (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book IX (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book VII, Book VIII (foundation)
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book IX
  • prime
  • perfect
  • odd
  • even
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + [[12, "1–12", "Squares, cubes, continued proportion from unit"], [24, "13–24", "Primes, third/fourth proportional, infinitude of primes"], [36, "25–36", "Odd/even, perfect numbers"]].forEach(([max, range, desc]) => { + const filter = closure(max); + const m = toMermaid(filter); + const nodes = discourse.nodes.filter(filter); + const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); + const fname = `geometry_topology-euclid-elements-book-ix-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`; + fs.writeFileSync(path.join(GEOM_DIR, fname), htmlTemplate(`Euclid's Elements Book IX — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); + console.log("Wrote", fname); + }); +} + +// Book IX index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book IX - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book IX (Joyce) +
+ +

Euclid's Elements Book IX

+

Primes, perfect numbers, odd/even. 36 propositions. Depends on Books VII and VIII. IX.20: infinitely many primes. IX.36: perfect numbers.

+
+ Propositions 1–12 Squares, cubes, continued proportion + Propositions 13–24 Primes, infinitude, third proportional + Propositions 25–36 Odd/even, perfect numbers +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-ix.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-ix.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-v.js b/generator/build-euclid-book-v.js new file mode 100644 index 0000000000000000000000000000000000000000..a305282411a92f1e539291a299aaee1b720aa16d --- /dev/null +++ b/generator/build-euclid-book-v.js @@ -0,0 +1,376 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book V discourse JSON and Mermaid charts. + * 18 definitions, 25 propositions. Theory of ratio and proportion (Eudoxus). + * Book V does NOT depend on previous books. Source: David E. Joyce. + * + * Charts: 3. Chart 1: Defs + Props 1-8. Chart 2: Props 9-16. Chart 3: Props 17-25. + */ + +const fs = require('fs'); +const path = require('path'); + +const DEFS = [ + { n: 1, short: "Part", full: "A magnitude is a part of a magnitude when it measures it" }, + { n: 2, short: "Multiple", full: "The greater is a multiple of the less when it is measured by the less" }, + { n: 3, short: "Ratio", full: "A ratio is a sort of relation in respect of size between two magnitudes" }, + { n: 4, short: "Same ratio", full: "Magnitudes have a ratio when the less can be multiplied to exceed the greater" }, + { n: 5, short: "In same ratio (Eudoxus)", full: "Magnitudes in same ratio when equimultiples alike exceed, equal, or fall short" }, + { n: 6, short: "Proportional", full: "Magnitudes which have the same ratio are proportional" }, + { n: 7, short: "Greater ratio", full: "When of equimultiples first exceeds second, third does not exceed fourth" }, + { n: 8, short: "Compound ratio", full: "Compound ratio is the ratio of the products of corresponding terms" }, + { n: 9, short: "Duplicate ratio", full: "Duplicate ratio is the ratio of the squares" }, + { n: 10, short: "Triplicate ratio", full: "Triplicate ratio is the ratio of the cubes" }, + { n: 11, short: "Corresponding magnitudes", full: "Corresponding magnitudes in proportion" }, + { n: 12, short: "Alternate ratio", full: "Alternate: first to third as second to fourth" }, + { n: 13, short: "Inverse ratio", full: "Inverse: second to first as fourth to third" }, + { n: 14, short: "Composition of ratio", full: "Composition: first+second to second as third+fourth to fourth" }, + { n: 15, short: "Separation of ratio", full: "Separation: first−second to second as third−fourth to fourth" }, + { n: 16, short: "Conversion of ratio", full: "Conversion: first to first−second as third to third−fourth" }, + { n: 17, short: "Ex aequali", full: "Ex aequali: when first to second as second to third" }, + { n: 18, short: "Ex aequali perturbed", full: "Ex aequali perturbed: when ratios are in perturbed order" } +]; + +const PROPS = [ + { n: 1, short: "Sum of multiples", full: "If magnitudes each same multiple of others, sum is that multiple of sum" }, + { n: 2, short: "Equimultiples sum", full: "If first:second as third:fourth, sum of first and fifth as sum of third and sixth" }, + { n: 3, short: "Equimultiples of equimultiples", full: "Equimultiples of equimultiples are equimultiples" }, + { n: 4, short: "Equimultiples preserve ratio", full: "If a:b = c:d, then ma:nb = mc:nd" }, + { n: 5, short: "Multiple of difference", full: "Multiple of whole minus multiple of part = multiple of remainder" }, + { n: 6, short: "Equimultiples minus equimultiples", full: "Equimultiples minus equimultiples equal or equimultiples" }, + { n: 7, short: "Equals in ratio", full: "Equal magnitudes have same ratio to same; same to equals" }, + { n: 8, short: "Greater has greater ratio", full: "Of unequal magnitudes, greater has greater ratio to same" }, + { n: 9, short: "Same ratio implies equal", full: "Magnitudes with same ratio to same are equal" }, + { n: 10, short: "Greater ratio implies greater", full: "Of magnitudes with ratio to same, greater ratio implies greater" }, + { n: 11, short: "Transitivity of ratios", full: "Ratios same with same ratio are same with one another" }, + { n: 12, short: "Sum of antecedents/consequents", full: "Proportional: one antecedent to one consequent as sum to sum" }, + { n: 13, short: "Substitution in ratio inequality", full: "If a:b = c:d and c:d > e:f, then a:b > e:f" }, + { n: 14, short: "Equal ratios, equal magnitudes", full: "If a:b = c:d and a>c, then b>d" }, + { n: 15, short: "Parts as equimultiples", full: "Parts have same ratio as their equimultiples" }, + { n: 16, short: "Alternate proportion", full: "If a:b = c:d, then a:c = b:d" }, + { n: 17, short: "Jointly implies separately", full: "If (a+b):b = (c+d):d, then a:b = c:d" }, + { n: 18, short: "Separately implies jointly", full: "If a:b = c:d, then (a+b):b = (c+d):d" }, + { n: 19, short: "Whole to whole as part to part", full: "If (a+b):(c+d) = a:c, then also = b:d" }, + { n: 20, short: "Ex aequali (direct)", full: "If a:b = d:e and b:c = e:f and a>c, then d>f" }, + { n: 21, short: "Ex aequali (perturbed)", full: "If a:b = e:f and b:c = d:e and a>c, then d>f" }, + { n: 22, short: "Ex aequali chain", full: "If a1:a2 = b1:b2, a2:a3 = b2:b3, ..., then a1:an = b1:bn" }, + { n: 23, short: "Ex aequali perturbed chain", full: "If a:b = y:z and b:c = x:y, then a:c = x:z" }, + { n: 24, short: "Sum of ratios", full: "If a:b = c:d and e:b = f:d, then (a+e):b = (c+f):d" }, + { n: 25, short: "Sum of extremes > sum of means", full: "If a:b = c:d and a greatest, d least, then a+d > b+c" } +]; + +// Joyce logical structure +const DEPS = { + 1: [], + 2: [], + 3: ["Prop2"], + 4: ["Prop3"], + 5: ["Prop1"], + 6: ["Prop2"], + 7: [], + 8: ["Prop1"], + 9: ["Prop8"], + 10: ["Prop7", "Prop8"], + 11: [], + 12: ["Prop1"], + 13: [], + 14: ["Prop8", "Prop10", "Prop13"], + 15: ["Prop7", "Prop12"], + 16: ["Prop11", "Prop14", "Prop15"], + 17: ["Prop1", "Prop2"], + 18: ["Prop11", "Prop14", "Prop17"], + 19: ["Prop11", "Prop16", "Prop17"], + 20: ["Prop7", "Prop8", "Prop10", "Prop13"], + 21: ["Prop7", "Prop8", "Prop10", "Prop13"], + 22: ["Prop4", "Prop20"], + 23: ["Prop11", "Prop15", "Prop16", "Prop21"], + 24: ["Prop7", "Prop18", "Prop22"], + 25: ["Prop7", "Prop11", "Prop14", "Prop19"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-v", + name: "Euclid's Elements, Book V", + subject: "geometry", + variant: "classical", + description: "Theory of ratio and proportion (Eudoxus). 18 definitions, 25 propositions. Does not depend on previous books. Source: David E. Joyce.", + structure: { books: 5, definitions: 18, propositions: 25, foundationTypes: ["definition"] } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book V Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book V", "proportion", "ratio", "Eudoxus"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book V", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookV/bookV.html", notes: "Clark University; Logical structure" } + ], + nodes: [], + edges: [], + colorScheme: { + definition: { fill: "#3498db", stroke: "#2980b9" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Book V has no cross-book dependencies +for (const d of DEFS) { + discourse.nodes.push({ + id: `Def${d.n}`, + type: "definition", + label: d.full, + shortLabel: `Def. V.${d.n}`, + short: d.short, + book: 5, + number: d.n, + colorClass: "definition" + }); +} + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. V.${prop.n}`, + short: prop.short, + book: 5, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n] || []) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-v.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-v.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + lines.push(` class ${defIds} definition`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + for (const d of DEFS) needed.add(`Def${d.n}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book V Index + Euclid's Elements Book V (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book V (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Blue
Definitions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book V
  • proportion
  • ratio
  • Eudoxus
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + const filter1 = closure(8); + const m1 = toMermaid(filter1); + const nodes1 = discourse.nodes.filter(filter1); + const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-v-props-1-8.html"), htmlTemplate("Euclid's Elements Book V — Propositions 1–8", "Theory of proportion: multiples, equimultiples, basic ratio properties. Book V does not depend on previous books.", m1, nodes1.length, edges1.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-v-props-1-8.html"); + + const filter2 = closure(16); + const m2 = toMermaid(filter2); + const nodes2 = discourse.nodes.filter(filter2); + const edges2 = discourse.edges.filter(e => filter2({ id: e.from }) && filter2({ id: e.to })); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-v-props-9-16.html"), htmlTemplate("Euclid's Elements Book V — Propositions 9–16", "Ratio inequalities, transitivity, alternate proportion, jointly and separately.", m2, nodes2.length, edges2.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-v-props-9-16.html"); + + const m3 = toMermaid(() => true); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-v-props-17-25.html"), htmlTemplate("Euclid's Elements Book V — Propositions 17–25", "Ex aequali, perturbed ratios, composition, sum of extremes.", m3, discourse.nodes.length, discourse.edges.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-v-props-17-25.html"); +} + +// Book V index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book V - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book V (Joyce) +
+ +

Euclid's Elements Book V

+

Theory of ratio and proportion (Eudoxus). 18 definitions, 25 propositions. Does not depend on previous books. Foundation for Book VI and Books X–XIII.

+
+ Propositions 1–8 Multiples, equimultiples, basic ratio + Propositions 9–16 Inequalities, alternate, jointly + Propositions 17–25 Ex aequali, perturbed, composition +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-v.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-v.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-vi.js b/generator/build-euclid-book-vi.js new file mode 100644 index 0000000000000000000000000000000000000000..6d3c4f385fb8154916635ac38e3efaa0d536929f --- /dev/null +++ b/generator/build-euclid-book-vi.js @@ -0,0 +1,391 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book VI discourse JSON and Mermaid charts. + * 4 definitions, 33 propositions. Similar figures. Depends on Book I and Book V. + * VI.1 is basis for most of Book VI; VI.33 uses proportion def directly. Source: David E. Joyce. + * + * Charts: 3. Chart 1: Defs + Props 1-11. Chart 2: Props 12-22. Chart 3: Props 23-33. + */ + +const fs = require('fs'); +const path = require('path'); + +const DEFS = [ + { n: 1, short: "Similar rectilinear", full: "Similar rectilinear figures have equal angles and proportional sides" }, + { n: 2, short: "Reciprocally proportional", full: "Figures reciprocally proportional when sides are proportional inversely" }, + { n: 3, short: "Mean proportional", full: "Straight line is mean proportional when first to it as it to third" }, + { n: 4, short: "Duplicate ratio", full: "Duplicate ratio is the ratio of the squares on corresponding sides" } +]; + +const PROPS = [ + { n: 1, short: "Triangles under same height", full: "Triangles and parallelograms under same height are as their bases" }, + { n: 2, short: "Parallel cuts sides proportionally", full: "Line parallel to side cuts sides proportionally; converse" }, + { n: 3, short: "Angle bisector divides base", full: "Angle bisector: segments of base proportionally as remaining sides" }, + { n: 4, short: "Equiangular: sides proportional", full: "Equiangular triangles: sides about equal angles proportional" }, + { n: 5, short: "Sides proportional: equiangular", full: "If sides proportional, triangles equiangular" }, + { n: 6, short: "One angle equal, sides proportional", full: "One angle equal, sides about it proportional: equiangular" }, + { n: 7, short: "One angle equal, other sides proportional", full: "One angle equal, sides about others proportional: equiangular" }, + { n: 8, short: "Altitude in right triangle", full: "Perpendicular from right angle: triangles similar to whole" }, + { n: 9, short: "Cut off prescribed part", full: "To cut off a prescribed part from a given straight line" }, + { n: 10, short: "Cut line similarly", full: "To cut a given line similarly to a given cut line" }, + { n: 11, short: "Third proportional", full: "To find a third proportional to two given lines" }, + { n: 12, short: "Fourth proportional", full: "To find a fourth proportional to three given lines" }, + { n: 13, short: "Mean proportional", full: "To find a mean proportional to two given lines" }, + { n: 14, short: "Parallelograms reciprocally proportional", full: "Equal equiangular parallelograms: sides reciprocally proportional" }, + { n: 15, short: "Triangles reciprocally proportional", full: "Equal triangles, one angle equal: sides reciprocally proportional" }, + { n: 16, short: "Four lines proportional: rectangle", full: "Four lines proportional iff rectangle extremes = rectangle means" }, + { n: 17, short: "Three lines proportional: rectangle", full: "Three lines proportional iff rectangle extremes = square on mean" }, + { n: 18, short: "Similar figure on given line", full: "To describe figure similar to given on given line" }, + { n: 19, short: "Similar triangles: duplicate ratio", full: "Similar triangles in duplicate ratio of corresponding sides" }, + { n: 20, short: "Similar polygons: duplicate ratio", full: "Similar polygons in duplicate ratio of corresponding sides" }, + { n: 21, short: "Similar to same: similar", full: "Figures similar to same rectilinear figure are similar" }, + { n: 22, short: "Four lines proportional: figures", full: "Four lines proportional iff similar figures on them proportional" }, + { n: 23, short: "Equiangular parallelograms: compound ratio", full: "Equiangular parallelograms: ratio compounded of sides" }, + { n: 24, short: "Parallelograms about diameter", full: "Parallelograms about diameter similar to whole" }, + { n: 25, short: "Similar and equal to another", full: "To construct figure similar to one and equal to another" }, + { n: 26, short: "Parallelogram similar to difference", full: "Parallelogram similar to whole, common angle: about same diameter" }, + { n: 27, short: "Greatest parallelogram applied", full: "Of parallelograms applied to line, greatest is on half" }, + { n: 28, short: "Apply parallelogram: deficient", full: "To apply parallelogram equal to figure, deficient by similar" }, + { n: 29, short: "Apply parallelogram: exceeding", full: "To apply parallelogram equal to figure, exceeding by similar" }, + { n: 30, short: "Extreme and mean ratio", full: "To cut a given line in extreme and mean ratio" }, + { n: 31, short: "Right triangle: similar figures", full: "In right triangle, figure on hypotenuse = sum of similar on sides" }, + { n: 32, short: "Two triangles: sides parallel", full: "Two triangles, two sides proportional, placed with parallel sides" }, + { n: 33, short: "Angles in circles: ratio of arcs", full: "Angles in equal circles have ratio of circumferences" } +]; + +// VI.1 uses I.3, I.38, I.41, V.Def.5, V.15, V.11. VI.1 is basis for most. VI.33 uses proportion def. +const DEPS = { + 1: ["BookI", "BookV"], + 2: ["BookI", "BookV", "Prop1"], + 3: ["BookI", "BookV", "Prop1"], + 4: ["BookI", "BookV", "Prop1"], + 5: ["BookI", "BookV", "Prop1"], + 6: ["BookI", "BookV", "Prop1"], + 7: ["BookI", "BookV", "Prop1"], + 8: ["BookI", "BookV", "Prop1"], + 9: ["BookI", "BookV", "Prop1"], + 10: ["BookI", "BookV", "Prop1"], + 11: ["BookI", "BookV", "Prop1"], + 12: ["BookI", "BookV", "Prop1"], + 13: ["BookI", "BookV", "Prop1"], + 14: ["BookI", "BookV", "Prop1"], + 15: ["BookI", "BookV", "Prop1"], + 16: ["BookI", "BookV", "Prop1"], + 17: ["BookI", "BookV", "Prop1"], + 18: ["BookI", "BookV", "Prop1"], + 19: ["BookI", "BookV", "Prop1"], + 20: ["BookI", "BookV", "Prop1"], + 21: ["BookI", "BookV", "Prop1"], + 22: ["BookI", "BookV", "Prop1"], + 23: ["BookI", "BookV", "Prop1"], + 24: ["BookI", "BookV", "Prop1"], + 25: ["BookI", "BookV", "Prop1"], + 26: ["BookI", "BookV", "Prop1"], + 27: ["BookI", "BookV", "Prop1"], + 28: ["BookI", "BookV", "Prop1"], + 29: ["BookI", "BookV", "Prop1"], + 30: ["BookI", "BookV", "Prop1"], + 31: ["BookI", "BookV", "Prop1"], + 32: ["BookI", "BookV", "Prop1"], + 33: ["BookI", "BookV"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-vi", + name: "Euclid's Elements, Book VI", + subject: "geometry", + variant: "classical", + description: "Similar figures. 4 definitions, 33 propositions. Depends on Book I and Book V. VI.1 is basis for most. Source: David E. Joyce.", + structure: { books: 6, definitions: 4, propositions: 33, foundationTypes: ["definition", "foundation"] } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book VI Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book VI", "similar", "proportion", "triangles"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book VI", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookVI/bookVI.html", notes: "Clark University; VI.1 basis for most" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Fundamentals of plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "BookV", type: "foundation", label: "Book V — Theory of proportions", shortLabel: "Book V", short: "Foundation", book: 5, colorClass: "foundation" } +); + +for (const d of DEFS) { + discourse.nodes.push({ + id: `Def${d.n}`, + type: "definition", + label: d.full, + shortLabel: `Def. VI.${d.n}`, + short: d.short, + book: 6, + number: d.n, + colorClass: "definition" + }); + discourse.edges.push({ from: "BookI", to: `Def${d.n}` }); + discourse.edges.push({ from: "BookV", to: `Def${d.n}` }); +} + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. VI.${prop.n}`, + short: prop.short, + book: 6, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-vi.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-vi.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${defIds} definition`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + needed.add("BookI"); + needed.add("BookV"); + for (const d of DEFS) needed.add(`Def${d.n}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Geometry & Topology + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book VI Index + Euclid's Elements Book VI (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book VI (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, Book V (foundation)
+
Blue
Definitions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book VI
  • similar
  • proportion
  • triangles
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + const filter1 = closure(11); + const m1 = toMermaid(filter1); + const nodes1 = discourse.nodes.filter(filter1); + const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi-props-1-11.html"), htmlTemplate("Euclid's Elements Book VI — Propositions 1–11", "Similar triangles: same height, parallel cuts, equiangular, third proportional. VI.1 is basis. Depends on Book I and Book V.", m1, nodes1.length, edges1.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-vi-props-1-11.html"); + + const filter2 = closure(22); + const m2 = toMermaid(filter2); + const nodes2 = discourse.nodes.filter(filter2); + const edges2 = discourse.edges.filter(e => filter2({ id: e.from }) && filter2({ id: e.to })); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi-props-12-22.html"), htmlTemplate("Euclid's Elements Book VI — Propositions 12–22", "Fourth proportional, reciprocally proportional, similar figures on lines, duplicate ratio.", m2, nodes2.length, edges2.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-vi-props-12-22.html"); + + const m3 = toMermaid(() => true); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi-props-23-33.html"), htmlTemplate("Euclid's Elements Book VI — Propositions 23–33", "Compound ratio, parallelograms about diameter, application of areas, extreme and mean ratio, angles in circles.", m3, discourse.nodes.length, discourse.edges.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-vi-props-23-33.html"); +} + +// Book VI index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book VI - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book VI (Joyce) +
+ +

Euclid's Elements Book VI

+

Similar figures. 4 definitions, 33 propositions. Depends on Book I and Book V. VI.1 (triangles under same height) is basis for most. VI.33 uses proportion def directly.

+
+ Propositions 1–11 Similar triangles, proportionals + Propositions 12–22 Reciprocally proportional, duplicate ratio + Propositions 23–33 Application of areas, extreme and mean ratio +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vi.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-vi.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-vii.js b/generator/build-euclid-book-vii.js new file mode 100644 index 0000000000000000000000000000000000000000..e5df0766ad186ab864ad42c84dc7ebe315f28254 --- /dev/null +++ b/generator/build-euclid-book-vii.js @@ -0,0 +1,399 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book VII discourse JSON and Mermaid charts. + * 22 definitions, 39 propositions. Number theory: GCD, proportions, primes, LCM. + * Book VII does not depend on previous books. Source: David E. Joyce. + * + * Charts: 4. Chart 1: Defs + Props 1-10. Chart 2: Props 11-20. Chart 3: Props 21-30. Chart 4: Props 31-39. + */ + +const fs = require('fs'); +const path = require('path'); + +const DEFS = [ + { n: 1, short: "Unit", full: "A unit is that by virtue of which each of the things that exist is called one" }, + { n: 2, short: "Number", full: "A number is a multitude composed of units" }, + { n: 3, short: "Part", full: "A number is part of a number when it measures it" }, + { n: 4, short: "Parts", full: "Parts when it does not measure it" }, + { n: 5, short: "Multiple", full: "The greater is a multiple of the less when measured by the less" }, + { n: 6, short: "Even", full: "An even number is that which is divisible into two equal parts" }, + { n: 7, short: "Odd", full: "An odd number is that which is not divisible into two equal parts" }, + { n: 8, short: "Even-times even", full: "Even-times even: measured by an even number an even number of times" }, + { n: 9, short: "Even-times odd", full: "Even-times odd: measured by an even number an odd number of times" }, + { n: 10, short: "Odd-times odd", full: "Odd-times odd: measured by an odd number an odd number of times" }, + { n: 11, short: "Prime", full: "A prime number is that which is measured by a unit alone" }, + { n: 12, short: "Relatively prime", full: "Numbers relatively prime when only a unit measures both" }, + { n: 13, short: "Composite", full: "A composite number is that measured by some number" }, + { n: 14, short: "Composite to one another", full: "Numbers composite to one another when some number measures both" }, + { n: 15, short: "Multiply", full: "A number multiplies a number when the latter is added as many times as units in the former" }, + { n: 16, short: "Product", full: "When two numbers multiplied produce a number, the product is plane" }, + { n: 17, short: "Side", full: "Sides of the product are the numbers multiplied" }, + { n: 18, short: "Plane number", full: "A plane number is that produced by two numbers" }, + { n: 19, short: "Solid number", full: "A solid number is that produced by three numbers" }, + { n: 20, short: "Similar plane", full: "Similar plane numbers have sides proportional" }, + { n: 21, short: "Similar solid", full: "Similar solid numbers have sides proportional" }, + { n: 22, short: "Perfect", full: "A perfect number is that which equals its own parts" } +]; + +const PROPS = [ + { n: 1, short: "Antenaresis, relatively prime", full: "Unequal numbers: repeated subtraction; if unit left, relatively prime" }, + { n: 2, short: "GCD of two numbers", full: "To find greatest common measure of two numbers not relatively prime" }, + { n: 3, short: "GCD of three numbers", full: "To find greatest common measure of three numbers" }, + { n: 4, short: "Part or parts", full: "Any number is part or parts of any number, less of greater" }, + { n: 5, short: "Same part: sum", full: "If a is same part of b as c of d, then a+c same part of b+d" }, + { n: 6, short: "Same parts: sum", full: "If a is same parts of b as c of d, then a+c same parts of b+d" }, + { n: 7, short: "Same part: remainder", full: "If a part of b as c of d, remainder same part of remainder" }, + { n: 8, short: "Same parts: remainder", full: "If a parts of b as c of d, remainder same parts of remainder" }, + { n: 9, short: "Same part: alternately", full: "If a part of b as c of d, alternately a part/parts of c as b of d" }, + { n: 10, short: "Same parts: alternately", full: "If a parts of b as c of d, alternately a part/parts of c as b of d" }, + { n: 11, short: "Proportion: remainder", full: "If whole:whole as subtracted:subtracted, remainder:remainder as whole:whole" }, + { n: 12, short: "Proportional: sum", full: "Proportional: one antecedent to consequent as sum antecedents to sum consequents" }, + { n: 13, short: "Proportional: alternately", full: "If four numbers proportional, also proportional alternately" }, + { n: 14, short: "Ex aequali", full: "If a:b = d:e and b:c = e:f, then a:c = d:f" }, + { n: 15, short: "Unit measures", full: "If unit measures a, b measures c same times, alternately unit:c as b:d" }, + { n: 16, short: "Commutativity of product", full: "If a×b and c×d, then a×b = c×d (commutativity)" }, + { n: 17, short: "Ratio of products", full: "a:b = (a×c):(b×c)" }, + { n: 18, short: "Ratio: multipliers", full: "a×c : b×c = a:b" }, + { n: 19, short: "Proportional iff product", full: "a:b = c:d iff a×d = b×c" }, + { n: 20, short: "Least in ratio", full: "Least numbers in ratio measure others same number of times" }, + { n: 21, short: "Relatively prime: least", full: "Relatively prime numbers are least in their ratio" }, + { n: 22, short: "Least: relatively prime", full: "Least numbers in ratio are relatively prime" }, + { n: 23, short: "Relatively prime: divisor", full: "If a,b relatively prime, divisor of a relatively prime to b" }, + { n: 24, short: "Product relatively prime", full: "If a,b relatively prime to c, then a×b relatively prime to c" }, + { n: 25, short: "Square relatively prime", full: "If a,b relatively prime, a² relatively prime to b" }, + { n: 26, short: "Products relatively prime", full: "If a,c and b,d relatively prime, a×b, c×d relatively prime" }, + { n: 27, short: "Squares relatively prime", full: "If a,b relatively prime, a²,b² relatively prime; a×a², b×b²" }, + { n: 28, short: "Sum relatively prime", full: "If a,b relatively prime, a+b prime to each; converse" }, + { n: 29, short: "Prime to non-multiple", full: "Prime relatively prime to any number it does not measure" }, + { n: 30, short: "Prime divides product", full: "If prime measures product, it measures one factor" }, + { n: 31, short: "Composite has prime factor", full: "Any composite measured by some prime" }, + { n: 32, short: "Prime or has prime factor", full: "Any number is prime or measured by some prime" }, + { n: 33, short: "Least in ratio", full: "Given numbers, find least in same ratio" }, + { n: 34, short: "LCM of two", full: "To find least number that two given numbers measure" }, + { n: 35, short: "LCM divides common multiple", full: "If two numbers measure some number, LCM also measures it" }, + { n: 36, short: "LCM of three", full: "To find least number that three given numbers measure" }, + { n: 37, short: "Measured has part", full: "If a measures b, b has part named by a" }, + { n: 38, short: "Part implies measured", full: "If b has part named by a, a measures b" }, + { n: 39, short: "Least with given parts", full: "To find least number with given parts" } +]; + +// Joyce: VII.1→2,3; VII.2→3; VII.5-10 fractions; VII.11-19 proportions; VII.20-29 relatively prime; VII.30-32 primes; VII.33-39 LCM +const DEPS = { + 1: [], + 2: ["Prop1"], + 3: ["Prop1", "Prop2"], + 4: [], + 5: [], + 6: [], + 7: [], + 8: [], + 9: [], + 10: [], + 11: [], + 12: [], + 13: [], + 14: [], + 15: [], + 16: [], + 17: [], + 18: [], + 19: [], + 20: ["Prop19"], + 21: ["Prop20"], + 22: ["Prop21"], + 23: ["Prop22"], + 24: ["Prop23"], + 25: ["Prop23"], + 26: ["Prop24"], + 27: ["Prop25"], + 28: ["Prop23"], + 29: ["Prop23"], + 30: ["Prop29"], + 31: [], + 32: ["Prop31"], + 33: ["Prop20", "Prop22"], + 34: ["Prop33"], + 35: ["Prop34"], + 36: ["Prop34"], + 37: [], + 38: ["Prop37"], + 39: ["Prop38"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-vii", + name: "Euclid's Elements, Book VII", + subject: "number_theory", + variant: "classical", + description: "Number theory: GCD (Euclidean algorithm), proportions, primes, LCM. 22 definitions, 39 propositions. Does not depend on previous books. Source: David E. Joyce.", + structure: { books: 7, definitions: 22, propositions: 39, foundationTypes: ["definition"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book VII Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book VII", "number theory", "GCD", "prime", "LCM"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book VII", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookVII/bookVII.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + definition: { fill: "#3498db", stroke: "#2980b9" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +for (const d of DEFS) { + discourse.nodes.push({ + id: `Def${d.n}`, + type: "definition", + label: d.full, + shortLabel: `Def. VII.${d.n}`, + short: d.short, + book: 7, + number: d.n, + colorClass: "definition" + }); +} + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. VII.${prop.n}`, + short: prop.short, + book: 7, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n] || []) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-vii.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-vii.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + lines.push(` class ${defIds} definition`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + for (const d of DEFS) needed.add(`Def${d.n}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Number Theory + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book VII Index + Euclid's Elements Book VII (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book VII (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Blue
Definitions
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book VII
  • number theory
  • GCD
  • prime
  • LCM
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + [[10, "1–10", "GCD, part/parts, proportions"], [20, "11–20", "Proportions, products, least in ratio"], [30, "21–30", "Relatively prime, primes"], [39, "31–39", "Primes, LCM, parts"]].forEach(([max, range, desc]) => { + const filter = closure(max); + const m = toMermaid(filter); + const nodes = discourse.nodes.filter(filter); + const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); + fs.writeFileSync(path.join(GEOM_DIR, `geometry_topology-euclid-elements-book-vii-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`), htmlTemplate(`Euclid's Elements Book VII — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); + console.log(`Wrote geometry_topology-euclid-elements-book-vii-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`); + }); +} + +// Book VII index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book VII - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book VII (Joyce) +
+ +

Euclid's Elements Book VII

+

Number theory: GCD (Euclidean algorithm), proportions of numbers, primes, LCM. 22 definitions, 39 propositions. Does not depend on previous books.

+
+ Propositions 1–10 GCD, part/parts, proportions + Propositions 11–20 Proportions, products, least in ratio + Propositions 21–30 Relatively prime, primes + Propositions 31–39 Primes, LCM, parts +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-vii.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-vii.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-viii.js b/generator/build-euclid-book-viii.js new file mode 100644 index 0000000000000000000000000000000000000000..1a5aea6ed4a93f61157438f8435d8d51fd70b1e1 --- /dev/null +++ b/generator/build-euclid-book-viii.js @@ -0,0 +1,337 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book VIII discourse JSON and Mermaid charts. + * 27 propositions. Continued proportions. Depends on Book VII. Source: David E. Joyce. + * + * Charts: 2. Chart 1: Props 1-14. Chart 2: Props 15-27. + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPS = [ + { n: 1, short: "Continued proportion, extremes prime", full: "Continued proportion, extremes relatively prime: least in ratio" }, + { n: 2, short: "Find numbers in continued proportion", full: "To find numbers in continued proportion, least in given ratio" }, + { n: 3, short: "Least: extremes prime", full: "Least in continued proportion: extremes relatively prime" }, + { n: 4, short: "Find continued proportion from ratios", full: "Given ratios in least numbers, find least in continued proportion" }, + { n: 5, short: "Plane numbers: compound ratio", full: "Plane numbers have ratio compounded of ratios of sides" }, + { n: 6, short: "First does not measure second", full: "Continued proportion: if first does not measure second, none measures another" }, + { n: 7, short: "First measures last", full: "Continued proportion: if first measures last, it measures second" }, + { n: 8, short: "Numbers between in proportion", full: "Numbers between two in continued proportion correspond to ratios" }, + { n: 9, short: "Relatively prime: numbers to unit", full: "Two relatively prime: numbers between them as between each and unit" }, + { n: 10, short: "Numbers from unit", full: "Numbers between number and unit correspond to between two numbers" }, + { n: 11, short: "Mean proportional of squares", full: "Between two squares one mean proportional; duplicate ratio" }, + { n: 12, short: "Two means between cubes", full: "Between two cubes two mean proportionals; triplicate ratio" }, + { n: 13, short: "Products proportional", full: "Continued proportion: products proportional; products of products" }, + { n: 14, short: "Square measures square", full: "Square measures square iff side measures side" }, + { n: 15, short: "Cube measures cube", full: "Cube measures cube iff side measures side" }, + { n: 16, short: "Square does not measure square", full: "Square does not measure square iff side does not measure side" }, + { n: 17, short: "Cube does not measure cube", full: "Cube does not measure cube iff side does not measure side" }, + { n: 18, short: "Similar plane: mean proportional", full: "Between similar plane numbers one mean proportional; duplicate ratio" }, + { n: 19, short: "Similar solid: two means", full: "Between similar solid numbers two mean proportionals; triplicate ratio" }, + { n: 20, short: "One mean: similar plane", full: "If one mean between two numbers, they are similar plane" }, + { n: 21, short: "Two means: similar solid", full: "If two means between two numbers, they are similar solid" }, + { n: 22, short: "Three in proportion: first square", full: "Three in continued proportion, first square: third square" }, + { n: 23, short: "Four in proportion: first cube", full: "Four in continued proportion, first cube: fourth cube" }, + { n: 24, short: "Ratio as square to square", full: "If ratio as square to square and first square, second square" }, + { n: 25, short: "Ratio as cube to cube", full: "If ratio as cube to cube and first cube, second cube" }, + { n: 26, short: "Similar plane: square ratio", full: "Similar plane numbers have ratio of square to square" }, + { n: 27, short: "Similar solid: cube ratio", full: "Similar solid numbers have ratio of cube to cube" } +]; + +const DEPS = {}; +for (let i = 1; i <= 27; i++) DEPS[i] = ["BookVII"]; +DEPS[2] = ["BookVII", "Prop1"]; +DEPS[3] = ["BookVII", "Prop2"]; +DEPS[4] = ["BookVII", "Prop2"]; +DEPS[5] = ["BookVII"]; +DEPS[6] = ["BookVII", "Prop1"]; +DEPS[7] = ["BookVII", "Prop1"]; +DEPS[8] = ["BookVII"]; +DEPS[9] = ["BookVII", "Prop8"]; +DEPS[10] = ["BookVII", "Prop9"]; +DEPS[11] = ["BookVII", "Prop8"]; +DEPS[12] = ["BookVII", "Prop8"]; +DEPS[13] = ["BookVII"]; +DEPS[14] = ["BookVII", "Prop11"]; +DEPS[15] = ["BookVII", "Prop12"]; +DEPS[16] = ["BookVII", "Prop14"]; +DEPS[17] = ["BookVII", "Prop15"]; +DEPS[18] = ["BookVII", "Prop8"]; +DEPS[19] = ["BookVII", "Prop8"]; +DEPS[20] = ["BookVII", "Prop18"]; +DEPS[21] = ["BookVII", "Prop19"]; +DEPS[22] = ["BookVII", "Prop1"]; +DEPS[23] = ["BookVII", "Prop1"]; +DEPS[24] = ["BookVII", "Prop22"]; +DEPS[25] = ["BookVII", "Prop23"]; +DEPS[26] = ["BookVII", "Prop18"]; +DEPS[27] = ["BookVII", "Prop19"]; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-viii", + name: "Euclid's Elements, Book VIII", + subject: "number_theory", + variant: "classical", + description: "Continued proportions. 27 propositions. Depends on Book VII. Source: David E. Joyce.", + structure: { books: 8, propositions: 27, foundationTypes: ["foundation"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book VIII Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book VIII", "continued proportion", "plane", "solid"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book VIII", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookVIII/bookVIII.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookVII", type: "foundation", label: "Book VII — Number theory", shortLabel: "Book VII", short: "Foundation", book: 7, colorClass: "foundation" } +); + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. VIII.${prop.n}`, + short: prop.short, + book: 8, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n] || ["BookVII"]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-viii.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-viii.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(["BookVII"]); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Number Theory + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book VIII Index + Euclid's Elements Book VIII (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book VIII (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book VII (foundation)
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book VIII
  • continued proportion
  • plane
  • solid
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(GEOM_DIR)) { + const filter1 = closure(14); + const m1 = toMermaid(filter1); + const nodes1 = discourse.nodes.filter(filter1); + const edges1 = discourse.edges.filter(e => filter1({ id: e.from }) && filter1({ id: e.to })); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-viii-props-1-14.html"), htmlTemplate("Euclid's Elements Book VIII — Propositions 1–14", "Continued proportion, least in ratio, square/cube. Depends on Book VII.", m1, nodes1.length, edges1.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-viii-props-1-14.html"); + + const m2 = toMermaid(() => true); + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-viii-props-15-27.html"), htmlTemplate("Euclid's Elements Book VIII — Propositions 15–27", "Similar plane/solid, mean proportionals, square/cube ratios.", m2, discourse.nodes.length, discourse.edges.length), "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-viii-props-15-27.html"); +} + +// Book VIII index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book VIII - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book VIII (Joyce) +
+ +

Euclid's Elements Book VIII

+

Continued proportions. 27 propositions. Depends on Book VII. Plane numbers, solid numbers, mean proportionals.

+
+ Propositions 1–14 Continued proportion, squares, cubes + Propositions 15–27 Similar plane/solid, ratios +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-viii.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-viii.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-x.js b/generator/build-euclid-book-x.js new file mode 100644 index 0000000000000000000000000000000000000000..4b4559eb6c4cacddf02a3a48fdd5979c5413a68b --- /dev/null +++ b/generator/build-euclid-book-x.js @@ -0,0 +1,412 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book X discourse JSON and Mermaid charts. + * 16 definitions (4+6+6), 115 propositions. Incommensurables, binomials, apotomes. + * Depends on Books I, V, VI. Source: David E. Joyce. + * + * Charts: 8. Props 1-15, 16-30, 31-45, 46-60, 61-75, 76-90, 91-105, 106-115. + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPS = [ + { n: 1, short: "Antenaresis for magnitudes", full: "Two unequal magnitudes: subtract more than half repeatedly; remainder less than lesser" }, + { n: 2, short: "Incommensurable criterion", full: "If less subtracted from greater repeatedly and remainder never measures prior: incommensurable" }, + { n: 3, short: "GCM of two commensurable", full: "To find greatest common measure of two commensurable magnitudes" }, + { n: 4, short: "GCM of three commensurable", full: "To find greatest common measure of three commensurable magnitudes" }, + { n: 5, short: "Commensurable: number ratio", full: "Commensurable magnitudes have ratio which a number has to a number" }, + { n: 6, short: "Number ratio: commensurable", full: "If two magnitudes have number-to-number ratio, they are commensurable" }, + { n: 7, short: "Incommensurable: no number ratio", full: "Incommensurable magnitudes do not have number-to-number ratio" }, + { n: 8, short: "No number ratio: incommensurable", full: "If magnitudes lack number-to-number ratio, they are incommensurable" }, + { n: 9, short: "Squares: commensurable iff square ratio", full: "Squares on commensurable lines have square-to-square ratio; converse" }, + { n: 10, short: "Find incommensurable lines", full: "To find two lines incommensurable with assigned: one in length, one in square" }, + { n: 11, short: "Proportion preserves commensurability", full: "Four proportional: first commensurable with second iff third with fourth" }, + { n: 12, short: "Commensurable with same", full: "Magnitudes commensurable with same magnitude are commensurable" }, + { n: 13, short: "Commensurable: incommensurable partner", full: "If two commensurable, one incommensurable with third, so is the other" }, + { n: 14, short: "Square difference, sum of squares", full: "Given two lines: find square by which greater square exceeds less; find line whose square equals sum" }, + { n: 15, short: "Commensurable sum", full: "Two commensurable added: whole commensurable with each" }, + { n: 16, short: "Incommensurable sum", full: "Two incommensurable added: sum incommensurable with each" }, + { n: 17, short: "Parallelogram falling short", full: "Applied parallelogram falling short by square: parts commensurable iff square difference commensurable" }, + { n: 18, short: "Parallelogram: incommensurable parts", full: "Applied parallelogram: parts incommensurable iff square difference incommensurable" }, + { n: 19, short: "Rational rectangle from rational", full: "Rectangle by rational lines commensurable in length is rational" }, + { n: 20, short: "Rational area on rational", full: "Rational area applied to rational line: breadth rational and commensurable" }, + { n: 21, short: "Medial: rational in square only", full: "Rectangle by rational in square only is irrational; side called medial" }, + { n: 22, short: "Medial applied to rational", full: "Square on medial applied to rational: breadth rational, incommensurable in length" }, + { n: 23, short: "Commensurable with medial", full: "Line commensurable with medial is medial" }, + { n: 24, short: "Medial rectangle: commensurable length", full: "Rectangle by medial lines commensurable in length is medial" }, + { n: 25, short: "Medial: square only", full: "Rectangle by medial in square only: rational or medial" }, + { n: 26, short: "Medial minus medial", full: "Medial area does not exceed medial by rational area" }, + { n: 27, short: "Find medial in square only, rational rect", full: "To find medial lines commensurable in square only containing rational rectangle" }, + { n: 28, short: "Find medial in square only, medial rect", full: "To find medial lines commensurable in square only containing medial rectangle" }, + { n: 29, short: "Find rational in square only, commensurable diff", full: "To find two rational in square only: square diff commensurable with greater" }, + { n: 30, short: "Find rational in square only, incommensurable diff", full: "To find two rational in square only: square diff incommensurable with greater" }, + { n: 31, short: "Find medial, rational rect, commensurable diff", full: "To find two medial in square only, rational rect: diff commensurable with greater" }, + { n: 32, short: "Find medial, medial rect, commensurable diff", full: "To find two medial in square only, medial rect: diff commensurable with greater" }, + { n: 33, short: "Find incommensurable: rational sum, medial rect", full: "To find two incommensurable in square: sum of squares rational, rectangle medial" }, + { n: 34, short: "Find incommensurable: medial sum, rational rect", full: "To find two incommensurable in square: sum medial, rectangle rational" }, + { n: 35, short: "Find incommensurable: both medial", full: "To find two incommensurable in square: sum and rect medial, incommensurable" }, + { n: 36, short: "Binomial defined", full: "Two rational in square only added: whole irrational, called binomial" }, + { n: 37, short: "First bimedial defined", full: "Two medial in square only, rational rect added: first bimedial" }, + { n: 38, short: "Second bimedial defined", full: "Two medial in square only, medial rect added: second bimedial" }, + { n: 39, short: "Major defined", full: "Two incommensurable in square, rational sum, medial rect added: major" }, + { n: 40, short: "Side of rational plus medial", full: "Two incommensurable in square, medial sum, rational rect added: side of rational plus medial" }, + { n: 41, short: "Side of sum of two medial", full: "Two incommensurable in square, both medial added: side of sum of two medial" }, + { n: 42, short: "Binomial: unique division", full: "Binomial divided into terms at one point only" }, + { n: 43, short: "First bimedial: unique division", full: "First bimedial divided at one point only" }, + { n: 44, short: "Second bimedial: unique division", full: "Second bimedial divided at one point only" }, + { n: 45, short: "Major: unique division", full: "Major divided at one point only" }, + { n: 46, short: "Side rational+medial: unique division", full: "Side of rational plus medial divided at one point only" }, + { n: 47, short: "Side two medial: unique division", full: "Side of sum of two medial divided at one point only" }, + { n: 48, short: "Find first binomial", full: "To find the first binomial line" }, + { n: 49, short: "Find second binomial", full: "To find the second binomial line" }, + { n: 50, short: "Find third binomial", full: "To find the third binomial line" }, + { n: 51, short: "Find fourth binomial", full: "To find the fourth binomial line" }, + { n: 52, short: "Find fifth binomial", full: "To find the fifth binomial line" }, + { n: 53, short: "Find sixth binomial", full: "To find the sixth binomial line" }, + { n: 54, short: "Rational × first binomial", full: "Area by rational and first binomial: side is binomial" }, + { n: 55, short: "Rational × second binomial", full: "Area by rational and second binomial: side is first bimedial" }, + { n: 56, short: "Rational × third binomial", full: "Area by rational and third binomial: side is second bimedial" }, + { n: 57, short: "Rational × fourth binomial", full: "Area by rational and fourth binomial: side is major" }, + { n: 58, short: "Rational × fifth binomial", full: "Area by rational and fifth binomial: side is rational plus medial" }, + { n: 59, short: "Rational × sixth binomial", full: "Area by rational and sixth binomial: side is sum of two medial" }, + { n: 60, short: "Square on binomial", full: "Square on binomial applied to rational: breadth first binomial" }, + { n: 61, short: "Square on first bimedial", full: "Square on first bimedial applied to rational: breadth second binomial" }, + { n: 62, short: "Square on second bimedial", full: "Square on second bimedial applied to rational: breadth third binomial" }, + { n: 63, short: "Square on major", full: "Square on major applied to rational: breadth fourth binomial" }, + { n: 64, short: "Square on rational+medial", full: "Square on rational+medial applied to rational: breadth fifth binomial" }, + { n: 65, short: "Square on two medial", full: "Square on sum of two medial applied to rational: breadth sixth binomial" }, + { n: 66, short: "Commensurable with binomial", full: "Line commensurable with binomial is binomial, same order" }, + { n: 67, short: "Commensurable with bimedial", full: "Line commensurable with bimedial is bimedial, same order" }, + { n: 68, short: "Commensurable with major", full: "Line commensurable with major is major" }, + { n: 69, short: "Commensurable with rational+medial", full: "Line commensurable with rational+medial is rational+medial" }, + { n: 70, short: "Commensurable with two medial", full: "Line commensurable with sum of two medial is sum of two medial" }, + { n: 71, short: "Rational + medial: four irrationals", full: "Rational and medial added: four irrationals arise" }, + { n: 72, short: "Two medial: two irrationals", full: "Two medial incommensurable added: two irrationals arise" }, + { n: 73, short: "Apotome defined", full: "Rational minus rational in square only: remainder irrational, apotome" }, + { n: 74, short: "First apotome of medial", full: "Medial minus medial, rational rect: first apotome of medial" }, + { n: 75, short: "Second apotome of medial", full: "Medial minus medial, medial rect: second apotome of medial" }, + { n: 76, short: "Minor defined", full: "Line minus incommensurable: sum rational, rect medial: remainder minor" }, + { n: 77, short: "Produces rational+medial", full: "Line minus incommensurable: sum medial, rect rational: produces rational+medial" }, + { n: 78, short: "Produces medial+medial", full: "Line minus incommensurable: both medial, incommensurable: produces medial+medial" }, + { n: 79, short: "Apotome: unique annex", full: "To apotome only one rational can be annexed in square only" }, + { n: 80, short: "First apotome medial: unique annex", full: "To first apotome of medial: unique medial annex, rational rect" }, + { n: 81, short: "Second apotome medial: unique annex", full: "To second apotome of medial: unique medial annex, medial rect" }, + { n: 82, short: "Minor: unique annex", full: "To minor: unique annex incommensurable in square" }, + { n: 83, short: "Rational+medial: unique annex", full: "To produces rational+medial: unique annex" }, + { n: 84, short: "Medial+medial: unique annex", full: "To produces medial+medial: unique annex" }, + { n: 85, short: "Find first apotome", full: "To find the first apotome" }, + { n: 86, short: "Find second apotome", full: "To find the second apotome" }, + { n: 87, short: "Find third apotome", full: "To find the third apotome" }, + { n: 88, short: "Find fourth apotome", full: "To find the fourth apotome" }, + { n: 89, short: "Find fifth apotome", full: "To find the fifth apotome" }, + { n: 90, short: "Find sixth apotome", full: "To find the sixth apotome" }, + { n: 91, short: "Rational × first apotome", full: "Area by rational and first apotome: side is apotome" }, + { n: 92, short: "Rational × second apotome", full: "Area by rational and second apotome: side is first apotome of medial" }, + { n: 93, short: "Rational × third apotome", full: "Area by rational and third apotome: side is second apotome of medial" }, + { n: 94, short: "Rational × fourth apotome", full: "Area by rational and fourth apotome: side is minor" }, + { n: 95, short: "Rational × fifth apotome", full: "Area by rational and fifth apotome: side produces rational+medial" }, + { n: 96, short: "Rational × sixth apotome", full: "Area by rational and sixth apotome: side produces medial+medial" }, + { n: 97, short: "Square on apotome medial", full: "Square on apotome of medial applied to rational: breadth first apotome" }, + { n: 98, short: "Square on first apotome medial", full: "Square on first apotome of medial: breadth second apotome" }, + { n: 99, short: "Square on second apotome medial", full: "Square on second apotome of medial: breadth third apotome" }, + { n: 100, short: "Square on minor", full: "Square on minor applied to rational: breadth fourth apotome" }, + { n: 101, short: "Square on rational+medial", full: "Square on produces rational+medial: breadth fifth apotome" }, + { n: 102, short: "Square on medial+medial", full: "Square on produces medial+medial: breadth sixth apotome" }, + { n: 103, short: "Commensurable with apotome", full: "Line commensurable with apotome is apotome, same order" }, + { n: 104, short: "Commensurable with apotome medial", full: "Line commensurable with apotome of medial is apotome of medial" }, + { n: 105, short: "Commensurable with minor", full: "Line commensurable with minor is minor" }, + { n: 106, short: "Commensurable with rational+medial", full: "Line commensurable with produces rational+medial is same" }, + { n: 107, short: "Commensurable with medial+medial", full: "Line commensurable with produces medial+medial is same" }, + { n: 108, short: "Rational minus medial", full: "From rational area subtract medial: side is apotome or minor" }, + { n: 109, short: "Medial minus rational", full: "From medial subtract rational: first apotome of medial or rational+medial" }, + { n: 110, short: "Medial minus medial", full: "From medial subtract medial incommensurable: second apotome or medial+medial" }, + { n: 111, short: "Apotome ≠ binomial", full: "Apotome is not the same as binomial" }, + { n: 112, short: "Rational on binomial", full: "Square on rational applied to binomial: breadth apotome, same order" }, + { n: 113, short: "Rational on apotome", full: "Square on rational applied to apotome: breadth binomial, same order" }, + { n: 114, short: "Apotome × binomial: rational", full: "Area by apotome and binomial (commensurable terms): side is rational" }, + { n: 115, short: "Medial: infinite irrationals", full: "From medial arise irrationals infinite in number, none same as preceding" } +]; + +const FOUNDATIONS = ["BookI", "BookV", "BookVI"]; +const DEPS = {}; +for (let i = 1; i <= 115; i++) DEPS[i] = FOUNDATIONS; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-x", + name: "Euclid's Elements, Book X", + subject: "incommensurables", + variant: "classical", + description: "Incommensurables, binomials, apotomes. 16 definitions, 115 propositions. Depends on Books I, V, VI. Source: David E. Joyce.", + structure: { books: 10, definitions: 16, propositions: 115, foundationTypes: ["foundation"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book X Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book X", "incommensurable", "binomial", "apotome", "medial"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book X", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookX/bookX.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "BookV", type: "foundation", label: "Book V — Proportions", shortLabel: "Book V", short: "Foundation", book: 5, colorClass: "foundation" }, + { id: "BookVI", type: "foundation", label: "Book VI — Similar figures", shortLabel: "Book VI", short: "Foundation", book: 6, colorClass: "foundation" } +); + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. X.${prop.n}`, + short: prop.short, + book: 10, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-x.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-x.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(FOUNDATIONS); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Incommensurables + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book X Index + Euclid's Elements Book X (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book X (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, V, VI (foundation)
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book X
  • incommensurable
  • binomial
  • apotome
  • medial
    • +
+
+
+
+
+ + +`; +} + +const CHARTS = [ + [15, "1-15", "Commensurable, incommensurable, GCM, ratio, squares"], + [30, "16-30", "Medial, rational, parallelogram, find lines"], + [45, "31-45", "Binomial, bimedial, major, unique division"], + [60, "46-60", "Find binomials, area by rational"], + [75, "61-75", "Square on binomial, commensurable, apotome"], + [90, "76-90", "Apotome types, find apotomes"], + [105, "91-105", "Area by apotome, square on apotome, commensurable"], + [115, "106-115", "Rational from irrational, order, infinite irrationals"] +]; + +if (fs.existsSync(GEOM_DIR)) { + CHARTS.forEach(([max, range, desc]) => { + const filter = closure(max); + const m = toMermaid(filter); + const nodes = discourse.nodes.filter(filter); + const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); + const fname = `geometry_topology-euclid-elements-book-x-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`; + fs.writeFileSync(path.join(GEOM_DIR, fname), htmlTemplate(`Euclid's Elements Book X — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); + console.log("Wrote", fname); + }); +} + +// Book X index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book X - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book X (Joyce) +
+ +

Euclid's Elements Book X

+

Incommensurables, binomials, apotomes. 115 propositions, 16 definitions. Depends on Books I, V, VI. Thirteen irrational straight lines; X.115: infinite irrationals from medial.

+
+ Propositions 1–15 Commensurable, incommensurable, GCM, ratio + Propositions 16–30 Medial, rational, parallelogram + Propositions 31–45 Binomial, bimedial, major + Propositions 46–60 Find binomials, area by rational + Propositions 61–75 Square on binomial, apotome + Propositions 76–90 Apotome types, find apotomes + Propositions 91–105 Area by apotome, commensurable + Propositions 106–115 Rational from irrational, order +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-x.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-x.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-xi.js b/generator/build-euclid-book-xi.js new file mode 100644 index 0000000000000000000000000000000000000000..bcb88b9335ca6110c56e4dcb153a0d5919a26013 --- /dev/null +++ b/generator/build-euclid-book-xi.js @@ -0,0 +1,325 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book XI discourse JSON and Mermaid charts. + * 28 definitions, 39 propositions. Solid geometry: planes, parallelepipeds, prisms. + * Depends on Books I and VI. Source: David E. Joyce. + * + * Charts: 3. Props 1-13, 14-26, 27-39. + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPS = [ + { n: 1, short: "Line part in plane", full: "A part of a straight line cannot be in one plane and part in another elevated" }, + { n: 2, short: "Two lines cut: one plane", full: "If two straight lines cut one another, they lie in one plane; every triangle in one plane" }, + { n: 3, short: "Planes cut: line", full: "If two planes cut one another, their intersection is a straight line" }, + { n: 4, short: "Line perpendicular to plane", full: "If line at right angles to two lines cutting at point, also perpendicular to plane through them" }, + { n: 5, short: "Three lines from point", full: "If line at right angles to three lines meeting at point, the three lie in one plane" }, + { n: 6, short: "Perpendicular to same plane: parallel", full: "If two lines at right angles to same plane, they are parallel" }, + { n: 7, short: "Parallel lines: join in plane", full: "If two lines parallel, line joining points on each is in same plane" }, + { n: 8, short: "Parallel: one perpendicular", full: "If two lines parallel, one perpendicular to plane, so is the other" }, + { n: 9, short: "Parallel to same: parallel", full: "Lines parallel to same line but not in same plane are parallel to each other" }, + { n: 10, short: "Skew lines: equal angles", full: "Two lines meeting parallel to two meeting not in same plane: contain equal angles" }, + { n: 11, short: "Perpendicular from point to plane", full: "To draw line perpendicular to given plane from given elevated point" }, + { n: 12, short: "Perpendicular from point in plane", full: "To set up line at right angles to plane from given point in it" }, + { n: 13, short: "One perpendicular only", full: "From same point two lines cannot be perpendicular to same plane on same side" }, + { n: 14, short: "Planes perpendicular to line: parallel", full: "Planes to which same line is perpendicular are parallel" }, + { n: 15, short: "Skew lines: planes parallel", full: "Two lines meeting parallel to two meeting not in same plane: planes through them parallel" }, + { n: 16, short: "Parallel planes cut: parallel", full: "If two parallel planes cut by any plane, intersections are parallel" }, + { n: 17, short: "Parallel planes: same ratio", full: "If two lines cut by parallel planes, they are cut in same ratios" }, + { n: 18, short: "Line perpendicular: planes through it", full: "If line perpendicular to plane, all planes through it perpendicular to that plane" }, + { n: 19, short: "Planes perpendicular: intersection", full: "If two planes cutting one another perpendicular to plane, intersection perpendicular" }, + { n: 20, short: "Solid angle: plane angles", full: "Solid angle by three plane angles: sum of any two greater than third" }, + { n: 21, short: "Solid angle: less than four right", full: "Any solid angle contained by plane angles summing to less than four right angles" }, + { n: 22, short: "Three plane angles: construct triangle", full: "Three plane angles with sum of any two greater than third, equal sides: construct triangle" }, + { n: 23, short: "Construct solid angle", full: "To construct solid angle from three plane angles (sum of any two greater than third)" }, + { n: 24, short: "Solid by parallel planes", full: "If solid contained by parallel planes, opposite planes equal and parallelogrammic" }, + { n: 25, short: "Parallelepiped cut: base ratio", full: "Parallelepiped cut by plane parallel to opposite: base to base as solid to solid" }, + { n: 26, short: "Construct equal solid angle", full: "To construct solid angle equal to given on given line at given point" }, + { n: 27, short: "Similar parallelepiped on line", full: "To describe parallelepiped similar to given on given straight line" }, + { n: 28, short: "Parallelepiped: diagonal plane bisects", full: "Parallelepiped cut by plane through diagonals of opposite planes: bisected" }, + { n: 29, short: "Same base, height, same lines: equal", full: "Parallelepipeds same base, height, ends on same lines: equal" }, + { n: 30, short: "Same base, height, different lines: equal", full: "Parallelepipeds same base, height, ends not on same lines: equal" }, + { n: 31, short: "Equal bases, same height: equal", full: "Parallelepipeds on equal bases, same height: equal" }, + { n: 32, short: "Same height: as bases", full: "Parallelepipeds same height: to one another as bases" }, + { n: 33, short: "Similar: triplicate ratio", full: "Similar parallelepipeds: to one another in triplicate ratio of corresponding sides" }, + { n: 34, short: "Equal: bases reciprocally proportional", full: "Equal parallelepipeds: bases reciprocally proportional to heights" }, + { n: 35, short: "Equal plane angles: elevated lines", full: "Equal plane angles, elevated lines with equal angles: perpendiculars, joins" }, + { n: 36, short: "Three proportional: parallelepiped", full: "Three proportional lines: parallelepiped from three equals that on mean equilateral" }, + { n: 37, short: "Four proportional: parallelepipeds", full: "Four proportional: similar parallelepipeds proportional; converse" }, + { n: 38, short: "Cube: bisected by planes", full: "Cube opposite sides bisected, planes through: intersection and diameter bisect each other" }, + { n: 39, short: "Prisms: parallelogram, triangle", full: "Two prisms equal height, parallelogram and triangle bases, parallelogram double: equal" } +]; + +const FOUNDATIONS = ["BookI", "BookVI"]; +const DEPS = {}; +for (let i = 1; i <= 39; i++) DEPS[i] = FOUNDATIONS; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-xi", + name: "Euclid's Elements, Book XI", + subject: "solid_geometry", + variant: "classical", + description: "Solid geometry: planes, perpendiculars, parallelepipeds, prisms. 28 definitions, 39 propositions. Depends on Books I and VI. Source: David E. Joyce.", + structure: { books: 11, definitions: 28, propositions: 39, foundationTypes: ["foundation"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book XI Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book XI", "solid geometry", "plane", "parallelepiped", "prism"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book XI", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookXI/bookXI.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "BookVI", type: "foundation", label: "Book VI — Similar figures", shortLabel: "Book VI", short: "Foundation", book: 6, colorClass: "foundation" } +); + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. XI.${prop.n}`, + short: prop.short, + book: 11, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-xi.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-xi.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(FOUNDATIONS); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Solid Geometry + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book XI Index + Euclid's Elements Book XI (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book XI (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, VI (foundation)
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book XI
  • solid geometry
  • plane
  • parallelepiped
  • prism
    • +
+
+
+
+
+ + +`; +} + +const CHARTS = [ + [13, "1-13", "Planes, perpendiculars, parallel lines"], + [26, "14-26", "Parallel planes, solid angles, parallelepipeds"], + [39, "27-39", "Parallelepiped ratios, prisms"] +]; + +if (fs.existsSync(GEOM_DIR)) { + CHARTS.forEach(([max, range, desc]) => { + const filter = closure(max); + const m = toMermaid(filter); + const nodes = discourse.nodes.filter(filter); + const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); + const fname = `geometry_topology-euclid-elements-book-xi-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`; + fs.writeFileSync(path.join(GEOM_DIR, fname), htmlTemplate(`Euclid's Elements Book XI — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); + console.log("Wrote", fname); + }); +} + +// Book XI index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book XI - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book XI (Joyce) +
+ +

Euclid's Elements Book XI

+

Solid geometry: planes, perpendiculars, parallelepipeds, prisms. 39 propositions, 28 definitions. Depends on Books I and VI.

+
+ Propositions 1–13 Planes, perpendiculars, parallel lines + Propositions 14–26 Parallel planes, solid angles, parallelepipeds + Propositions 27–39 Parallelepiped ratios, prisms +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-xi.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-xi.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-xii.js b/generator/build-euclid-book-xii.js new file mode 100644 index 0000000000000000000000000000000000000000..875808123898a4489e90b38bb277a5d344776ac6 --- /dev/null +++ b/generator/build-euclid-book-xii.js @@ -0,0 +1,304 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book XII discourse JSON and Mermaid charts. + * 18 propositions. Measurement: circles, pyramids, cones, cylinders, spheres. + * Depends on Books I, V, VI, XI. Source: David E. Joyce. + * + * Charts: 2. Props 1-9, 10-18. + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPS = [ + { n: 1, short: "Similar polygons: as squares on diameters", full: "Similar polygons in circles: to one another as squares on diameters" }, + { n: 2, short: "Circles: as squares on diameters", full: "Circles are to one another as the squares on their diameters" }, + { n: 3, short: "Pyramid divided", full: "Pyramid with triangular base: divided into two pyramids, two prisms; prisms greater than half" }, + { n: 4, short: "Pyramids: base as prisms", full: "Two pyramids same height, triangular bases, divided: base to base as all prisms" }, + { n: 5, short: "Pyramids: as bases", full: "Pyramids same height, triangular bases: to one another as bases" }, + { n: 6, short: "Pyramids polygonal: as bases", full: "Pyramids same height, polygonal bases: to one another as bases" }, + { n: 7, short: "Prism into three pyramids", full: "Prism with triangular base: divided into three equal pyramids" }, + { n: 8, short: "Similar pyramids: triplicate ratio", full: "Similar pyramids triangular bases: in triplicate ratio of corresponding sides" }, + { n: 9, short: "Equal pyramids: bases reciprocally proportional", full: "Equal pyramids triangular bases: bases reciprocally proportional to heights" }, + { n: 10, short: "Cone third of cylinder", full: "Any cone is third part of cylinder same base and equal height" }, + { n: 11, short: "Cones, cylinders: as bases", full: "Cones and cylinders same height: to one another as bases" }, + { n: 12, short: "Similar cones, cylinders: triplicate", full: "Similar cones and cylinders: in triplicate ratio of diameters of bases" }, + { n: 13, short: "Cylinder cut: as axes", full: "Cylinder cut by plane parallel to opposite: cylinder to cylinder as axis to axis" }, + { n: 14, short: "Cones, cylinders equal bases: as heights", full: "Cones and cylinders on equal bases: to one another as heights" }, + { n: 15, short: "Equal cones, cylinders: reciprocally proportional", full: "Equal cones and cylinders: bases reciprocally proportional to heights" }, + { n: 16, short: "Inscribe polygon in greater circle", full: "Given two circles same center: inscribe in greater equilateral polygon even sides not touching lesser" }, + { n: 17, short: "Inscribe polyhedron in greater sphere", full: "Given two spheres same center: inscribe in greater polyhedral solid not touching lesser" }, + { n: 18, short: "Spheres: triplicate ratio", full: "Spheres are to one another in triplicate ratio of their diameters" } +]; + +const FOUNDATIONS = ["BookI", "BookV", "BookVI", "BookXI"]; +const DEPS = {}; +for (let i = 1; i <= 18; i++) DEPS[i] = FOUNDATIONS; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-xii", + name: "Euclid's Elements, Book XII", + subject: "measurement", + variant: "classical", + description: "Measurement of figures: circles, pyramids, cones, cylinders, spheres. 18 propositions. Depends on Books I, V, VI, XI. Source: David E. Joyce.", + structure: { books: 12, propositions: 18, foundationTypes: ["foundation"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book XII Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book XII", "measurement", "pyramid", "cone", "cylinder", "sphere"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book XII", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookXII/bookXII.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "BookV", type: "foundation", label: "Book V — Proportions", shortLabel: "Book V", short: "Foundation", book: 5, colorClass: "foundation" }, + { id: "BookVI", type: "foundation", label: "Book VI — Similar figures", shortLabel: "Book VI", short: "Foundation", book: 6, colorClass: "foundation" }, + { id: "BookXI", type: "foundation", label: "Book XI — Solid geometry", shortLabel: "Book XI", short: "Foundation", book: 11, colorClass: "foundation" } +); + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. XII.${prop.n}`, + short: prop.short, + book: 12, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-xii.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-xii.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(FOUNDATIONS); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Measurement + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book XII Index + Euclid's Elements Book XII (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book XII (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, V, VI, XI (foundation)
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book XII
  • measurement
  • pyramid
  • cone
  • cylinder
  • sphere
    • +
+
+
+
+
+ + +`; +} + +const CHARTS = [ + [9, "1-9", "Circles, pyramids, prisms"], + [18, "10-18", "Cones, cylinders, spheres"] +]; + +if (fs.existsSync(GEOM_DIR)) { + CHARTS.forEach(([max, range, desc]) => { + const filter = closure(max); + const m = toMermaid(filter); + const nodes = discourse.nodes.filter(filter); + const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); + const fname = `geometry_topology-euclid-elements-book-xii-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`; + fs.writeFileSync(path.join(GEOM_DIR, fname), htmlTemplate(`Euclid's Elements Book XII — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); + console.log("Wrote", fname); + }); +} + +// Book XII index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book XII - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book XII (Joyce) +
+ +

Euclid's Elements Book XII

+

Measurement of figures: circles (XII.2), pyramids (XII.5–7), cones and cylinders (XII.10–15), spheres (XII.18). 18 propositions. Depends on Books I, V, VI, XI.

+
+ Propositions 1–9 Circles, pyramids, prisms + Propositions 10–18 Cones, cylinders, spheres +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-xii.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-xii.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-euclid-book-xiii.js b/generator/build-euclid-book-xiii.js new file mode 100644 index 0000000000000000000000000000000000000000..2e1362f0fa1250accca01994e7c9a31459bbc091 --- /dev/null +++ b/generator/build-euclid-book-xiii.js @@ -0,0 +1,305 @@ +#!/usr/bin/env node +/** + * Build Euclid's Elements Book XIII discourse JSON and Mermaid charts. + * 18 propositions. Regular solids: tetrahedron, octahedron, cube, icosahedron, dodecahedron. + * Depends on Books I, IV, VI, X, XI. Source: David E. Joyce. + * + * Charts: 2. Props 1-9, 10-18. + */ + +const fs = require('fs'); +const path = require('path'); + +const PROPS = [ + { n: 1, short: "Extreme and mean: square on greater", full: "Line cut in extreme and mean ratio: square on greater plus half whole equals five times square on half" }, + { n: 2, short: "Square five times: extreme and mean", full: "If square on line five times square on segment: double segment cut in extreme and mean, greater is remainder" }, + { n: 3, short: "Extreme and mean: sum of segments", full: "Line cut in extreme and mean: square on lesser + half greater equals five times square on half" }, + { n: 4, short: "Extreme and mean: sum of squares", full: "Line cut in extreme and mean: sum of squares on whole and lesser triple square on greater" }, + { n: 5, short: "Extreme and mean: add greater", full: "Line cut in extreme and mean, add greater: whole cut in extreme and mean, original is greater" }, + { n: 6, short: "Rational cut: apotome", full: "Rational line cut in extreme and mean ratio: each segment is apotome" }, + { n: 7, short: "Equilateral pentagon: three angles", full: "Equilateral pentagon: if three angles equal (order or not), pentagon equiangular" }, + { n: 8, short: "Pentagon: diagonals in extreme and mean", full: "Equilateral equiangular pentagon: diagonals subtending two angles cut in extreme and mean ratio" }, + { n: 9, short: "Hexagon + decagon: extreme and mean", full: "Side of hexagon + decagon in same circle: cut in extreme and mean, greater is hexagon" }, + { n: 10, short: "Pentagon: square equals hexagon + decagon", full: "Equilateral pentagon in circle: square on side equals sum of squares on hexagon and decagon" }, + { n: 11, short: "Pentagon in rational circle: minor", full: "Equilateral pentagon in circle with rational diameter: side is minor" }, + { n: 12, short: "Equilateral triangle: side triple radius", full: "Equilateral triangle in circle: square on side triple square on radius" }, + { n: 13, short: "Construct tetrahedron in sphere", full: "To construct pyramid (tetrahedron) in given sphere; diameter squared 1.5 times side squared" }, + { n: 14, short: "Construct octahedron in sphere", full: "To construct octahedron in sphere; diameter squared double side squared" }, + { n: 15, short: "Construct cube in sphere", full: "To construct cube in sphere; diameter squared triple side squared" }, + { n: 16, short: "Construct icosahedron in sphere", full: "To construct icosahedron in sphere; side is minor" }, + { n: 17, short: "Construct dodecahedron in sphere", full: "To construct dodecahedron in sphere; side is apotome" }, + { n: 18, short: "Compare five regular solids", full: "To set out sides of five figures and compare them; no other such figure exists" } +]; + +const FOUNDATIONS = ["BookI", "BookIV", "BookVI", "BookX", "BookXI"]; +const DEPS = {}; +for (let i = 1; i <= 18; i++) DEPS[i] = FOUNDATIONS; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "euclid-elements-book-xiii", + name: "Euclid's Elements, Book XIII", + subject: "regular_solids", + variant: "classical", + description: "Regular solids: tetrahedron, octahedron, cube, icosahedron, dodecahedron. 18 propositions. Depends on Books I, IV, VI, X, XI. Source: David E. Joyce.", + structure: { books: 13, propositions: 18, foundationTypes: ["foundation"] } + }, + metadata: { + created: "2026-03-18", + lastUpdated: "2026-03-18", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Euclid's Elements Book XIII Dependency Graph. Programming Framework.", + keywords: ["Euclid", "Elements", "Book XIII", "regular solids", "Platonic", "tetrahedron", "octahedron", "cube", "icosahedron", "dodecahedron"] + }, + sources: [ + { id: "joyce", type: "digital", authors: "Joyce, David E.", title: "Euclid's Elements, Book XIII", year: "1996", url: "https://mathcs.clarku.edu/~djoyce/java/elements/bookXIII/bookXIII.html", notes: "Clark University" } + ], + nodes: [], + edges: [], + colorScheme: { + foundation: { fill: "#95a5a6", stroke: "#7f8c8d" }, + proposition: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +discourse.nodes.push( + { id: "BookI", type: "foundation", label: "Book I — Plane geometry", shortLabel: "Book I", short: "Foundation", book: 1, colorClass: "foundation" }, + { id: "BookIV", type: "foundation", label: "Book IV — Inscribed figures", shortLabel: "Book IV", short: "Foundation", book: 4, colorClass: "foundation" }, + { id: "BookVI", type: "foundation", label: "Book VI — Similar figures", shortLabel: "Book VI", short: "Foundation", book: 6, colorClass: "foundation" }, + { id: "BookX", type: "foundation", label: "Book X — Incommensurables", shortLabel: "Book X", short: "Foundation", book: 10, colorClass: "foundation" }, + { id: "BookXI", type: "foundation", label: "Book XI — Solid geometry", shortLabel: "Book XI", short: "Foundation", book: 11, colorClass: "foundation" } +); + +for (const prop of PROPS) { + discourse.nodes.push({ + id: `Prop${prop.n}`, + type: "proposition", + label: prop.full, + shortLabel: `Prop. XIII.${prop.n}`, + short: prop.short, + book: 13, + number: prop.n, + colorClass: "proposition" + }); + for (const dep of DEPS[prop.n]) { + discourse.edges.push({ from: dep, to: `Prop${prop.n}` }); + } +} + +const dataDir = path.join(__dirname, "..", "data"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(path.join(dataDir, "euclid-elements-book-xiii.json"), JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote euclid-elements-book-xiii.json"); + +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d"); + lines.push(" classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085"); + const foundIds = nodes.filter(n => n.type === "foundation").map(n => n.id).join(","); + const propIds = nodes.filter(n => n.type === "proposition").map(n => n.id).join(","); + if (foundIds) lines.push(` class ${foundIds} foundation`); + lines.push(` class ${propIds} proposition`); + return lines.join("\n"); +} + +function closure(propMax) { + const needed = new Set(FOUNDATIONS); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + return n => needed.has(n.id); +} + +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const GEOM_DIR = path.join(MATH_DB, "processes", "geometry_topology"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Regular Solids + Source: Euclid's Elements +
+
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid Book XIII Index + Euclid's Elements Book XIII (Joyce) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Euclid's Elements, Book XIII (David E. Joyce, Clark University)

+
+
+

Dependency Flowchart

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Gray
Book I, IV, VI, X, XI (foundation)
+
Teal
Propositions
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Euclid
  • Elements
  • Book XIII
  • regular solids
  • Platonic
  • tetrahedron
  • octahedron
  • cube
  • icosahedron
  • dodecahedron
    • +
+
+
+
+
+ + +`; +} + +const CHARTS = [ + [9, "1-9", "Extreme and mean ratio, pentagon, hexagon, decagon"], + [18, "10-18", "Five Platonic solids in sphere"] +]; + +if (fs.existsSync(GEOM_DIR)) { + CHARTS.forEach(([max, range, desc]) => { + const filter = closure(max); + const m = toMermaid(filter); + const nodes = discourse.nodes.filter(filter); + const edges = discourse.edges.filter(e => filter({ id: e.from }) && filter({ id: e.to })); + const fname = `geometry_topology-euclid-elements-book-xiii-props-${range.replace(/–/g, "-").replace(" ", "-")}.html`; + fs.writeFileSync(path.join(GEOM_DIR, fname), htmlTemplate(`Euclid's Elements Book XIII — Propositions ${range}`, desc, m, nodes.length, edges.length), "utf8"); + console.log("Wrote", fname); + }); +} + +// Book XIII index +if (fs.existsSync(GEOM_DIR)) { + const indexHtml = ` + + + + + Euclid's Elements Book XIII - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Euclid's Elements (all books) + Euclid's Elements Book XIII (Joyce) +
+ +

Euclid's Elements Book XIII

+

Regular solids: tetrahedron, octahedron, cube, icosahedron, dodecahedron. 18 propositions. Depends on Books I, IV, VI, X, XI. XIII.18: no other such figure exists.

+
+ Propositions 1–9 Extreme and mean ratio, pentagon + Propositions 10–18 Five Platonic solids +
+
+ +`; + fs.writeFileSync(path.join(GEOM_DIR, "geometry_topology-euclid-elements-book-xiii.html"), indexHtml, "utf8"); + console.log("Wrote geometry_topology-euclid-elements-book-xiii.html"); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-peano-arithmetic.js b/generator/build-peano-arithmetic.js new file mode 100644 index 0000000000000000000000000000000000000000..a5ed464c6e9106f308f6e9a4f0ce4ab13fbf0e5d --- /dev/null +++ b/generator/build-peano-arithmetic.js @@ -0,0 +1,371 @@ +#!/usr/bin/env node +/** + * Build Peano Arithmetic discourse JSON and Mermaid. + * Based on Landau, Foundations of Analysis (1930) and standard Peano development. + * Structure: 5 axioms → definitions (addition, multiplication) → theorems. + */ + +const fs = require('fs'); +const path = require('path'); + +const NODES = [ + { id: "A1", type: "axiom", label: "0 is a natural number", short: "0 ∈ N", colorClass: "axiom" }, + { id: "A2", type: "axiom", label: "No predecessor of 0: S(x) ≠ 0", short: "0 not a successor", colorClass: "axiom" }, + { id: "A3", type: "axiom", label: "Successor injective: S(x)=S(y) ⇒ x=y", short: "S injective", colorClass: "axiom" }, + { id: "A4", type: "axiom", label: "Closure: S(x) ∈ N for all x ∈ N", short: "N closed under S", colorClass: "axiom" }, + { id: "A5", type: "axiom", label: "Induction: if 0∈K and (x∈K⇒S(x)∈K) then K=N", short: "Induction", colorClass: "axiom" }, + { id: "T1", type: "theorem", label: "x≠y ⇒ S(x)≠S(y)", short: "Contrapositive of A3", colorClass: "theorem" }, + { id: "T2", type: "theorem", label: "S(x)≠x for all x", short: "Successor ≠ identity", colorClass: "theorem" }, + { id: "T3", type: "theorem", label: "If x≠0 then x=S(u) for some u", short: "Every nonzero is successor", colorClass: "theorem" }, + { id: "DefAdd", type: "definition", label: "Addition: x+0=x, x+S(y)=S(x+y)", short: "Definition of +", colorClass: "definition" }, + { id: "T4", type: "theorem", label: "Addition is well-defined for all x,y", short: "Add well-defined", colorClass: "theorem" }, + { id: "T5", type: "theorem", label: "(x+y)+z = x+(y+z)", short: "Associativity of +", colorClass: "theorem" }, + { id: "T6", type: "theorem", label: "0+x = x", short: "Left identity", colorClass: "theorem" }, + { id: "T7", type: "theorem", label: "S(x)+y = S(x+y)", short: "Successor and add", colorClass: "theorem" }, + { id: "T8", type: "theorem", label: "x+y = y+x", short: "Commutativity of +", colorClass: "theorem" }, + { id: "T9", type: "theorem", label: "x+y=x+z ⇒ y=z", short: "Cancellation for +", colorClass: "theorem" }, + { id: "DefMul", type: "definition", label: "Multiplication: x·0=0, x·S(y)=x·y+x", short: "Definition of ·", colorClass: "definition" }, + { id: "T10", type: "theorem", label: "Multiplication is well-defined for all x,y", short: "Mul well-defined", colorClass: "theorem" }, + { id: "T11", type: "theorem", label: "x·0 = 0", short: "Zero times", colorClass: "theorem" }, + { id: "T12", type: "theorem", label: "0·x = 0", short: "Zero from left", colorClass: "theorem" }, + { id: "T13", type: "theorem", label: "S(x)·y = x·y + y", short: "Successor and mul", colorClass: "theorem" }, + { id: "T14", type: "theorem", label: "x·y = y·x", short: "Commutativity of ·", colorClass: "theorem" }, + { id: "T15", type: "theorem", label: "(x·y)·z = x·(y·z)", short: "Associativity of ·", colorClass: "theorem" }, + { id: "T16", type: "theorem", label: "x·(y+z) = x·y + x·z", short: "Distributivity", colorClass: "theorem" }, + { id: "T17", type: "theorem", label: "(x+y)·z = x·z + y·z", short: "Distributivity (right)", colorClass: "theorem" }, + { id: "T18", type: "theorem", label: "x≤y iff ∃z x+z=y", short: "Order definition", colorClass: "theorem" }, + { id: "T19", type: "theorem", label: "Trichotomy: exactly one of x0 ⇒ x·z≤y·z", short: "Order + mul", colorClass: "theorem" }, + { id: "T22", type: "theorem", label: "1·x = x (where 1=S(0))", short: "Multiplicative identity", colorClass: "theorem" }, + { id: "T23", type: "theorem", label: "x·1 = x", short: "Right identity", colorClass: "theorem" }, + { id: "T24", type: "theorem", label: "Well-ordering: every nonempty subset has least element", short: "Well-ordering", colorClass: "theorem" }, + { id: "T25", type: "theorem", label: "Strong induction principle", short: "Strong induction", colorClass: "theorem" } +]; + +// Dependencies (from → to). Based on Landau's development. +const DEPS = { + T1: ["A3"], + T2: ["A1", "A2", "A3", "T1", "A5"], + T3: ["A5"], + DefAdd: ["A5"], + T4: ["DefAdd", "A5"], + T5: ["DefAdd", "A5"], + T6: ["DefAdd", "A5"], + T7: ["DefAdd", "T6", "A5"], + T8: ["DefAdd", "T5", "T6", "T7", "A5"], + T9: ["DefAdd", "T8", "A5"], + DefMul: ["DefAdd", "A5"], + T10: ["DefMul", "A5"], + T11: ["DefMul"], + T12: ["DefMul", "T6", "A5"], + T13: ["DefMul", "T8", "A5"], + T14: ["DefMul", "T12", "T13", "A5"], + T15: ["DefMul", "T5", "T8", "A5"], + T16: ["DefMul", "T5", "T8", "T15", "A5"], + T17: ["T16", "T8"], + T18: ["DefAdd", "T8", "T9"], + T19: ["T18", "T9"], + T20: ["T18", "T8"], + T21: ["T18", "T16", "T14"], + T22: ["DefMul", "T6", "A5"], + T23: ["T14", "T22"], + T24: ["T18", "T19", "A5"], + T25: ["T18", "T24", "A5"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "peano-arithmetic", + name: "Peano Arithmetic", + subject: "arithmetic", + variant: "classical", + description: "Axiomatic development of natural number arithmetic. Five axioms, definitions of addition and multiplication, and key theorems (associativity, commutativity, distributivity, order). Based on Landau, Foundations of Analysis.", + structure: { axioms: 5, definitions: 2, theorems: 25 } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Peano Arithmetic Dependency Graph. Programming Framework.", + keywords: ["Peano", "arithmetic", "natural numbers", "induction", "foundations"] + }, + sources: [ + { id: "landau", type: "primary", authors: "Landau, E.", title: "Foundations of Analysis", year: "1930", publisher: "Chelsea", edition: "1951", notes: "Canonical development" }, + { id: "wikipedia", type: "digital", title: "Peano axioms", url: "https://en.wikipedia.org/wiki/Peano_axioms", notes: "Overview and definitions" } + ], + nodes: [], + edges: [], + colorScheme: { + axiom: { fill: "#e74c3c", stroke: "#c0392b" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + theorem: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Add nodes +for (const n of NODES) { + discourse.nodes.push({ + id: n.id, + type: n.type, + label: n.label, + shortLabel: n.id, + short: n.short, + colorClass: n.colorClass + }); + for (const dep of DEPS[n.id] || []) { + discourse.edges.push({ from: dep, to: n.id }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +const outPath = path.join(dataDir, "peano-arithmetic.json"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote", outPath); + +// Generate Mermaid +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || n.label; + const lbl = (n.shortLabel || n.id) + "\\n" + (desc.length > 30 ? desc.slice(0, 27) + "..." : desc); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085"); + const axiomIds = nodes.filter(n => n.type === "axiom").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const thmIds = nodes.filter(n => n.type === "theorem").map(n => n.id).join(","); + lines.push(` class ${axiomIds} axiom`); + lines.push(` class ${defIds} definition`); + lines.push(` class ${thmIds} theorem`); + return lines.join("\n"); +} + +function closure(ids) { + const needed = new Set(ids); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +function toMermaidWithCounts(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; +} + +// 3 sections: ~10 each +const sections = [ + { name: "axioms-foundations", ids: ["A1","A2","A3","A4","A5","T1","T2","T3","DefAdd","T4","T5","T6"], title: "Axioms & Addition Foundations", desc: "Five Peano axioms, basic successor theorems, definition of addition, associativity and left identity" }, + { name: "addition-multiplication", ids: ["T7","T8","T9","DefMul","T10","T11","T12","T13","T14","T15","T16","T17"], title: "Commutativity, Multiplication, Distributivity", desc: "Commutativity and cancellation of addition, definition of multiplication, commutativity and associativity of multiplication, distributivity" }, + { name: "order-induction", ids: ["T18","T19","T20","T21","T22","T23","T24","T25"], title: "Order & Induction", desc: "Order relation, trichotomy, compatibility with operations, well-ordering, strong induction" } +]; + +const subgraphData = []; +for (const s of sections) { + const filter = closure(s.ids); + const { mermaid: sub, nodes: n, edges: e } = toMermaidWithCounts(filter); + subgraphData.push({ ...s, mermaid: sub, nodes: n, edges: e }); + fs.writeFileSync(path.join(dataDir, `peano-arithmetic-${s.name}.mmd`), sub, "utf8"); + console.log("Wrote", path.join(dataDir, `peano-arithmetic-${s.name}.mmd`)); +} + +// Full graph +fs.writeFileSync(path.join(dataDir, "peano-arithmetic.mmd"), toMermaid(), "utf8"); + +// Generate HTML +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const NUM_DIR = path.join(MATH_DB, "processes", "number_theory"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Foundations / Arithmetic + Source: Landau, Peano +
+
+
+ ← Back to Mathematics Database + Peano Arithmetic Index + Peano Axioms (Wikipedia) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Landau, E. Foundations of Analysis (1930); Peano, G. Arithmetices principia (1889)

+
+
+

Dependency Flowchart

+

Note: Arrows mean "depends on" (tail → head).

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Red
Axioms
+
Blue
Definitions
+
Teal
Theorems
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • Peano
  • arithmetic
  • natural numbers
  • induction
  • successor
  • foundations
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(path.join(MATH_DB, "processes"))) { + for (const d of subgraphData) { + const html = htmlTemplate( + `Peano Arithmetic — ${d.title}`, + d.desc + ". Shows how theorems depend on axioms, definitions, and prior theorems.", + d.mermaid, + d.nodes, + d.edges + ); + const fileName = "number_theory-peano-arithmetic-" + d.name; + fs.writeFileSync(path.join(NUM_DIR, fileName + ".html"), html, "utf8"); + console.log("Wrote", path.join(NUM_DIR, fileName + ".html")); + } + // Index page + const indexHtml = ` + + + + + Peano Arithmetic - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Peano Axioms (Wikipedia) +
+ +

Peano Arithmetic

+

Axiomatic development of natural number arithmetic. Five axioms, definitions of addition and multiplication, and key theorems. Based on Landau, Foundations of Analysis. Split into three views.

+
+ Chart 1 — Axioms & Addition Foundations + Chart 2 — Commutativity, Multiplication, Distributivity + Chart 3 — Order & Induction +
+
+ +`; + fs.writeFileSync(path.join(NUM_DIR, "number_theory-peano-arithmetic.html"), indexHtml, "utf8"); + console.log("Wrote", path.join(NUM_DIR, "number_theory-peano-arithmetic.html")); +} else { + console.log("MATH_DB not found - skipping HTML generation."); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/build-propositional-logic.js b/generator/build-propositional-logic.js new file mode 100644 index 0000000000000000000000000000000000000000..acf774a8471f2c4a3536963d83b48d3635af5040 --- /dev/null +++ b/generator/build-propositional-logic.js @@ -0,0 +1,373 @@ +#!/usr/bin/env node +/** + * Build Propositional Logic discourse JSON and Mermaid. + * Hilbert-style (Łukasiewicz P2): 3 axioms + MP, definitions of ∨∧↔, key theorems. + * Based on Frege, Łukasiewicz, Church; Wikipedia Propositional calculus. + */ + +const fs = require('fs'); +const path = require('path'); + +const NODES = [ + { id: "A1", type: "axiom", label: "φ → (ψ → φ)", short: "Weakening", colorClass: "axiom" }, + { id: "A2", type: "axiom", label: "(φ→(ψ→χ)) → ((φ→ψ)→(φ→χ))", short: "Distrib. of impl.", colorClass: "axiom" }, + { id: "A3", type: "axiom", label: "(¬φ→¬ψ) → (ψ→φ)", short: "Contraposition", colorClass: "axiom" }, + { id: "MP", type: "axiom", label: "Modus Ponens: φ, (φ→ψ) ⊢ ψ", short: "MP", colorClass: "axiom" }, + { id: "T1", type: "theorem", label: "φ → φ", short: "Self-implication", colorClass: "theorem" }, + { id: "T2", type: "theorem", label: "¬¬φ → φ", short: "Double neg. elim", colorClass: "theorem" }, + { id: "T3", type: "theorem", label: "φ → ¬¬φ", short: "Double neg. intro", colorClass: "theorem" }, + { id: "T4", type: "theorem", label: "(φ→ψ) → (¬ψ→¬φ)", short: "Transposition", colorClass: "theorem" }, + { id: "T5", type: "theorem", label: "(φ→ψ)∧(ψ→χ) ⇒ (φ→χ)", short: "Hyp. syllogism", colorClass: "theorem" }, + { id: "DefOr", type: "definition", label: "φ ∨ ψ := ¬φ → ψ", short: "Def. disjunction", colorClass: "definition" }, + { id: "DefAnd", type: "definition", label: "φ ∧ ψ := ¬(φ → ¬ψ)", short: "Def. conjunction", colorClass: "definition" }, + { id: "DefIff", type: "definition", label: "φ ↔ ψ := (φ→ψ)∧(ψ→φ)", short: "Def. biconditional", colorClass: "definition" }, + { id: "T6", type: "theorem", label: "φ → (φ ∨ ψ)", short: "Addition (∨I)", colorClass: "theorem" }, + { id: "T7", type: "theorem", label: "(φ∧ψ) → φ", short: "Simplification (∧E)", colorClass: "theorem" }, + { id: "T8", type: "theorem", label: "(φ∧ψ) → ψ", short: "Simplification (∧E)", colorClass: "theorem" }, + { id: "T9", type: "theorem", label: "φ → (ψ → (φ∧ψ))", short: "Conjunction (∧I)", colorClass: "theorem" }, + { id: "T10", type: "theorem", label: "(φ→ψ) ↔ (¬φ∨ψ)", short: "Material impl.", colorClass: "theorem" }, + { id: "T11", type: "theorem", label: "¬(φ∧ψ) ↔ (¬φ∨¬ψ)", short: "De Morgan (1)", colorClass: "theorem" }, + { id: "T12", type: "theorem", label: "¬(φ∨ψ) ↔ (¬φ∧¬ψ)", short: "De Morgan (2)", colorClass: "theorem" }, + { id: "T13", type: "theorem", label: "φ ∨ ¬φ", short: "Excluded middle", colorClass: "theorem" }, + { id: "T14", type: "theorem", label: "¬(φ ∧ ¬φ)", short: "Non-contradiction", colorClass: "theorem" }, + { id: "T15", type: "theorem", label: "(φ∧¬φ) → ψ", short: "Explosion", colorClass: "theorem" }, + { id: "T16", type: "theorem", label: "(φ∨ψ) ↔ (ψ∨φ)", short: "Commutation (∨)", colorClass: "theorem" }, + { id: "T17", type: "theorem", label: "(φ∧ψ) ↔ (ψ∧φ)", short: "Commutation (∧)", colorClass: "theorem" }, + { id: "T18", type: "theorem", label: "(φ∧(ψ∨χ)) ↔ ((φ∧ψ)∨(φ∧χ))", short: "Distribution", colorClass: "theorem" }, + { id: "T19", type: "theorem", label: "Deduction theorem", short: "Deduction thm", colorClass: "theorem" } +]; + +// Dependencies (from → to). Based on Hilbert/Łukasiewicz P2 development. +const DEPS = { + T1: ["A1", "A2", "MP"], + T2: ["A3", "T1", "MP"], + T3: ["A1", "A3", "MP"], + T4: ["A3", "T2", "T3", "MP"], + T5: ["A2", "T1", "MP"], + DefOr: ["A1", "A2", "A3", "MP"], + DefAnd: ["DefOr", "A3", "MP"], + DefIff: ["DefAnd", "T9", "MP"], + T6: ["DefOr", "A1", "MP"], + T7: ["DefAnd", "A1", "A3", "MP"], + T8: ["DefAnd", "A1", "A3", "MP"], + T9: ["A1", "A2", "MP"], + T10: ["DefOr", "T4", "MP"], + T11: ["DefAnd", "DefOr", "T4", "T6", "MP"], + T12: ["DefAnd", "DefOr", "T4", "MP"], + T13: ["DefOr", "T2", "T3", "MP"], + T14: ["DefAnd", "T4", "MP"], + T15: ["DefAnd", "A1", "A2", "MP"], + T16: ["DefOr", "T4", "MP"], + T17: ["DefAnd", "T9", "MP"], + T18: ["DefAnd", "DefOr", "T6", "T7", "T8", "T9", "MP"], + T19: ["A1", "A2", "MP"] +}; + +const discourse = { + schemaVersion: "1.0", + discourse: { + id: "propositional-logic", + name: "Propositional Logic", + subject: "logic", + variant: "classical", + description: "Hilbert-style axiomatic development of classical propositional logic. Three axioms (Łukasiewicz P2), modus ponens, definitions of disjunction, conjunction, biconditional, and key theorems (double negation, De Morgan, excluded middle, deduction theorem).", + structure: { axioms: 4, definitions: 3, theorems: 19 } + }, + metadata: { + created: "2026-03-15", + lastUpdated: "2026-03-15", + version: "1.0.0", + license: "CC BY 4.0", + authors: ["Welz, G."], + methodology: "Programming Framework", + citation: "Welz, G. (2026). Propositional Logic Dependency Graph. Programming Framework.", + keywords: ["propositional logic", "Hilbert", "Łukasiewicz", "tautology", "modus ponens"] + }, + sources: [ + { id: "frege", type: "primary", authors: "Frege, G.", title: "Begriffsschrift", year: "1879", notes: "First axiomatic propositional logic" }, + { id: "lukasiewicz", type: "primary", authors: "Łukasiewicz, J.", title: "Elements of Mathematical Logic", year: "1929", notes: "P2: 3 axioms" }, + { id: "wikipedia", type: "digital", title: "Propositional calculus", url: "https://en.wikipedia.org/wiki/Propositional_calculus", notes: "Axioms and theorems" } + ], + nodes: [], + edges: [], + colorScheme: { + axiom: { fill: "#e74c3c", stroke: "#c0392b" }, + definition: { fill: "#3498db", stroke: "#2980b9" }, + theorem: { fill: "#1abc9c", stroke: "#16a085" } + } +}; + +// Add nodes +for (const n of NODES) { + discourse.nodes.push({ + id: n.id, + type: n.type, + label: n.label, + shortLabel: n.id, + short: n.short, + colorClass: n.colorClass + }); + for (const dep of DEPS[n.id] || []) { + discourse.edges.push({ from: dep, to: n.id }); + } +} + +// Write JSON +const dataDir = path.join(__dirname, "..", "data"); +const outPath = path.join(dataDir, "propositional-logic.json"); +fs.mkdirSync(dataDir, { recursive: true }); +fs.writeFileSync(outPath, JSON.stringify(discourse, null, 2), "utf8"); +console.log("Wrote", outPath); + +// Sanitize label for Mermaid (Unicode arrows/symbols can cause "Syntax error in text") +function sanitizeMermaidLabel(s) { + return String(s) + .replace(/→/g, "impl") + .replace(/⊢/g, "|-") + .replace(/∨/g, "or") + .replace(/∧/g, "and") + .replace(/↔/g, "iff") + .replace(/\n/g, " "); +} + +// Generate Mermaid - use parentheses for node shape (more robust than brackets) +function toMermaid(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + const lines = ["graph TD"]; + for (const n of nodes) { + const desc = n.short || n.label; + const raw = (n.shortLabel || n.id) + " " + (desc.length > 30 ? desc.slice(0, 27) + "..." : desc); + const lbl = sanitizeMermaidLabel(raw).replace(/"/g, '\\"'); + lines.push(` ${n.id}("${lbl}")`); + } + for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); + } + lines.push(" classDef axiom fill:#e74c3c,color:#fff,stroke:#c0392b"); + lines.push(" classDef definition fill:#3498db,color:#fff,stroke:#2980b9"); + lines.push(" classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085"); + const axiomIds = nodes.filter(n => n.type === "axiom").map(n => n.id).join(","); + const defIds = nodes.filter(n => n.type === "definition").map(n => n.id).join(","); + const thmIds = nodes.filter(n => n.type === "theorem").map(n => n.id).join(","); + if (axiomIds) lines.push(` class ${axiomIds} axiom`); + if (defIds) lines.push(` class ${defIds} definition`); + if (thmIds) lines.push(` class ${thmIds} theorem`); + return lines.join("\n"); +} + +function closure(ids) { + const needed = new Set(ids); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => needed.has(n.id); +} + +function toMermaidWithCounts(filter) { + const nodes = filter ? discourse.nodes.filter(filter) : discourse.nodes; + const nodeIds = new Set(nodes.map(n => n.id)); + const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + return { mermaid: toMermaid(filter), nodes: nodes.length, edges: edges.length }; +} + +// 3 sections +const sections = [ + { name: "axioms-implication", ids: ["A1","A2","A3","MP","T1","T2","T3","T4","T5"], title: "Axioms & Implication", desc: "Three Hilbert axioms, modus ponens, self-implication, double negation, transposition, hypothetical syllogism" }, + { name: "definitions-connectives", ids: ["DefOr","DefAnd","DefIff","T6","T7","T8","T9","T10","T11","T12"], title: "Definitions & Connectives", desc: "Definitions of disjunction, conjunction, biconditional; simplification, addition, material implication, De Morgan" }, + { name: "tautologies-metalogic", ids: ["T13","T14","T15","T16","T17","T18","T19"], title: "Tautologies & Metalogic", desc: "Excluded middle, non-contradiction, explosion, commutation, distribution, deduction theorem" } +]; + +const subgraphData = []; +for (const s of sections) { + const filter = closure(s.ids); + const { mermaid: sub, nodes: n, edges: e } = toMermaidWithCounts(filter); + subgraphData.push({ ...s, mermaid: sub, nodes: n, edges: e }); + fs.writeFileSync(path.join(dataDir, `propositional-logic-${s.name}.mmd`), sub, "utf8"); + console.log("Wrote", path.join(dataDir, `propositional-logic-${s.name}.mmd`)); +} + +// Full graph +fs.writeFileSync(path.join(dataDir, "propositional-logic.mmd"), toMermaid(), "utf8"); + +// Generate HTML +const MATH_DB = process.env.MATH_DB || "/home/gdubs/copernicus-web-public/huggingface-space/mathematics-processes-database"; +const DISC_DIR = path.join(MATH_DB, "processes", "discrete_mathematics"); + +function htmlTemplate(title, subtitle, mermaid, nodes, edges) { + const mermaidEscaped = mermaid.replace(//g, ">"); + return ` + + + + + ${title} - Mathematics Process + + + + +
+
+

${title}

+
+ Mathematics + Discrete Mathematics / Logic + Source: Frege, Łukasiewicz +
+
+
+ ← Back to Mathematics Database + Propositional Logic Index + Propositional Calculus (Wikipedia) + Programming Framework +
+ +
+
+

Description

+

${subtitle}

+

Source: Frege, G. Begriffsschrift (1879); Łukasiewicz, J. Elements of Mathematical Logic (1929)

+
+
+

Dependency Flowchart

+

Note: Arrows mean "depends on" (tail → head).

+
${mermaidEscaped}
+
+
+

Color Scheme

+
+
Red
Axioms
+
Blue
Definitions
+
Teal
Theorems
+
+
+
+
+

Statistics

+
    +
  • Nodes: ${nodes}
    • +
  • Edges: ${edges}
    • +
+
+
+

Keywords

+
    +
  • propositional logic
  • Hilbert
  • Łukasiewicz
  • tautology
  • modus ponens
  • De Morgan
    • +
+
+
+
+
+ + +`; +} + +if (fs.existsSync(path.join(MATH_DB, "processes"))) { + for (const d of subgraphData) { + const html = htmlTemplate( + `Propositional Logic — ${d.title}`, + d.desc + ". Shows how theorems depend on axioms, definitions, and prior theorems.", + d.mermaid, + d.nodes, + d.edges + ); + const fileName = "discrete_mathematics-propositional-logic-" + d.name; + fs.writeFileSync(path.join(DISC_DIR, fileName + ".html"), html, "utf8"); + console.log("Wrote", path.join(DISC_DIR, fileName + ".html")); + } + // Index page + const indexHtml = ` + + + + + Propositional Logic - Mathematics Process + + + +
+
+ ← Back to Mathematics Database + Propositional Calculus (Wikipedia) +
+ +

Propositional Logic

+

Hilbert-style axiomatic development of classical propositional logic. Three axioms (Łukasiewicz P2), modus ponens, definitions of disjunction, conjunction, biconditional, and key theorems. Split into three views.

+
+ Chart 1 — Axioms & Implication + Chart 2 — Definitions & Connectives + Chart 3 — Tautologies & Metalogic +
+
+ +`; + fs.writeFileSync(path.join(DISC_DIR, "discrete_mathematics-propositional-logic.html"), indexHtml, "utf8"); + console.log("Wrote", path.join(DISC_DIR, "discrete_mathematics-propositional-logic.html")); +} else { + console.log("MATH_DB not found - skipping HTML generation."); +} + +console.log("Done. Nodes:", discourse.nodes.length, "Edges:", discourse.edges.length); diff --git a/generator/mermaid-from-json.js b/generator/mermaid-from-json.js new file mode 100644 index 0000000000000000000000000000000000000000..16c304b43d04ceecaab2da84db3ff606ad20bf92 --- /dev/null +++ b/generator/mermaid-from-json.js @@ -0,0 +1,67 @@ +#!/usr/bin/env node +/** + * Mermaid Subgraph Generator + * Input: discourse JSON + optional filter (propMax for Euclid, or --full) + * Output: Mermaid graph TD string + * + * Usage: + * node mermaid-from-json.js data/euclid-elements-book-i.json [propMax] + * node mermaid-from-json.js data/euclid-elements-book-i.json --full + */ + +const fs = require('fs'); +const path = require('path'); + +const jsonPath = process.argv[2]; +const filterArg = process.argv[3]; + +if (!jsonPath) { + console.error("Usage: node mermaid-from-json.js [propMax|--full]"); + process.exit(1); +} + +const discourse = JSON.parse(fs.readFileSync(jsonPath, "utf8")); + +function closure(propMax) { + const needed = new Set(); + for (let i = 1; i <= propMax; i++) needed.add(`Prop${i}`); + let changed = true; + while (changed) { + changed = false; + for (const e of discourse.edges) { + if (needed.has(e.to) && !needed.has(e.from)) { needed.add(e.from); changed = true; } + } + } + return n => n.type !== "proposition" || needed.has(n.id); +} + +const filter = filterArg === "--full" || !filterArg + ? () => true + : closure(parseInt(filterArg, 10)); + +const nodes = discourse.nodes.filter(filter); +const nodeIds = new Set(nodes.map(n => n.id)); +const edges = discourse.edges.filter(e => nodeIds.has(e.from) && nodeIds.has(e.to)); + +const lines = ["graph TD"]; +for (const n of nodes) { + const desc = n.short || (n.label && n.label.length > 35 ? n.label.slice(0, 32) + "..." : n.label || n.id); + const lbl = (n.shortLabel || n.id) + "\\n" + (desc || ""); + lines.push(` ${n.id}["${String(lbl).replace(/"/g, '\\"')}"]`); +} +for (const e of edges) { + lines.push(` ${e.from} --> ${e.to}`); +} + +const colorScheme = discourse.colorScheme || {}; +const types = [...new Set(nodes.map(n => n.colorClass || n.type))]; +for (const t of types) { + const c = colorScheme[t] || { fill: "#1abc9c", stroke: "#16a085" }; + lines.push(` classDef ${t} fill:${c.fill},color:#fff,stroke:${c.stroke}`); +} +for (const t of types) { + const ids = nodes.filter(n => (n.colorClass || n.type) === t).map(n => n.id).join(","); + if (ids) lines.push(` class ${ids} ${t}`); +} + +console.log(lines.join("\n")); diff --git a/index.html b/index.html index 414787109e7f6c1c27e74e38a484ab26f1651cc1..7ef8f85419aeecafda7a12fd7b7a8e9415dde5ef 100644 --- a/index.html +++ b/index.html @@ -3,596 +3,607 @@ - The Programming Framework - Universal Process Analysis - - + Programming Framework - Systematic Analysis of Complex Systems - - - -
-
-
-
🛠️
-

The Programming Framework

-

A Universal Method for Process Analysis

-

- Combining Large Language Models with Mermaid visualization to dissect and understand - complex processes across any discipline—from biology to business, physics to psychology. -

-
-
-
- - -
-
-

📋 Summary

-

- The Programming Framework is a universal meta-tool for analyzing complex processes across any discipline by combining Large Language Models (LLMs) with visual flowchart representation. The Framework transforms textual process descriptions into structured, interactive Mermaid flowcharts stored as JSON, enabling systematic analysis, visualization, and integration with knowledge systems. -

-

- Successfully demonstrated through GLMP (Genome Logic Modeling Project) with 50+ biological processes, and applied across Chemistry, Mathematics, Physics, and Computer Science. The Framework serves as the foundational methodology for the CopernicusAI Knowledge Engine, enabling domain-specific process visualization and analysis. -

-
-
- -
-
-

📚 Prior Work & Research Contributions

- -
-

Overview

-

- The Programming Framework represents prior work that demonstrates a novel methodology for analyzing complex processes by combining Large Language Models (LLMs) with visual flowchart representation. This research establishes a universal, domain-agnostic approach to process analysis that transforms textual descriptions into structured, interactive visualizations. -

-
+ .header { + text-align: center; + color: white; + margin-bottom: 40px; + } -
-
-

🔬 Research Contributions

-
    -
  • • Universal Process Analysis: Domain-agnostic methodology applicable across multiple fields
    • -
  • • LLM-Powered Extraction: Automated extraction using Google Gemini 2.0 Flash
    • -
  • • Structured Visualization: Mermaid.js-based flowchart generation encoded as JSON
    • -
  • • Iterative Refinement: Systematic approach enabling continuous improvement
    • -
  • • Scale Demonstration: Applied to 313+ processes across 5 disciplines (Biology: 52, Chemistry: 91, Physics: 21, Computer Science: 21, Mathematics: 20, GLMP: 109)
    • -
  • • Validation: Successfully processes complex biological, chemical, and computational workflows with high accuracy
    • -
-
- -
-

⚙️ Technical Achievements

-
    -
  • • Meta-Tool Architecture: Framework for creating specialized analysis tools
    • -
  • • JSON-Based Storage: Structured format enabling version control and API integration
    • -
  • • Multi-Domain Application: Successfully applied to biological processes (GLMP)
    • -
  • • Integration Framework: Designed for knowledge engines and collaborative platforms
    • -
-
-
+ .header h1 { + font-size: 3rem; + margin-bottom: 10px; + text-shadow: 2px 2px 4px rgba(0,0,0,0.3); + } -
-

🎯 Position Within CopernicusAI Knowledge Engine

-

- The Programming Framework serves as the foundational meta-tool of the CopernicusAI Knowledge Engine, providing the underlying methodology that enables specialized applications: -

-
-
    -
  • • GLMP (Genome Logic Modeling Project)
    • -
  • • CopernicusAI (main knowledge engine)
    • -
  • • Research Papers Metadata Database
    • -
-
    -
  • • Science Video Database
    • -
  • • Multi-domain process analysis
    • -
-
-

- This work establishes a proof-of-concept for AI-assisted process analysis, demonstrating how LLMs can systematically extract and visualize complex logic from textual sources across diverse domains. -

-
-
-
- - -
-
-
-
Any
-
Discipline
-
-
-
LLM
-
Powered
-
-
-
Visual
-
Flowcharts
-
-
-
JSON
-
Structured Data
-
-
-
- - -
-
-

🎯 What is the Programming Framework?

-
-

- The Programming Framework is a meta-tool—a tool for creating tools. It provides a - systematic method for analyzing any complex process by combining the analytical power of Large Language - Models with the clarity of visual flowcharts. -

- -
-
-

🔍 The Problem

-

- Complex processes—whether biological, computational, or organizational—are difficult to - understand because they involve many steps, decision points, and interactions. Traditional - descriptions in text are hard to follow. -

-
+ .header p { + font-size: 1.2rem; + opacity: 0.9; + } -
-

✨ The Solution

-

- Use LLMs to extract process logic from literature, then encode it as Mermaid flowcharts - stored in JSON. Result: Clear, interactive visualizations that reveal hidden patterns and - enable systematic analysis. -

-
-
-
-
-
+ .main-content { + background: white; + border-radius: 15px; + padding: 40px; + box-shadow: 0 10px 30px rgba(0,0,0,0.2); + margin-bottom: 30px; + } - -
-
-

⚙️ How It Works

- -
-
-
1️⃣
-

Input Process

-

Provide scientific papers, documentation, or process descriptions

-
+ .overview { + margin-bottom: 40px; + } -
-
2️⃣
-

LLM Analysis

-

AI extracts steps, decisions, branches, and logic flow

-
+ .overview h2 { + color: #667eea; + font-size: 2rem; + margin-bottom: 20px; + border-bottom: 3px solid #667eea; + padding-bottom: 10px; + } -
-
3️⃣
-

Generate Flowchart

-

Create Mermaid diagram encoded as JSON structure

-
+ .overview p { + font-size: 1.1rem; + margin-bottom: 15px; + text-align: justify; + } -
-
4️⃣
-

Visualize & Iterate

-

Interactive flowchart reveals insights and enables refinement

-
-
+ .color-system { + margin-bottom: 40px; + } -
-

📝 Concrete Example:

-
-

Input:

-

- "DNA replication begins when the origin recognition complex (ORC) binds to DNA replication origins. This triggers the loading of the MCM2-7 helicase complex, which unwinds the DNA double helix. DNA polymerases then synthesize new strands using the unwound strands as templates..." -

-

LLM Analysis:

-

- Extracts 15 steps, identifies 3 decision points (origin recognition, helicase loading, polymerase binding), recognizes 4 key enzymes (ORC, MCM2-7, DNA polymerase, ligase), and maps regulatory checkpoints. -

-

Output:

-

- Mermaid flowchart with 25 nodes, 28 edges, 3 decision gates, properly colored using the 5-color scheme (red for inputs, yellow for structures, green for operations, blue for intermediates, violet for products), stored as structured JSON enabling interactive visualization and programmatic access. -

-
-
+ .color-system h2 { + color: #667eea; + font-size: 2rem; + margin-bottom: 20px; + border-bottom: 3px solid #667eea; + padding-bottom: 10px; + } -
-

📊 Live Interactive Example:

-
- graph TD - A[Complex Process Input] --> B{LLM Analysis} - B -->|Extract Logic| C[Identify Steps] - B -->|Extract Decisions| D[Identify Branches] - C --> E[Create Flowchart Nodes] - D --> F[Create Decision Points] - E --> G[Generate Mermaid Syntax] - F --> G - G --> H[Store as JSON] - H --> I[Interactive Visualization] - I --> J{Insights Gained?} - J -->|No| K[Refine Analysis] - J -->|Yes| L[Apply Knowledge] - K --> B - - style A fill:#ff6b6b,color:#fff - style B fill:#74c0fc,color:#fff - style C fill:#51cf66,color:#fff - style D fill:#51cf66,color:#fff - style E fill:#ffd43b,color:#000 - style F fill:#ffd43b,color:#000 - style G fill:#51cf66,color:#fff - style H fill:#74c0fc,color:#fff - style I fill:#74c0fc,color:#fff - style J fill:#74c0fc,color:#fff - style K fill:#51cf66,color:#fff - style L fill:#b197fc,color:#fff -
-
-

Color Legend:

-
- Red - Triggers & Inputs - Yellow - Structures & Objects - Green - Processing & Operations - Blue - Intermediates & States - Violet - Products & Outputs -
-
-
-
-
- - -
-

💡 Core Principles

- -
-
-
🌍
-

Domain Agnostic

-

- Works across any field: biology, chemistry, software engineering, business processes, - legal workflows, manufacturing, and beyond. -

-
+ .color-grid { + display: grid; + grid-template-columns: repeat(auto-fit, minmax(300px, 1fr)); + gap: 20px; + margin-bottom: 30px; + } -
-
🔄
-

Iterative Refinement

-

- Start with rough analysis, visualize, identify gaps, refine with LLM, repeat until - the process logic is crystal clear. -

-
+ .color-card { + border-radius: 10px; + padding: 20px; + color: white; + text-align: center; + box-shadow: 0 5px 15px rgba(0,0,0,0.2); + transition: transform 0.3s ease; + } -
-
📦
-

Structured Data

-

- JSON storage enables programmatic access, version control, cross-referencing, - and integration with other tools and databases. -

-
-
-
+ .color-card:hover { + transform: translateY(-5px); + } + .color-card h3 { + font-size: 1.5rem; + margin-bottom: 10px; + } - -
-
-

📚 Process Diagram Collections

-

- The Programming Framework has been applied across multiple scientific disciplines. Explore interactive flowchart collections organized by domain: -

- -
- -
-

- 🧬 Biology -

-

- Biological process visualizations: GLMP covers biochemical/molecular processes; Biology Database covers higher-level organismal processes. -

-
- - 🗄️ Biology Processes Database → - - - 🗄️ GLMP Database Table → - -
-

- Biology Database: 52 processes (organismal/ecological) | GLMP: 50+ processes (biochemical/molecular) -

-
+ .color-card p { + font-size: 1rem; + opacity: 0.9; + } - -
-

- ⚗️ Chemistry -

-

- Comprehensive chemistry process diagrams across all major branches. -

- - 🗄️ Chemistry Database Table → - -

- 56 processes across 14 subcategories -

-
+ .red { background: linear-gradient(135deg, #ff6b6b, #ee5a52); } + .yellow { background: linear-gradient(135deg, #ffd43b, #fcc419); color: #333; } + .green { background: linear-gradient(135deg, #51cf66, #40c057); } + .blue { background: linear-gradient(135deg, #74c0fc, #4dabf7); } + .violet { background: linear-gradient(135deg, #b197fc, #9775fa); } - -
-

- 🔢 Mathematics -

-

- Mathematical algorithms, proof methods, and computational processes. -

- - 🗄️ Mathematics Database Table → - -

- 20 processes across 7 subcategories -

-
+ .resources { + margin-bottom: 40px; + } - -
-

- ⚛️ Physics -

-

- Physical processes including quantum mechanics, thermodynamics, and particle physics. -

- - 🗄️ Physics Database Table → - -

- 21 processes across 7 subcategories -

-
+ .resources h2 { + color: #667eea; + font-size: 2rem; + margin-bottom: 20px; + border-bottom: 3px solid #667eea; + padding-bottom: 10px; + } - -
-

- 💻 Computer Science -

-

- Algorithms, software engineering workflows, and computational processes. -

- - 🗄️ Computer Science Database Table → - -

- 21 processes across 7 subcategories -

-
-
-
-
+ .resource-grid { + display: grid; + grid-template-columns: repeat(auto-fit, minmax(250px, 1fr)); + gap: 20px; + } + + .resource-card { + background: #f8f9fa; + border-radius: 10px; + padding: 25px; + text-align: center; + border: 2px solid #e9ecef; + transition: all 0.3s ease; + } + + .resource-card:hover { + border-color: #667eea; + transform: translateY(-3px); + box-shadow: 0 5px 15px rgba(0,0,0,0.1); + } + + .resource-card h3 { + color: #667eea; + margin-bottom: 10px; + font-size: 1.3rem; + } + + .resource-card p { + margin-bottom: 15px; + color: #666; + } + + .resource-card a { + display: inline-block; + background: #667eea; + color: white; + padding: 10px 20px; + text-decoration: none; + border-radius: 25px; + transition: background 0.3s ease; + } + + .resource-card a:hover { + background: #5a6fd8; + } + + .discipline-databases { + margin-bottom: 40px; + } + + .discipline-databases h2 { + color: #667eea; + font-size: 2rem; + margin-bottom: 12px; + border-bottom: 3px solid #667eea; + padding-bottom: 10px; + } + + .discipline-databases .db-lead { + color: #555; + font-size: 1.05rem; + margin-bottom: 20px; + text-align: center; + } + + .db-grid { + display: grid; + grid-template-columns: repeat(auto-fit, minmax(280px, 1fr)); + gap: 20px; + } + + .db-card { + background: #f8f9fa; + border-radius: 10px; + padding: 22px; + text-align: center; + border: 2px solid #e9ecef; + transition: all 0.3s ease; + } + + .db-card:hover { + border-color: #667eea; + box-shadow: 0 5px 15px rgba(0,0,0,0.08); + } + + .db-card h3 { + color: #667eea; + margin-bottom: 10px; + font-size: 1.25rem; + } + + .db-card p { + margin-bottom: 14px; + color: #555; + font-size: 0.98rem; + line-height: 1.5; + } + + .db-card .db-stats { + margin-top: 12px; + margin-bottom: 0; + font-size: 0.88rem; + color: #666; + } + + .db-card .db-badge { + display: inline-block; + margin-bottom: 12px; + padding: 4px 12px; + border-radius: 999px; + font-size: 0.8rem; + font-weight: 600; + letter-spacing: 0.02em; + background: #fff3bf; + color: #946c00; + border: 1px solid #fcc419; + } + + .db-actions { + display: flex; + flex-wrap: wrap; + gap: 10px; + justify-content: center; + align-items: center; + margin-bottom: 6px; + } + + .db-actions a { + display: inline-block; + background: #667eea; + color: white; + padding: 8px 16px; + text-decoration: none; + border-radius: 25px; + font-size: 0.9rem; + transition: background 0.3s ease; + } + + .db-actions a:hover { + background: #5a6fd8; + } + + .db-card.under-development { + background: #f1f3f5; + border-style: dashed; + border-color: #ced4da; + } + + .db-card.under-development:hover { + border-color: #adb5bd; + } + + .db-card.under-development .db-actions a { + background: #868e96; + } + + .db-card.under-development .db-actions a:hover { + background: #6c757d; + } - -
-
-

⚙️ Technical Architecture

+ .footer { + background: rgba(255,255,255,0.1); + color: white; + text-align: center; + padding: 30px; + border-radius: 15px; + backdrop-filter: blur(10px); + } + + .footer h3 { + margin-bottom: 15px; + font-size: 1.5rem; + } + + .footer p { + margin-bottom: 5px; + opacity: 0.9; + } + + .footer a { + color: #ffd43b; + text-decoration: none; + } + + .footer a:hover { + text-decoration: underline; + } + + @media (max-width: 768px) { + .header h1 { + font-size: 2rem; + } -
-
-

🤖 LLM Integration

-
    -
  • • Google Gemini 2.0 Flash for analysis
    • -
  • • Vertex AI for enterprise deployment
    • -
  • • Custom prompts for process extraction
    • -
  • • Structured JSON output formatting
    • -
-
+ .main-content { + padding: 20px; + } + + .color-grid { + grid-template-columns: 1fr; + } + + .resource-grid { + grid-template-columns: 1fr; + } -
-

📊 Visualization Stack

-
    -
  • • Mermaid.js for flowchart rendering
    • -
  • • JSON schema for data validation
    • -
  • • Interactive SVG output
    • -
  • • Export to PNG/PDF supported
    • -
-
+ .db-grid { + grid-template-columns: 1fr; + } + } + + + +
+
+

🎨 Programming Framework

+

Systematic Analysis of Complex Systems Across Disciplines

+
-
-

💾 Data Storage

-
    -
  • • Google Cloud Storage for JSON files
    • -
  • • Firestore for metadata indexing
    • -
  • • Version control with Git
    • -
  • • Cross-referencing with papers database
    • -
-
+
+
+

Project Overview

+

The Programming Framework is a systematic visualization methodology for analyzing complex systems across disciplines using Mermaid Markdown and a universal five-color code.

+ +

Complex systems across biology, chemistry, and physics exhibit remarkable similarities in their organizational principles despite operating at vastly different scales and domains. Traditional analysis methods often remain siloed within specific disciplines, limiting our ability to identify common patterns and computational logic that govern system behavior.

+ +

Here, we present the Programming Framework, a systematic methodology that translates complex system dynamics into standardized computational representations using Mermaid Markdown syntax and LLM processing.

+
-
-

🔗 Integration Points

-
    -
  • • GLMP specialized collections
    • -
  • • CopernicusAI knowledge graph
    • -
  • • Research papers database
    • -
  • • API endpoints for programmatic access
    • -
-
+
+

Technical Foundation: Mermaid Markdown

+ +

The Invention of Mermaid

+

Knut Sveidqvist invented the Mermaid markdown format. He created Mermaid, a JavaScript-based diagramming and charting tool, to simplify diagram creation in documentation workflows. The project was inspired by his experience trying to update a diagram in a document, which was difficult due to the file format.

+ +

Sveidqvist's innovation revolutionized how diagrams are created and maintained in documentation by providing a text-based syntax that can be version-controlled, easily edited, and automatically rendered into visual diagrams. This approach eliminates the need for external diagramming tools and ensures diagrams stay synchronized with their documentation.

+ +

Mermaid Markdown (.mmd) Format

+

The Programming Framework leverages Mermaid's .mmd file format, which provides:

+
    +
  • Text-based syntax for creating complex flowcharts and diagrams
    • +
  • Version control compatibility - diagrams can be tracked in Git repositories
    • +
  • LLM-friendly format - AI systems can generate and modify diagram code
    • +
  • Cross-platform compatibility - works in any environment that supports JavaScript
    • +
  • Embeddable rendering - diagrams can be displayed in HTML, Markdown, and other formats
    • +
+ +

LLM Integration and Workflow

+

Our methodology uses Large Language Models to:

+
    +
  1. Generate .mmd files - LLMs create detailed Mermaid syntax for complex processes
    2. +
  2. Apply color coding - Systematic application of the 5-category color system
    3. +
  3. Ensure consistency - Standardized node naming and connection patterns
    4. +
  4. Embed in HTML - .mmd files are embedded in HTML for web display
    5. +
  5. Maintain quality - LLMs can validate and optimize diagram structure
    6. +
+ +

This workflow enables rapid creation of sophisticated visualizations that would be impractical to create manually, while maintaining the flexibility and editability of text-based formats.

-
-
- -
-
-

✅ Validation & Accuracy

- -
-
-

🔍 Quality Assurance Process

-
    -
  • • Automated Validation: All flowcharts validated for Mermaid syntax correctness before publication
    • -
  • • Metadata Quality Checks: JSON schema validation ensures >=85% metadata completeness (NSF standard)
    • -
  • • Source Citation Verification: All processes include verified research paper citations with DOI/PubMed links
    • -
  • • Cross-Reference Validation: Automated checks ensure discipline links and back-references are correct
    • -
  • • Color Scheme Consistency: All processes follow standardized 5-color scheme for visual consistency
    • -
-
+
+

Universal Color Coding System

+

The framework uses a standardized five-color system across all disciplines:

-
-

📊 Scale & Coverage

-
    -
  • • 314 Processes Validated: Successfully applied across 6 discipline databases (Biology, Chemistry, Physics, CS, Mathematics, GLMP)
    • -
  • • Multi-Domain Testing: Framework validated on biological pathways, chemical reactions, computational algorithms, and mathematical proofs
    • -
  • • Iterative Refinement: Processes refined through multiple LLM analysis cycles to improve accuracy
    • -
  • • User Feedback Integration: Community feedback mechanism enables continuous improvement (see "Improve this process" on each flowchart)
    • -
  • • Expert Validation: GLMP processes validated against established biochemical pathway databases
    • -
+
+
+

🔴 Red (#ff6b6b)

+

Triggers & Inputs
+ Environmental signals, reactants, input data, energy sources, axioms

+
+ +
+

🟡 Yellow (#ffd43b)

+

Structures & Objects
+ Enzymes, catalysts, data structures, fields, theorems

+
+ +
+

🟢 Green (#51cf66)

+

Processing & Operations
+ Metabolic reactions, chemical reactions, algorithms, quantum operations

+
+ +
+

🔵 Blue (#74c0fc)

+

Intermediates & States
+ Metabolites, intermediates, variables, states, measurement results

+
+ +
+

🟣 Violet (#b197fc)

+

Products & Outputs
+ Biomolecules, final products, program outputs, phenomena, proven results

+
-
-

🎯 Accuracy Measures

-
-
-

Syntax Accuracy

-

100% of published flowcharts render without Mermaid syntax errors

+
+

📊 Batch Architecture Status

+
+
+

📐 Mathematics

+

Status: Complete ✅

+

Batches: 7/7 (21 processes)

+

Number Theory, Analysis & Calculus, Abstract Algebra, Geometry & Topology, Applied Mathematics, Discrete Mathematics, Historical & Educational

+
+ +
+

⚗️ Chemistry

+

Status: Completed ✅

+

Batches: 14/14 (70 processes)

+

Organic Chemistry, Physical Chemistry, Analytical Chemistry, Inorganic Chemistry, Biochemistry, Materials Chemistry, Environmental Chemistry, Electrochemical Processes, Surface Chemistry & Catalysis, Thermodynamic Processes, Kinetic Processes, Spectroscopy & Analysis, Quantum Chemistry, Materials Chemistry

-
-

Metadata Completeness

-

>=85% average quality score across all processes (exceeds NSF requirements)

+ +
+

💻 Computer Science

+

Status: In Progress 🔄

+

Batches: 1/7 (3 processes)

+

Algorithms & Data Structures, Software Engineering, Artificial Intelligence, Computer Security, Computer Networks, Database Systems, Computer Graphics

-
-

Source Coverage

-

All processes include 1-3 verified research paper citations with accessible links

+ +
+

⚛️ Physics

+

Status: In Progress 🔄

+

Batches: 1/7 (3 processes)

+

Classical Mechanics, Electromagnetism, Thermodynamics, Quantum Mechanics, Relativity, Astrophysics, Particle Physics

+
+ +
+

🧬 Biology

+

Status: External GLMP ✅

+

Location: Hugging Face Space

+

Comprehensive biological systems analysis with genome logic modeling and metabolic pathway visualization

-
-

⚠️ Known Limitations

-
    -
  • • LLM-Dependent Accuracy: Flowchart accuracy depends on LLM interpretation of source material; complex processes may require multiple refinement cycles
    • -
  • • Domain Expertise Required: While the Framework is domain-agnostic, optimal results benefit from domain-specific knowledge for validation
    • -
  • • Source Material Quality: Accuracy is limited by the quality and completeness of input source material
    • -
  • • Continuous Improvement: Framework is actively refined based on user feedback and validation results
    • -
-
-
-
- - -
-

🔗 Related Projects

- -
-
-

🧬 GLMP - Genome Logic Modeling

-

- First specialized application of the Programming Framework to biochemical processes. - 100+ biological pathways visualized as interactive flowcharts. -

- - Explore GLMP → (opens in new tab) - -
+
+

🗄️ Discipline databases

+

Live searchable tables on cloud storage where deployed; other disciplines use static batch pages while the database spine is built out.

+
+
+

🧬 Biology

+

Biological process visualizations: GLMP covers biochemical and molecular processes; the Biology Database covers higher-level organismal pathways, mechanisms, and lab-style protocols.

+
+ 🗄️ Biology database table + 📚 Theme collections + 🧬 GLMP (HF Space) +
+

Biology database: 20 processes (3 groups: pathways, mechanisms, assay protocols) · GLMP: 50+ processes (biochemical / molecular)

+
-
-

🔬 CopernicusAI

-

- Knowledge engine integrating the Programming Framework with AI podcasts, research papers, - and knowledge graph for scientific discovery. -

- - Visit CopernicusAI → (opens in new tab) - -
-
-
- - -
-
-

How to Cite This Work

-
-
-

- Welz, G. (2024–2025). The Programming Framework: A Universal Method for Process Analysis.
- Hugging Face Spaces. https://huggingface.co/spaces/garywelz/programming_framework (opens in new tab) -

-
-

BibTeX Format:

- 
@misc{welz2025programmingframework,
-  title={The Programming Framework: A Universal Method for Process Analysis},
-  author={Welz, Gary},
-  year={2024--2025},
-  url={https://huggingface.co/spaces/garywelz/programming_framework},
-  note={Hugging Face Spaces}
-}
+
+

⚗️ Chemistry

+ Under development +

Comprehensive chemistry process diagrams across major branches. A public interactive database table (like Mathematics and Biology) is not live yet; batch HTML pages in this Space are the current entry point.

+
+ Browse chemistry batches +
+
+ +
+

🔢 Mathematics

+

Algorithms, proof methods, dependency graphs, and computational processes — main table plus named collections (mathematicians, theorems) and a whole-of-mathematics graph view.

+
+ 🗄️ Mathematics database table + 📚 Named collections + 🌐 Whole of mathematics +
+

216 processes across 23 subcategories (see live table for the exact index)

+
+ +
+

⚛️ Physics

+ Under development +

Physical processes including quantum mechanics, thermodynamics, and particle physics. Interactive cloud table coming; use static physics batches for now.

+
+ Browse physics batches +
+
+ +
+

💻 Computer Science

+ Under development +

Algorithms, software-engineering workflows, and computational processes. Interactive cloud table coming; use static CS batches for now.

+
+ Browse computer science batches +
-
-
-

- Welz, G. (2024). From Inspiration to AI: Biology as Visual Programming.
- Medium. https://medium.com/@garywelz_47126/from-inspiration-to-ai-biology-as-visual-programming-520ee523029a (opens in new tab) -

-
-

- This project serves as a foundational meta-tool for AI-assisted process analysis, enabling systematic extraction and visualization of complex logic from textual sources across diverse scientific and technical domains. -

-

- The Programming Framework is designed as infrastructure for AI-assisted science, providing a universal methodology that can be specialized for domain-specific applications. -

+ +
+

Key Resources & Documentation

+
+
+

📚 Complete Documentation

+

Detailed methodology, implementation guidelines, and theoretical foundation

+ View README +
+ +
+

🧬 Biology

+

Biological system analysis with GLMP integration

+ Explore Biology (GLMP) +
+ +
+

⚗️ Chemistry

+

Chemical reaction mechanisms and visualizations

+ Explore Chemistry +
+ +
+

💻 Computer Science

+

Algorithm and computational analysis

+ Explore CS +
+ +
+

⚛️ Physics

+

Physical system dynamics and quantum processes

+ Explore Physics +
+ +
+

📐 Mathematics

+

Mathematical proof and calculation processes

+ Explore Math +
+ +
+

📖 Academic Article

+

Comprehensive framework documentation and methodology

+ Read Article +
+ +
+

🔬 GLMP Foundation

+

Original biological systems analysis project

+ Visit GLMP +
+ +
+

🧪 Experimental Validation

+

Comprehensive validation protocols and experimental design

+ View Validation Paper +
+ +
+

🔬 Validation Flowcharts

+

Core validation flowcharts supporting experimental protocols

+ Catalytic Hydrogenation + RAFT Polymerization + Surface Catalysis + Electrochemical ORR + Quantum Chemistry +
+ +
+

📄 Journal Submission Paper

+

Self-contained academic paper suitable for journal submission or arXiv

+ View Journal Paper +
+
-
- - -
-
-

The Programming Framework

-

A Universal Method for Process Analysis

-

© 2025 Gary Welz. All rights reserved.

-
-
- +
+

About the Author

+

Gary Welz

+

Retired Faculty Member

+

John Jay College, CUNY (Department of Mathematics and Computer Science)

+

Borough of Manhattan Community College, CUNY

+

CUNY Graduate Center (New Media Lab)

+

Email: gwelz@jjay.cuny.edu

+
+
- diff --git a/mathematics-database-table.html b/mathematics-database-table.html deleted file mode 100644 index 92459522dfa7018da09947f85246a6167fc561c0..0000000000000000000000000000000000000000 --- a/mathematics-database-table.html +++ /dev/null @@ -1,543 +0,0 @@ - - - - - - Mathematics Processes Database - - - -
-
-

🔢 Mathematics Processes Database

-

Programming Framework - Interactive Database Analysis

- -
- -
-

Loading mathematics processes database...

-

Fetching process data from metadata.json

-
- - - - -
- - - - \ No newline at end of file diff --git a/mathematics_charts.json b/mathematics_charts.json new file mode 100644 index 0000000000000000000000000000000000000000..788cdd6d1db1be08bf1239e20e54f36a70299905 --- /dev/null +++ b/mathematics_charts.json @@ -0,0 +1,20 @@ +{ + "collection": { + "name": "Mathematics Flowcharts", + "discipline": "mathematics", + "description": "Programming Framework flowcharts for mathematical processes, proofs, and constructions. Dependency graphs showing how axioms, postulates, and propositions relate.", + "version": "1.0", + "source": "Programming Framework methodology" + }, + "charts": [ + { + "id": "euclid-elements-i-1-5", + "title": "Euclid's Elements Book I — Propositions 1–5 Dependencies", + "description": "Dependency graph showing how the first five propositions of Euclid's Elements depend on postulates (P1–P3), common notions (CN1, CN3, CN4, CN5), and each other. Demonstrates the axiomatic structure of Euclidean geometry.", + "category": "Geometry", + "subcategory": "Euclidean Geometry", + "tags": ["Euclid", "Elements", "axioms", "postulates", "propositions", "geometry", "foundations"], + "mermaid": "graph TD\n %% ── Foundations ──────────────────────────────────────────\n P1[\"Post. 1\\nDraw a straight line\\nbetween two points\"]\n P2[\"Post. 2\\nExtend a straight line\\ncontinuously\"]\n P3[\"Post. 3\\nDraw a circle with given\\ncenter and radius\"]\n CN1[\"CN 1\\nThings equal to the same\\nthing are equal to each other\"]\n CN3[\"CN 3\\nIf equals subtracted from\\nequals, remainders are equal\"]\n CN4[\"CN 4\\nThings coinciding with\\none another are equal\"]\n CN5[\"CN 5\\nThe whole is greater\\nthan the part\"]\n\n %% ── Propositions ─────────────────────────────────────────\n Prop1[\"Prop. I.1\\nConstruct an equilateral\\ntriangle on a given line\"]\n Prop2[\"Prop. I.2\\nPlace a line segment equal\\nto a given segment at a point\"]\n Prop3[\"Prop. I.3\\nCut off from the greater of\\ntwo lines a segment equal to the less\"]\n Prop4[\"Prop. I.4\\nSAS Congruence:\\ntwo triangles with two equal sides\\nand included angle are congruent\"]\n Prop5[\"Prop. I.5\\nBase angles of an\\nisosceles triangle are equal\"]\n\n %% ── Dependencies ─────────────────────────────────────────\n P1 --> Prop1\n P3 --> Prop1\n\n Prop1 --> Prop2\n P1 --> Prop2\n P2 --> Prop2\n P3 --> Prop2\n\n Prop2 --> Prop3\n P3 --> Prop3\n\n CN4 --> Prop4\n CN5 --> Prop4\n\n Prop1 --> Prop5\n P1 --> Prop5\n P2 --> Prop5\n CN1 --> Prop5\n CN3 --> Prop5\n Prop4 --> Prop5\n\n %% ── Styling ──────────────────────────────────────────────\n classDef postulate fill:#e74c3c,color:#fff,stroke:#c0392b\n classDef commonnotion fill:#9b59b6,color:#fff,stroke:#8e44ad\n classDef proposition fill:#1abc9c,color:#fff,stroke:#16a085\n\n class P1,P2,P3 postulate\n class CN1,CN3,CN4,CN5 commonnotion\n class Prop1,Prop2,Prop3,Prop4,Prop5 proposition" + } + ] +} diff --git a/mathematics_charts_viewer.html b/mathematics_charts_viewer.html new file mode 100644 index 0000000000000000000000000000000000000000..3f43f86292338ef7b64b6792c696ee8b3ef6ce67 --- /dev/null +++ b/mathematics_charts_viewer.html @@ -0,0 +1,332 @@ + + + + + + Mathematics Flowcharts - Programming Framework + + + + + +
+
+

📐 Mathematics Flowcharts

+

Programming Framework — Dependency graphs and computational logic

+
+
+ +
+
Loading mathematics charts…
+ +
+ ← Mathematics Index + ← Programming Framework +
+
+
+ + + + + + diff --git a/mathematics_index.html b/mathematics_index.html index 4d744655172c8850e566ab8d345fa3e48cb0c390..9ad6a8707495ebe562ce9b1bd252b1efc9393954 100644 --- a/mathematics_index.html +++ b/mathematics_index.html @@ -221,7 +221,17 @@
-

Mathematics Process Batches

+

Mathematics Flowcharts (JSON Collection)

+

Interactive viewer for mathematics dependency graphs and flowcharts, stored in JSON format (GLMP-style collection).

+
+ + 📐 Charts Viewer + Mathematics Flowcharts Collection + Euclid's Elements and more + +
+ +

Mathematics Process Batches

🔢 Number Theory

@@ -299,6 +309,54 @@
+ +

Priority 2 — Dependency Graph Charts

+

Definition–theorem dependency charts for PDEs, differential geometry, spectral theory, symplectic geometry, and metric geometry.

+
+

📜 Partial Differential Equations

+
+ + 4 charts + Classical PDEs, Well-posedness, Sobolev, Maximum Principles + +
+
+
+

📐 Differential Geometry

+
+ + 4 charts + Manifolds, Riemannian, Connections, Differential Forms + +
+
+
+

🔮 Spectral Theory

+
+ + 4 charts + Spectrum, Self-Adjoint, Compact, Schrödinger Operators + +
+
+
+

🌿 Symplectic Geometry

+
+ + 4 charts + Symplectic Form, Hamiltonian, Darboux, Poisson + +
+
+
+

📏 Metric Geometry

+
+ + 4 charts + Metric Spaces, Geodesics, Curvature, Hyperbolic + +
+
@@ -308,7 +366,7 @@ Biology Processes Chemistry Processes Computer Science Processes - Physics Processes + Physics Processes
diff --git a/physics_processes.html b/physics_processes.html index 2f5e2972bea0fe4fc58b2e9bd78a0201b09fd38c..9980b97b985f1d155124e0a3b057b5265eeeb5c9 100644 --- a/physics_processes.html +++ b/physics_processes.html @@ -1,158 +1,653 @@ - - - Physics Processes - Programming Framework + + + Physics Processes - Programming Framework Analysis + +
-

⚛️ Physics Processes

-

- Programming Framework Process Visualizations -

+

Physics Processes - Programming Framework Analysis

+ +

This document presents physics processes analyzed using the Programming Framework methodology. Each process is represented as a computational flowchart with standardized color coding: Red for triggers/inputs, Yellow for structures/objects, Green for processing/operations, Blue for intermediates/states, and Violet for products/outputs. Yellow nodes use black text for optimal readability, while all other colors use white text.

-
-

Overview

-

- This collection contains physics process visualizations created using the Programming Framework methodology. - Each process has been analyzed using Large Language Models and represented as interactive Mermaid flowcharts. -

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1. Quantum Tunneling Process

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+graph TD + %% Initial Conditions + A1[Particle Energy E] --> B1[Energy Assessment] + C1[Barrier Height V0] --> D1[Barrier Analysis] + E1[Barrier Width a] --> F1[Geometric Constraints] + + %% Quantum State Preparation + B1 --> G1[Wave Function Initialization] + D1 --> H1[Potential Energy Profile] + F1 --> I1[Spatial Boundary Conditions] + + %% Wave Function Evolution + G1 --> J1[Incident Wave Function psi1] + H1 --> K1[Barrier Region psi2] + I1 --> L1[Transmitted Wave Function psi3] + + %% Quantum Processing + J1 --> M1[Wave Function Matching] + K1 --> N1[Exponential Decay in Barrier] + L1 --> O1[Transmission Coefficient Calculation] + + %% Quantum State Analysis + M1 --> P1[Boundary Condition Equations] + N1 --> Q1[Quantum Amplitude Processing] + O1 --> R1[Probability Density Analysis] + + %% Transmission Calculation + P1 --> S1[Wave Function Continuity] + Q1 --> T1[Quantum Interference Effects] + R1 --> U1[Transmission Probability T] + + %% Classical vs Quantum Logic + S1 --> V1{Classical Prediction} + T1 --> W1{Quantum Reality} + U1 --> X1[Measured Transmission] + + %% Decision Points + V1 --> Y1[Classical Forbidden] + W1 --> Z1[Quantum Tunneling] + X1 --> AA1[Particle Detection Beyond Barrier] + + %% Measurement and Detection + Y1 --> BB1[Classical Prediction Failure] + Z1 --> CC1[Quantum Tunneling Success] + AA1 --> DD1[Energy Verification] + + %% Energy Conservation + BB1 --> EE1[Wave Function Collapse] + CC1 --> FF1[Final Particle State] + DD1 --> GG1[Energy Conservation Check] + + %% Final Results + EE1 --> HH1[Measurement Complete] + FF1 --> II1[Quantum Effect Confirmed] + GG1 --> JJ1[Energy Conservation Verified] + + %% Styling - Physics Color Scheme + style A1 fill:#ff6b6b,color:#fff + style C1 fill:#ff6b6b,color:#fff + style E1 fill:#ff6b6b,color:#fff + + style G1 fill:#ffd43b,color:#000 + style H1 fill:#ffd43b,color:#000 + style I1 fill:#ffd43b,color:#000 + style J1 fill:#ffd43b,color:#000 + style K1 fill:#ffd43b,color:#000 + style L1 fill:#ffd43b,color:#000 + + style M1 fill:#51cf66,color:#fff + style N1 fill:#51cf66,color:#fff + style O1 fill:#51cf66,color:#fff + style P1 fill:#51cf66,color:#fff + style Q1 fill:#51cf66,color:#fff + style R1 fill:#51cf66,color:#fff + style S1 fill:#51cf66,color:#fff + style T1 fill:#51cf66,color:#fff + style U1 fill:#51cf66,color:#fff + + style B1 fill:#74c0fc,color:#fff + style D1 fill:#74c0fc,color:#fff + style F1 fill:#74c0fc,color:#fff + style V1 fill:#74c0fc,color:#fff + style W1 fill:#74c0fc,color:#fff + style X1 fill:#74c0fc,color:#fff + style Y1 fill:#74c0fc,color:#fff + style Z1 fill:#74c0fc,color:#fff + style AA1 fill:#74c0fc,color:#fff + style BB1 fill:#74c0fc,color:#fff + style CC1 fill:#74c0fc,color:#fff + style DD1 fill:#74c0fc,color:#fff + style EE1 fill:#74c0fc,color:#fff + style FF1 fill:#74c0fc,color:#fff + style GG1 fill:#74c0fc,color:#fff + + style HH1 fill:#b197fc,color:#fff + style II1 fill:#b197fc,color:#fff + style JJ1 fill:#b197fc,color:#fff +
+ +
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+ Energy & Geometric Inputs +
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+ Wave Functions & Fields +
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+ Quantum Processing +
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+ Intermediates +
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+ Products +
+
+ +
+ Figure 1. Quantum Tunneling Process. This physics process visualization demonstrates quantum mechanical phenomena. The flowchart shows energy inputs, wave functions and fields, quantum processing operations, intermediate calculations, and final measurement outcomes. +
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Physics Process Batches

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2. Nuclear Fusion Process

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+
+graph TD + %% Initial Setup + %% Input Conditions + A2[High Temperature Plasma] --> B2[Thermal Energy Input] + C2[High Pressure Environment] --> D2[Pressure Confinement] + E2[Deuterium-Tritium Fuel] --> F2[Fuel Preparation] + %% Plasma State + B2 --> G2[Ionization Process] + D2 --> H2[Magnetic Confinement] + F2 --> I2[Fuel Injection] + %% Fusion Conditions + G2 --> J2[Plasma Heating] + H2 --> K2[Confinement Stability] + I2 --> L2[Fuel Mixing] + %% Nuclear Reactions + J2 --> M2[Collision Frequency] + K2 --> N2[Confinement Time] + L2 --> O2[Reaction Rate] + %% Fusion Process + M2 --> P2[Deuterium-Tritium Collision] + N2 --> Q2[Plasma Containment] + O2 --> R2[Fusion Cross Section] + %% Energy Release + P2 --> S2[Helium-4 Formation] + Q2 --> T2[Neutron Emission] + R2 --> U2[Energy Release] + %% Energy Conversion + S2 --> V2[Kinetic Energy Transfer] + T2 --> W2[Neutron Capture] + U2 --> X2[Heat Generation] + %% Power Generation + V2 --> Y2[Plasma Heating] + W2 --> Z2[Breeding Blanket] + X2 --> AA2[Steam Generation] + %% Final Output + Y2 --> BB2[Self-Sustaining Fusion] + Z2 --> CC2[Tritium Breeding] + AA2 --> DD2[Electrical Power] + %% Process Control + BB2 --> EE2[Fusion Reactor Operation] + CC2 --> FF2[Fuel Cycle Management] + DD2 --> GG2[Power Grid Integration] + %% Styling - Physics Color Scheme + %% Styling - Biological Color Scheme + style A2 fill:#ff6b6b,color:#fff + style C2 fill:#ff6b6b,color:#fff + style E2 fill:#ff6b6b,color:#fff + style G2 fill:#ffd43b,color:#000 + style H2 fill:#ffd43b,color:#000 + style I2 fill:#ffd43b,color:#000 + style J2 fill:#ffd43b,color:#000 + style K2 fill:#ffd43b,color:#000 + style L2 fill:#ffd43b,color:#000 + style M2 fill:#51cf66,color:#fff + style N2 fill:#51cf66,color:#fff + style O2 fill:#51cf66,color:#fff + style P2 fill:#51cf66,color:#fff + style Q2 fill:#51cf66,color:#fff + style R2 fill:#51cf66,color:#fff + style S2 fill:#51cf66,color:#fff + style T2 fill:#51cf66,color:#fff + style U2 fill:#51cf66,color:#fff + style V2 fill:#51cf66,color:#fff + style W2 fill:#51cf66,color:#fff + style X2 fill:#51cf66,color:#fff + style B2 fill:#74c0fc,color:#fff + style D2 fill:#74c0fc,color:#fff + style F2 fill:#74c0fc,color:#fff + style Y2 fill:#74c0fc,color:#fff + style Z2 fill:#74c0fc,color:#fff + style AA2 fill:#74c0fc,color:#fff + style BB2 fill:#74c0fc,color:#fff + style CC2 fill:#74c0fc,color:#fff + style DD2 fill:#74c0fc,color:#fff + style EE2 fill:#74c0fc,color:#fff + style FF2 fill:#74c0fc,color:#fff + style GG2 fill:#74c0fc,color:#fff + style HH2 fill:#b197fc,color:#fff + style II2 fill:#b197fc,color:#fff + style JJ2 fill:#b197fc,color:#fff +
+ +
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+ Plasma & Fuel Inputs +
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+ Confinement Systems +
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+ Nuclear Fusion Reactions +
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+ Intermediates +
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+ Products +
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- - Batch 01 - Physics Processes - Batch 1 - +
+ Figure 2. Nuclear Fusion Process. This physics process visualization demonstrates nuclear energy production. The flowchart shows plasma inputs, confinement systems, nuclear fusion reactions, intermediate processes, and final energy output.
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- - Batch 02 - Physics Processes - Batch 2 - +

3. Electromagnetic Wave Propagation

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+
+graph TD + %% Initial Setup + %% Input Conditions + A3[Electromagnetic Source] --> B3[Source Analysis] + C3[Medium Properties] --> D3[Medium Analysis] + E3[Boundary Conditions] --> F3[Boundary Definition] + %% Wave Generation + B3 --> G3[Electric Field Generation] + D3 --> H3[Dielectric Properties] + F3 --> I3[Interface Conditions] + %% Wave Propagation + G3 --> J3[Maxwell's Equations] + H3 --> K3[Wave Speed Calculation] + I3 --> L3[Reflection/Refraction] + %% Field Evolution + J3 --> M3[Electric Field E] + K3 --> N3[Magnetic Field B] + L3 --> O3[Wave Vector k] + %% Wave Dynamics + M3 --> P3[Field Oscillation] + N3 --> Q3[Energy Density] + O3 --> R3[Phase Velocity] + %% Energy Transport + P3 --> S3[Poynting Vector] + Q3 --> T3[Energy Conservation] + R3 --> U3[Group Velocity] + %% Wave Interaction + S3 --> V3[Energy Flux] + T3 --> W3[Power Transmission] + U3 --> X3[Dispersion Effects] + %% Detection + V3 --> Y3[Wave Detection] + W3 --> Z3[Signal Processing] + X3 --> AA3[Interference Patterns] + %% Final Results + Y3 --> BB3[Wave Amplitude] + Z3 --> CC3[Phase Information] + AA3 --> DD3[Interference Fringes] + %% Output + BB3 --> EE3[Electromagnetic Wave Detected] + CC3 --> FF3[Phase Information Extracted] + DD3 --> GG3[Interference Pattern Analyzed] + %% Styling - Physics Color Scheme + %% Styling - Biological Color Scheme + style A3 fill:#ff6b6b,color:#fff + style C3 fill:#ff6b6b,color:#fff + style E3 fill:#ff6b6b,color:#fff + style G3 fill:#ffd43b,color:#000 + style H3 fill:#ffd43b,color:#000 + style I3 fill:#ffd43b,color:#000 + style J3 fill:#ffd43b,color:#000 + style K3 fill:#ffd43b,color:#000 + style L3 fill:#ffd43b,color:#000 + style M3 fill:#51cf66,color:#fff + style N3 fill:#51cf66,color:#fff + style O3 fill:#51cf66,color:#fff + style P3 fill:#51cf66,color:#fff + style Q3 fill:#51cf66,color:#fff + style R3 fill:#51cf66,color:#fff + style S3 fill:#51cf66,color:#fff + style T3 fill:#51cf66,color:#fff + style U3 fill:#51cf66,color:#fff + style V3 fill:#51cf66,color:#fff + style W3 fill:#51cf66,color:#fff + style X3 fill:#51cf66,color:#fff + style B3 fill:#74c0fc,color:#fff + style D3 fill:#74c0fc,color:#fff + style F3 fill:#74c0fc,color:#fff + style Y3 fill:#74c0fc,color:#fff + style Z3 fill:#74c0fc,color:#fff + style AA3 fill:#74c0fc,color:#fff + style BB3 fill:#74c0fc,color:#fff + style CC3 fill:#74c0fc,color:#fff + style DD3 fill:#74c0fc,color:#fff + style EE3 fill:#74c0fc,color:#fff + style FF3 fill:#74c0fc,color:#fff + style GG3 fill:#74c0fc,color:#fff + style HH3 fill:#b197fc,color:#fff + style II3 fill:#b197fc,color:#fff + style JJ3 fill:#b197fc,color:#fff +
+ +
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+ Source & Medium Inputs +
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+ Electromagnetic Fields +
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+ Wave Propagation +
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+ Intermediates +
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+ Products +
+
+ +
+ Figure 3. Electromagnetic Wave Propagation. This physics process visualization demonstrates electromagnetic wave dynamics. The flowchart shows source inputs, electromagnetic fields, wave propagation processes, intermediate calculations, and final detection results.
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Navigation

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- ← Back to Programming Framework - Biology Processes - Chemistry Processes - Mathematics Processes - Computer Science Processes +

4. Thermodynamic Cycle Process

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+
+graph TD + %% Initial Setup + %% Input Conditions + A4[Heat Source] --> B4[Heat Supply] + C4[Working Fluid] --> D4[Fluid Properties] + E4[System Boundaries] --> F4[Boundary Definition] + %% Initial State + B4 --> G4[High Temperature Reservoir] + D4 --> H4[Fluid State Analysis] + F4 --> I4[System Isolation] + %% Isothermal Expansion + G4 --> J4[Heat Addition Q1] + H4 --> K4[Volume Expansion] + I4 --> L4[Work Output W1] + %% Adiabatic Expansion + J4 --> M4[Temperature Decrease] + K4 --> N4[Pressure Reduction] + L4 --> O4[Work Output W2] + %% Isothermal Compression + M4 --> P4[Heat Rejection Q2] + N4 --> Q4[Volume Compression] + O4 --> R4[Work Input W3] + %% Adiabatic Compression + P4 --> S4[Temperature Increase] + Q4 --> T4[Pressure Increase] + R4 --> U4[Work Input W4] + %% Cycle Completion + S4 --> V4[Return to Initial State] + T4 --> W4[System Reset] + U4 --> X4[Net Work Output] + %% Efficiency Calculation + V4 --> Y4[Cycle Efficiency eta] + W4 --> Z4[Energy Conservation] + X4 --> AA4[Power Generation] + %% Final Results + Y4 --> BB4[Thermal Efficiency] + Z4 --> CC4[Energy Balance] + AA4 --> DD4[Mechanical Power] + %% Output + BB4 --> EE4[Thermodynamic Cycle Complete] + CC4 --> FF4[Energy Conversion Efficient] + DD4 --> GG4[Power Output Maximized] + %% Styling - Physics Color Scheme + %% Styling - Biological Color Scheme + style A4 fill:#ff6b6b,color:#fff + style C4 fill:#ff6b6b,color:#fff + style E4 fill:#ff6b6b,color:#fff + style G4 fill:#ffd43b,color:#000 + style H4 fill:#ffd43b,color:#000 + style I4 fill:#ffd43b,color:#000 + style J4 fill:#ffd43b,color:#000 + style K4 fill:#ffd43b,color:#000 + style L4 fill:#ffd43b,color:#000 + style M4 fill:#51cf66,color:#fff + style N4 fill:#51cf66,color:#fff + style O4 fill:#51cf66,color:#fff + style P4 fill:#51cf66,color:#fff + style Q4 fill:#51cf66,color:#fff + style R4 fill:#51cf66,color:#fff + style S4 fill:#51cf66,color:#fff + style T4 fill:#51cf66,color:#fff + style U4 fill:#51cf66,color:#fff + style V4 fill:#51cf66,color:#fff + style W4 fill:#51cf66,color:#fff + style X4 fill:#51cf66,color:#fff + style B4 fill:#74c0fc,color:#fff + style D4 fill:#74c0fc,color:#fff + style F4 fill:#74c0fc,color:#fff + style Y4 fill:#74c0fc,color:#fff + style Z4 fill:#74c0fc,color:#fff + style AA4 fill:#74c0fc,color:#fff + style BB4 fill:#74c0fc,color:#fff + style CC4 fill:#74c0fc,color:#fff + style DD4 fill:#74c0fc,color:#fff + style EE4 fill:#74c0fc,color:#fff + style FF4 fill:#74c0fc,color:#fff + style GG4 fill:#74c0fc,color:#fff + style HH4 fill:#b197fc,color:#fff + style II4 fill:#b197fc,color:#fff + style JJ4 fill:#b197fc,color:#fff +
+ +
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+ Heat & Fluid Inputs +
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+ Thermodynamic Systems +
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+ Thermodynamic Processes +
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+ Intermediates +
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+ Products +
+
+ +
+ Figure 4. Thermodynamic Cycle Process. This physics process visualization demonstrates energy conversion cycles. The flowchart shows heat inputs, thermodynamic systems, thermodynamic processes, intermediate states, and final power output.
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Generated using the Programming Framework methodology

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Each flowchart preserves maximum detail through optimized Mermaid configuration

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-

Gary Welz

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Retired Faculty Member

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John Jay College, CUNY (Department of Mathematics and Computer Science)

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Borough of Manhattan Community College, CUNY

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CUNY Graduate Center (New Media Lab)

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Email: gwelz@jjay.cuny.edu

+

5. Particle Accelerator Process

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+graph TD + %% Initial Setup + %% Input Conditions + A5[Particle Source] --> B5[Source Analysis] + C5[Accelerating Fields] --> D5[Field Generation] + E5[Beam Optics] --> F5[Optics Setup] + %% Particle Preparation + B5 --> G5[Particle Generation] + D5 --> H5[Electric Field E] + F5 --> I5[Magnetic Field B] + %% Initial Acceleration + G5 --> J5[Particle Injection] + H5 --> K5[Linear Acceleration] + I5 --> L5[Beam Focusing] + %% Acceleration Process + J5 --> M5[Velocity Increase] + K5 --> N5[Energy Gain] + L5 --> O5[Beam Confinement] + %% Circular Motion + M5 --> P5[Centripetal Force] + N5 --> Q5[Relativistic Effects] + O5 --> R5[Orbital Motion] + %% Energy Build-up + P5 --> S5[Radius of Curvature] + Q5 --> T5[Mass Increase] + R5 --> U5[Angular Velocity] + %% Beam Dynamics + S5 --> V5[Beam Stability] + T5 --> W5[Energy Synchronization] + U5 --> X5[Revolution Frequency] + %% Collision Process + V5 --> Y5[Beam Crossing] + W5 --> Z5[Particle Collisions] + X5 --> AA5[Reaction Products] + %% Detection + Y5 --> BB5[Collision Detection] + Z5 --> CC5[Particle Tracking] + AA5 --> DD5[Energy Measurement] + %% Final Results + BB5 --> EE5[Collision Events] + CC5 --> FF5[Particle Trajectories] + DD5 --> GG5[Energy Distribution] + %% Output + EE5 --> HH5[Particle Accelerator Active] + FF5 --> II5[Beam Dynamics Analyzed] + GG5 --> JJ5[Physics Data Collected] + %% Styling - Physics Color Scheme + %% Styling - Biological Color Scheme + style A5 fill:#ff6b6b,color:#fff + style C5 fill:#ff6b6b,color:#fff + style E5 fill:#ff6b6b,color:#fff + style G5 fill:#ffd43b,color:#000 + style H5 fill:#ffd43b,color:#000 + style I5 fill:#ffd43b,color:#000 + style J5 fill:#ffd43b,color:#000 + style K5 fill:#ffd43b,color:#000 + style L5 fill:#ffd43b,color:#000 + style M5 fill:#51cf66,color:#fff + style N5 fill:#51cf66,color:#fff + style O5 fill:#51cf66,color:#fff + style P5 fill:#51cf66,color:#fff + style Q5 fill:#51cf66,color:#fff + style R5 fill:#51cf66,color:#fff + style S5 fill:#51cf66,color:#fff + style T5 fill:#51cf66,color:#fff + style U5 fill:#51cf66,color:#fff + style V5 fill:#51cf66,color:#fff + style W5 fill:#51cf66,color:#fff + style X5 fill:#51cf66,color:#fff + style B5 fill:#74c0fc,color:#fff + style D5 fill:#74c0fc,color:#fff + style F5 fill:#74c0fc,color:#fff + style Y5 fill:#74c0fc,color:#fff + style Z5 fill:#74c0fc,color:#fff + style AA5 fill:#74c0fc,color:#fff + style BB5 fill:#74c0fc,color:#fff + style CC5 fill:#74c0fc,color:#fff + style DD5 fill:#74c0fc,color:#fff + style EE5 fill:#74c0fc,color:#fff + style FF5 fill:#74c0fc,color:#fff + style GG5 fill:#74c0fc,color:#fff + style HH5 fill:#b197fc,color:#fff + style II5 fill:#b197fc,color:#fff + style JJ5 fill:#b197fc,color:#fff +
+ +
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+ Particle & Field Inputs +
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+ Accelerating Fields +
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+ Acceleration Processes +
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+ Intermediates +
+
+ Products +
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+ +
+ Figure 5. Particle Accelerator Process. This physics process visualization demonstrates particle acceleration mechanisms. The flowchart shows particle inputs, accelerating fields, acceleration processes, intermediate states, and final collision data.
+ +

Generated using the Programming Framework methodology

+ +

This collection demonstrates the computational nature of physical processes and systems

+ +

Each flowchart preserves maximum detail through optimized Mermaid configuration

- - + \ No newline at end of file diff --git a/processes/differential_geometry/differential_geometry-connections.html b/processes/differential_geometry/differential_geometry-connections.html new file mode 100644 index 0000000000000000000000000000000000000000..1bda510ef839b86baf29c51f4d2a208d7d1c8c39 --- /dev/null +++ b/processes/differential_geometry/differential_geometry-connections.html @@ -0,0 +1,108 @@ + + + + + + Connections on Manifolds - Mathematics Process + + + + +
+
+

Connections on Manifolds

+
+ Differential Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Differential Geometry Index + arXiv: Differential Geometry (math.DG) +
+
+
+

Description

+

Affine connections, parallel transport, holonomy, and curvature. Dependency graph for covariant derivatives and the structure equations.

+
+
+

Dependency Flowchart

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+graph TD + D1["D1 Affine connection ∇\nKoszul axioms: C^∞-linear in X, Leibniz in Y"] + D2["D2 Parallel transport\nP_γ: T_p M → T_q M along γ"] + D3["D3 Holonomy group Hol_p\nCurvature at p from parallel transport"] + D4["D4 Torsion tensor T\nT(X,Y) = ∇_X Y − ∇_Y X − [X,Y]"] + + T1["T1 Existence of parallel sections\nFlat connection ⇒ local parallel frames"] + T2["T2 Ambrose-Singer\nHolonomy algebra = curvature derivatives"] + T3["T3 Frobenius for distributions\nInvolutive ⇒ integrable"] + T4["T4 Ricci identity\n[∇_X, ∇_Y]σ − ∇_[X,Y] σ = R(X,Y)σ"] + T5["T5 Geodesic equation\nConnection defines autoparallel curves"] + + D1 --> D2 + D1 --> D4 + D2 --> D3 + D1 --> T1 + D3 --> T2 + D1 --> T3 + D1 --> T4 + D1 --> T5 + D2 --> T1 + D4 --> T4 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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+
+

Color Scheme

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+
Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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+
+
+

Info

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    +
  • Subcategory: differential_geometry
    • +
  • Keywords: connection, parallel transport, holonomy, torsion, curvature
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  • Research frontier: arXiv math.DG
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+
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+ + + diff --git a/processes/differential_geometry/differential_geometry-forms.html b/processes/differential_geometry/differential_geometry-forms.html new file mode 100644 index 0000000000000000000000000000000000000000..122bb3462ffe71bee168e95b1392f1fdde65c0d1 --- /dev/null +++ b/processes/differential_geometry/differential_geometry-forms.html @@ -0,0 +1,109 @@ + + + + + + Differential Forms - Mathematics Process + + + + +
+
+

Differential Forms

+
+ Differential Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Differential Geometry Index + arXiv: Differential Geometry (math.DG) +
+
+
+

Description

+

Exterior algebra, differential forms, exterior derivative, and integration. Stokes theorem and de Rham cohomology.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Exterior algebra Λ^k T*M\nAlternating k-forms on tangent space"] + D2["D2 Exterior derivative d\nCartan formula: dω(X,Y) = X ω(Y) − Y ω(X) − ω([X,Y])"] + D3["D3 Closed and exact forms\ndω = 0 vs ω = dη"] + D4["D4 Integration of n-forms\nOriented manifold, ∫_M ω"] + + T1["T1 d² = 0\nExterior derivative squared is zero"] + T2["T2 Stokes theorem\n∫_M dω = ∫_∂M ω"] + T3["T3 Poincaré lemma\nContractible ⇒ closed = exact locally"] + T4["T4 de Rham cohomology H^k\nClosed / exact forms; topological invariant"] + T5["T5 Hodge decomposition\nΩ^k = im d ⊕ im d* ⊕ harmonic"] + + D1 --> D2 + D2 --> D3 + D1 --> D4 + D2 --> T1 + D2 --> T2 + D4 --> T2 + D3 --> T3 + D3 --> T4 + D2 --> T5 + T1 --> T4 + T2 --> T3 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

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+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: differential_geometry
    • +
  • Keywords: differential form, exterior derivative, Stokes, de Rham, Hodge
    • +
  • Research frontier: arXiv math.DG
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+
+
+
+ + + diff --git a/processes/differential_geometry/differential_geometry-index.html b/processes/differential_geometry/differential_geometry-index.html new file mode 100644 index 0000000000000000000000000000000000000000..ff43ce1c5f903594067ac04f3ee7bfdbfdcbb753 --- /dev/null +++ b/processes/differential_geometry/differential_geometry-index.html @@ -0,0 +1,37 @@ + + + + + + Differential Geometry - Mathematics Processes + + + +
+
+ ← Back to Mathematics Index + arXiv math.DG +
+

Differential Geometry

+

Dependency graphs for manifolds, Riemannian geometry, connections, and differential forms.

+ +
+ + diff --git a/processes/differential_geometry/differential_geometry-manifolds.html b/processes/differential_geometry/differential_geometry-manifolds.html new file mode 100644 index 0000000000000000000000000000000000000000..748a1fc2f7cfa31bbe36ec76e851a642a773a75d --- /dev/null +++ b/processes/differential_geometry/differential_geometry-manifolds.html @@ -0,0 +1,109 @@ + + + + + + Smooth Manifolds - Mathematics Process + + + + +
+
+

Smooth Manifolds

+
+ Differential Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Differential Geometry Index + arXiv: Differential Geometry (math.DG) +
+
+
+

Description

+

Dependency graph for smooth manifolds: charts, atlases, tangent spaces, and smooth maps. Foundations for differential geometry.

+
+
+

Dependency Flowchart

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+graph TD + D1["D1 Smooth manifold\nHausdorff, 2nd countable, charts"] + D2["D2 Atlas\nMaximal collection of compatible charts"] + D3["D3 Tangent space T_p M\nDerivations at a point"] + D4["D4 Smooth map\nInfinitely differentiable between manifolds"] + + T1["T1 Tangent space is vector space\ndim T_p M = n"] + T2["T2 Inverse function theorem\nLocal diffeomorphism criterion"] + T3["T3 Submersion theorem\nRegular value gives submanifold"] + T4["T4 Whitney embedding\nCompact M embeds in R^{2n}"] + T5["T5 Partition of unity\nExistence on paracompact manifolds"] + + D1 --> D2 + D1 --> D3 + D4 --> D3 + D2 --> D1 + D3 --> T1 + D4 --> T2 + D4 --> T3 + D1 --> T4 + D1 --> T5 + D2 --> T5 + T2 --> T3 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: differential_geometry
    • +
  • Keywords: manifold, atlas, tangent space, smooth map, Whitney embedding
    • +
  • Research frontier: arXiv math.DG
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+
+
+ + + diff --git a/processes/differential_geometry/differential_geometry-riemannian.html b/processes/differential_geometry/differential_geometry-riemannian.html new file mode 100644 index 0000000000000000000000000000000000000000..fedbe57de9962c99e9208c0158a13a38ccb20cfe --- /dev/null +++ b/processes/differential_geometry/differential_geometry-riemannian.html @@ -0,0 +1,108 @@ + + + + + + Riemannian Geometry - Mathematics Process + + + + +
+
+

Riemannian Geometry

+
+ Differential Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Differential Geometry Index + arXiv: Differential Geometry (math.DG) +
+
+
+

Description

+

Riemannian metrics, curvature tensors, and geodesics. Dependency graph for the Levi-Civita connection, sectional curvature, and comparison theorems.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Riemannian metric g\nPositive definite smooth 2-tensor"] + D2["D2 Levi-Civita connection ∇\nMetric compatibility, torsion-free"] + D3["D3 Riemann curvature tensor R\nR(X,Y)Z = ∇_X∇_Y Z − ∇_Y∇_X Z − ∇_[X,Y] Z"] + D4["D4 Geodesic\n∇_γ' γ' = 0"] + + T1["T1 Fundamental theorem\nUnique Levi-Civita connection"] + T2["T2 Gauss-Bonnet\n∫ K dA = 2πχ for surfaces"] + T3["T3 Comparison: K ≥ 0 ⇒ geodesics diverge\nBonnet-Myers for K ≥ κ > 0"] + T4["T4 Cartan-Hadamard\nSimply connected, K ≤ 0 ⇒ diffeo to R^n"] + T5["T5 Parallel transport\nPreserves inner product along curves"] + + D1 --> D2 + D1 --> T1 + D2 --> D3 + D2 --> D4 + D2 --> T5 + D3 --> T2 + D3 --> T3 + D3 --> T4 + D4 --> T3 + T1 --> D2 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: differential_geometry
    • +
  • Keywords: Riemannian metric, curvature, Levi-Civita, geodesic, Gauss-Bonnet
    • +
  • Research frontier: arXiv math.DG
    • +
+
+
+
+ + + diff --git a/processes/metric_geometry/metric_geometry-curvature.html b/processes/metric_geometry/metric_geometry-curvature.html new file mode 100644 index 0000000000000000000000000000000000000000..4c55d6c78faf14f313d62a8e5573700e97f3d8ba --- /dev/null +++ b/processes/metric_geometry/metric_geometry-curvature.html @@ -0,0 +1,108 @@ + + + + + + Curvature in Metric Geometry - Mathematics Process + + + + +
+
+

Curvature in Metric Geometry

+
+ Metric Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Metric Geometry Index + arXiv: Metric Geometry (math.MG) +
+
+
+

Description

+

CAT(κ) and Alexandrov curvature. Triangle comparison, sectional curvature bounds, and Toponogov theorem.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 CAT(κ) space\nTriangles thinner than in M²_κ"] + D2["D2 Alexandrov curvature ≥ κ\nQuadruple comparison"] + D3["D3 Model space M²_κ\nCurvature κ: sphere, plane, hyperbolic"] + D4["D4 Sectional curvature\nK(σ) for 2-plane σ in Riemannian"] + + T1["T1 CAT(0) ⇒ unique geodesics\nNonpositive curvature"] + T2["T2 Toponogov comparison\nRiemannian K ≥ κ ⇒ triangle comparison"] + T3["T3 Hadamard-Cartan\nSimply connected CAT(0) ⇒ contractible"] + T4["T4 Globalization\nLocal CAT(κ) + geodesic ⇒ CAT(κ)"] + T5["T5 Reshetnyak quadrilateral\nFour-point comparison in CAT(0)"] + + D1 --> D3 + D2 --> D1 + D3 --> T2 + D4 --> T2 + D1 --> T1 + D1 --> T3 + D1 --> T4 + D1 --> T5 + T2 --> D1 + T1 --> T3 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: metric_geometry
    • +
  • Keywords: CAT(κ), Alexandrov, Toponogov, curvature, Hadamard
    • +
  • Research frontier: arXiv math.MG
    • +
+
+
+
+ + + diff --git a/processes/metric_geometry/metric_geometry-geodesics.html b/processes/metric_geometry/metric_geometry-geodesics.html new file mode 100644 index 0000000000000000000000000000000000000000..847f99c67b5d53f70591a7bf2bbb1caa795a31be --- /dev/null +++ b/processes/metric_geometry/metric_geometry-geodesics.html @@ -0,0 +1,109 @@ + + + + + + Geodesics and Length Spaces - Mathematics Process + + + + +
+
+

Geodesics and Length Spaces

+
+ Metric Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Metric Geometry Index + arXiv: Metric Geometry (math.MG) +
+
+
+

Description

+

Length space: metric = inf of curve lengths. Geodesic: length-minimizing curve. Hopf-Rinow, length metric, and intrinsic metric.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Length of curve γ\nL(γ) = sup Σ d(γ(t_i), γ(t_{i+1}))"] + D2["D2 Length space\nd(x,y) = inf L(γ) over curves from x to y"] + D3["D3 Geodesic\nCurve realizing d(x,y)"] + D4["D4 Intrinsic metric\nMetric induced by length structure"] + + T1["T1 Geodesic space\nAny two points joined by geodesic"] + T2["T2 Hopf-Rinow\nComplete + Geodesic ⇒ bounded closed balls compact"] + T3["T3 Length space completion\nCompletions preserve length structure"] + T4["T4 Alexandrov triangle\nComparison with model space"] + T5["T5 Local geodesic extends\nIn complete space, local geodesic ⇒ geodesic"] + + D1 --> D2 + D2 --> D3 + D2 --> D4 + D3 --> T1 + D2 --> T2 + D2 --> T3 + D3 --> T4 + D3 --> T5 + T1 --> T2 + T2 --> T5 + T4 --> T2 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: metric_geometry
    • +
  • Keywords: geodesic, length space, Hopf-Rinow, Alexandrov, intrinsic metric
    • +
  • Research frontier: arXiv math.MG
    • +
+
+
+
+ + + diff --git a/processes/metric_geometry/metric_geometry-hyperbolic.html b/processes/metric_geometry/metric_geometry-hyperbolic.html new file mode 100644 index 0000000000000000000000000000000000000000..879b580b0d3464453512efde953957b1677d55db --- /dev/null +++ b/processes/metric_geometry/metric_geometry-hyperbolic.html @@ -0,0 +1,109 @@ + + + + + + Hyperbolic Geometry - Mathematics Process + + + + +
+
+

Hyperbolic Geometry

+
+ Metric Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Metric Geometry Index + arXiv: Metric Geometry (math.MG) +
+
+
+

Description

+

Hyperbolic space ℍⁿ, Poincaré disk and half-plane. Constant curvature −1, ideal boundary, and Mostow rigidity.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Hyperbolic space H^n\nComplete simply connected K ≡ −1"] + D2["D2 Poincaré disk model\nUnit ball with ds² = 4(dx²)/(1−|x|²)²"] + D3["D3 Ideal boundary ∂∞ H^n\nAsymptotic geodesic classes"] + D4["D4 Hyperbolic isometry\nMöbius or fractional linear"] + + T1["T1 Geodesics are lines/circles\nPerpendicular to boundary in disk"] + T2["T2 Mostow rigidity\nn ≥ 3: isom π₁M ≅ π₁N ⇒ M ≅ N"] + T3["T3 Triangle area\nArea = π − (angles) for geodesic triangle"] + T4["T4 Thin triangles\nSides within δ of each other"] + T5["T5 Classification of isometries\nElliptic, parabolic, hyperbolic"] + + D1 --> D2 + D1 --> D3 + D1 --> D4 + D2 --> T1 + D1 --> T2 + D2 --> T3 + D1 --> T4 + D4 --> T5 + T1 --> T3 + T1 --> T4 + T2 --> D4 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: metric_geometry
    • +
  • Keywords: hyperbolic space, Poincaré, Mostow rigidity, ideal boundary
    • +
  • Research frontier: arXiv math.MG
    • +
+
+
+
+ + + diff --git a/processes/metric_geometry/metric_geometry-index.html b/processes/metric_geometry/metric_geometry-index.html new file mode 100644 index 0000000000000000000000000000000000000000..5943a3f5c6ed40c6206e9999ba9d3e449f42de3e --- /dev/null +++ b/processes/metric_geometry/metric_geometry-index.html @@ -0,0 +1,37 @@ + + + + + + Metric Geometry - Mathematics Processes + + + +
+
+ ← Back to Mathematics Index + arXiv math.MG +
+

Metric Geometry

+

Dependency graphs for metric spaces, geodesics, curvature (CAT spaces), and hyperbolic geometry.

+ +
+ + diff --git a/processes/metric_geometry/metric_geometry-metric-spaces.html b/processes/metric_geometry/metric_geometry-metric-spaces.html new file mode 100644 index 0000000000000000000000000000000000000000..5a17edc5cf784d963a8471fa216236e250b5bbb8 --- /dev/null +++ b/processes/metric_geometry/metric_geometry-metric-spaces.html @@ -0,0 +1,109 @@ + + + + + + Metric Spaces - Mathematics Process + + + + +
+
+

Metric Spaces

+
+ Metric Geometry + Mathematics +
+
+
+ ← Back to Mathematics Index + Metric Geometry Index + arXiv: Metric Geometry (math.MG) +
+
+
+

Description

+

Metric space axioms, completeness, compactness, and Baire. Lipschitz maps, isometries, and completion. Foundation for CAT(0) and Gromov-Hausdorff.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Metric space (X,d)\nNonnegativity, symmetry, triangle, d=0⇔x=y"] + D2["D2 Complete metric space\nEvery Cauchy sequence converges"] + D3["D3 Totally bounded\nFinite ε-net for every ε > 0"] + D4["D4 Lipschitz map\n|f(x)−f(y)| ≤ L d(x,y)"] + + T1["T1 Completion unique\n(X,d) embeds in complete (X̄,d̄)"] + T2["T2 Heine-Borel (metric)\nCompact ⇔ complete + totally bounded"] + T3["T3 Baire category\nComplete metric space is Baire"] + T4["T4 Banach fixed point\nContraction on complete X has unique fixed point"] + T5["T5 Arzelà-Ascoli\nEquicontinuous + bounded ⇒ compact closure"] + + D1 --> D2 + D1 --> D3 + D1 --> D4 + D2 --> T1 + D2 --> T3 + D2 --> T4 + D2 --> T2 + D3 --> T2 + D4 --> T5 + T1 --> D2 + T3 --> T4 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: metric_geometry
    • +
  • Keywords: metric space, completeness, compactness, Baire, fixed point
    • +
  • Research frontier: arXiv math.MG
    • +
+
+
+
+ + + diff --git a/processes/partial_differential_equations/partial_differential_equations-classical.html b/processes/partial_differential_equations/partial_differential_equations-classical.html new file mode 100644 index 0000000000000000000000000000000000000000..76da2329a6734dd585f2bf189c5f4e33378fc093 --- /dev/null +++ b/processes/partial_differential_equations/partial_differential_equations-classical.html @@ -0,0 +1,110 @@ + + + + + + Classical PDEs - Mathematics Process + + + + +
+
+

Classical Partial Differential Equations

+
+ Partial Differential Equations + Mathematics +
+
+
+ ← Back to Mathematics Index + Partial Differential Equations Index + arXiv: Analysis of PDEs (math.AP) +
+
+
+

Description

+

Dependency graph for classical PDEs: Laplace, heat, and wave equations. Shows how definitions of elliptic, parabolic, and hyperbolic operators lead to existence, uniqueness, and regularity theorems.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Laplace operator\nΔu = Σ ∂²u/∂xᵢ²"] + D2["D2 Heat operator\n∂u/∂t − αΔu = 0"] + D3["D3 Wave operator\n∂²u/∂t² − c²Δu = 0"] + D4["D4 Classification\nElliptic, Parabolic, Hyperbolic"] + + T1["T1 Existence of Laplace solutions\nDirichlet problem has solution"] + T2["T2 Uniqueness for heat equation\nMaximum principle"] + T3["T3 Uniqueness for wave equation\nEnergy method"] + T4["T4 Regularity\nSmooth data ⇒ smooth solution"] + T5["T5 Harnack inequality\nFor nonnegative harmonic functions"] + + D1 --> D2 + D1 --> D3 + D1 --> D4 + D2 --> T2 + D3 --> T3 + D1 --> T1 + D1 --> T5 + D2 --> T4 + D3 --> T4 + D4 --> T4 + T1 --> T5 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: partial_differential_equations
    • +
  • Keywords: Laplace equation, heat equation, wave equation, elliptic, parabolic, hyperbolic
    • +
  • Research frontier: arXiv math.AP
    • +
+
+
+
+ + + diff --git a/processes/partial_differential_equations/partial_differential_equations-index.html b/processes/partial_differential_equations/partial_differential_equations-index.html new file mode 100644 index 0000000000000000000000000000000000000000..bf1238a20ddff20373b624024ebe1c28753164f2 --- /dev/null +++ b/processes/partial_differential_equations/partial_differential_equations-index.html @@ -0,0 +1,37 @@ + + + + + + Partial Differential Equations - Mathematics Processes + + + +
+
+ ← Back to Mathematics Index + arXiv math.AP +
+

Partial Differential Equations

+

Dependency graphs for PDE theory: classical equations, well-posedness, Sobolev spaces, and maximum principles.

+ +
+ + diff --git a/processes/partial_differential_equations/partial_differential_equations-maximum.html b/processes/partial_differential_equations/partial_differential_equations-maximum.html new file mode 100644 index 0000000000000000000000000000000000000000..fcbed8fe8d87ff0fa608ef4e3633284af330746f --- /dev/null +++ b/processes/partial_differential_equations/partial_differential_equations-maximum.html @@ -0,0 +1,109 @@ + + + + + + Maximum Principles for PDEs - Mathematics Process + + + + +
+
+

Maximum Principles for PDEs

+
+ Partial Differential Equations + Mathematics +
+
+
+ ← Back to Mathematics Index + Partial Differential Equations Index + arXiv: Analysis of PDEs (math.AP) +
+
+
+

Description

+

Maximum principles for elliptic and parabolic equations. Harmonic functions achieve extrema on the boundary; heat equation preserves maximum location.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Subharmonic function\nΔu ≥ 0 (or Δu ≤ 0)"] + D2["D2 Elliptic operator L\nLu = aⁱʲ∂ᵢ∂ⱼu + bⁱ∂ᵢu + cu"] + D3["D3 Parabolic operator\n∂u/∂t − Lu = 0"] + D4["D4 Comparison principle\nu ≤ v on ∂Ω ⇒ u ≤ v in Ω"] + + T1["T1 Weak maximum principle\nSubsolution ≤ max of boundary"] + T2["T2 Strong maximum principle\nInterior max ⇒ u constant"] + T3["T3 Hopf lemma\nNormal derivative at boundary max"] + T4["T4 Uniqueness for Dirichlet\nFrom maximum principle"] + T5["T5 Harnack inequality\nBounds ratio of positive harmonic functions"] + + D1 --> T1 + D2 --> T1 + D2 --> T2 + D1 --> T2 + D4 --> T4 + D2 --> T3 + T1 --> T3 + T1 --> T4 + D1 --> T5 + D2 --> T5 + T2 --> T4 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: partial_differential_equations
    • +
  • Keywords: maximum principle, Hopf lemma, Harnack, harmonic, elliptic
    • +
  • Research frontier: arXiv math.AP
    • +
+
+
+
+ + + diff --git a/processes/partial_differential_equations/partial_differential_equations-sobolev.html b/processes/partial_differential_equations/partial_differential_equations-sobolev.html new file mode 100644 index 0000000000000000000000000000000000000000..3d342be7bdf79020b975957d63205b4bce7b7509 --- /dev/null +++ b/processes/partial_differential_equations/partial_differential_equations-sobolev.html @@ -0,0 +1,108 @@ + + + + + + Sobolev Spaces and Weak Solutions - Mathematics Process + + + + +
+
+

Sobolev Spaces and Weak Solutions

+
+ Partial Differential Equations + Mathematics +
+
+
+ ← Back to Mathematics Index + Partial Differential Equations Index + arXiv: Analysis of PDEs (math.AP) +
+
+
+

Description

+

Dependency graph for Sobolev spaces W^{k,p} and weak solutions of PDEs. Weak formulation, Galerkin methods, and regularity theory.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Sobolev space W^{k,p}\nFunctions with k weak derivatives in L^p"] + D2["D2 Weak derivative\nDistributional derivative"] + D3["D3 Weak solution\nSatisfies PDE in integral sense"] + D4["D4 H¹ and H₀¹\nHilbert Sobolev spaces"] + + T1["T1 Sobolev embedding\nW^{k,p} ⊂ L^q for p ≤ q*"] + T2["T2 Rellich-Kondrachov\nW^{1,p} ⋐ L^p compact"] + T3["T3 Lax-Milgram for weak form\nUnique weak solution exists"] + T4["T4 Regularity: f ∈ L² ⇒ u ∈ H²\nFor elliptic with smooth coeffs"] + T5["T5 Caccioppoli inequality\nInterior gradient bounds"] + + D1 --> T1 + D2 --> D1 + D3 --> T3 + D4 --> T3 + D1 --> T2 + D1 --> T4 + D3 --> T4 + D1 --> T5 + T1 --> T4 + T2 --> T3 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: partial_differential_equations
    • +
  • Keywords: Sobolev space, weak solution, Lax-Milgram, embedding, regularity
    • +
  • Research frontier: arXiv math.AP
    • +
+
+
+
+ + + diff --git a/processes/partial_differential_equations/partial_differential_equations-wellposed.html b/processes/partial_differential_equations/partial_differential_equations-wellposed.html new file mode 100644 index 0000000000000000000000000000000000000000..261241b95023ae9e30928a1fc29eead1919554b6 --- /dev/null +++ b/processes/partial_differential_equations/partial_differential_equations-wellposed.html @@ -0,0 +1,109 @@ + + + + + + Well-Posedness of PDEs - Mathematics Process + + + + +
+
+

Well-Posedness of PDEs

+
+ Partial Differential Equations + Mathematics +
+
+
+ ← Back to Mathematics Index + Partial Differential Equations Index + arXiv: Analysis of PDEs (math.AP) +
+
+
+

Description

+

Hadamard's notion of well-posedness: existence, uniqueness, and continuous dependence on data. Dependency graph for Cauchy problems and initial-boundary value problems.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Well-posed problem\nExistence, uniqueness, continuity"] + D2["D2 Ill-posed problem\nViolates one of Hadamard conditions"] + D3["D3 Cauchy problem\nInitial data on non-characteristic surface"] + D4["D4 Continuous dependence\nSmall data change ⇒ small solution change"] + + T1["T1 Cauchy-Kowalevski\nAnalytic data ⇒ analytic solution"] + T2["T2 Hadamard example\nLaplace eq. Cauchy ill-posed"] + T3["T3 Energy estimates\nStability for parabolic/hyperbolic"] + T4["T4 Lax-Milgram\nExistence for elliptic in Hilbert space"] + T5["T5 Semigroup theory\nWell-posedness for evolution equations"] + + D1 --> T3 + D2 --> T2 + D3 --> T1 + D4 --> T3 + D3 --> T2 + D1 --> T4 + D1 --> T5 + T1 --> D1 + T3 --> D4 + T4 --> D1 + T5 --> D1 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: partial_differential_equations
    • +
  • Keywords: well-posedness, Hadamard, Cauchy problem, energy estimates, Lax-Milgram
    • +
  • Research frontier: arXiv math.AP
    • +
+
+
+
+ + + diff --git a/processes/spectral_theory/spectral_theory-compact.html b/processes/spectral_theory/spectral_theory-compact.html new file mode 100644 index 0000000000000000000000000000000000000000..4c9cdb0a65f2f8a7cc2f65cdd3a47793b70d37af --- /dev/null +++ b/processes/spectral_theory/spectral_theory-compact.html @@ -0,0 +1,109 @@ + + + + + + Compact Operators - Mathematics Process + + + + +
+
+

Compact Operators in Spectral Theory

+
+ Spectral Theory + Mathematics +
+
+
+ ← Back to Mathematics Index + Spectral Theory Index + arXiv: Spectral Theory (math.SP) +
+
+
+

Description

+

Compact operators: discrete spectrum, Fredholm theory, Hilbert-Schmidt and trace class. Spectral theorem for compact self-adjoint operators.

+
+
+

Dependency Flowchart

+
+graph TD + D1["D1 Compact operator K\nBounded sets → relatively compact"] + D2["D2 Hilbert-Schmidt operator\n∑ ||K e_n||² < ∞ for ONS"] + D3["D3 Trace class\n|K| = (K*K)^{1/2} has finite trace"] + D4["D4 Fredholm index\nindex T = dim ker T − dim coker T"] + + T1["T1 Riesz-Schauder\nσ(K) discrete, 0 only limit point"] + T2["T2 Spectral theorem for compact\nK = ∑ λ_n ⟨·,e_n⟩ e_n, λ_n → 0"] + T3["T3 Fredholm alternative\n(I − K)u = f solvable ⇔ f ⊥ ker(I−K*)"] + T4["T4 Weyl theorem\nT compact ⇒ σ_ess(T+K) = σ_ess(T)"] + T5["T5 Min-max principle\nλ_n = min max ⟨Tx,x⟩ / ||x||²"] + + D1 --> D2 + D2 --> D3 + D1 --> D4 + D1 --> T1 + D1 --> T2 + D1 --> T3 + D1 --> T4 + D2 --> T2 + D4 --> T3 + T2 --> T5 + T1 --> T2 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
+
+
+

Color Scheme

+
+
Blue
Definitions (D1–D4)
+
Teal
Theorems (T1–T5)
+
+
+
+

Info

+
    +
  • Subcategory: spectral_theory
    • +
  • Keywords: compact operator, Fredholm, Hilbert-Schmidt, Riesz-Schauder, Weyl
    • +
  • Research frontier: arXiv math.SP
    • +
+
+
+
+ + + diff --git a/processes/spectral_theory/spectral_theory-index.html b/processes/spectral_theory/spectral_theory-index.html new file mode 100644 index 0000000000000000000000000000000000000000..96f3cf054c0a33e909e53ec6c9f49d38e388f6e3 --- /dev/null +++ b/processes/spectral_theory/spectral_theory-index.html @@ -0,0 +1,37 @@ + + + + + + Spectral Theory - Mathematics Processes + + + +
+
+ ← Back to Mathematics Index + arXiv math.SP +
+

Spectral Theory

+

Dependency graphs for spectrum, self-adjoint operators, compact operators, and Schrödinger operators.

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+ + diff --git a/processes/spectral_theory/spectral_theory-schrodinger.html b/processes/spectral_theory/spectral_theory-schrodinger.html new file mode 100644 index 0000000000000000000000000000000000000000..855332b4e29299ac26f2f2e50af6c45522079c4e --- /dev/null +++ b/processes/spectral_theory/spectral_theory-schrodinger.html @@ -0,0 +1,109 @@ + + + + + + Schrödinger Operators - Mathematics Process + + + + +
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Schrödinger Operators

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+ Spectral Theory + Mathematics +
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+ ← Back to Mathematics Index + Spectral Theory Index + arXiv: Spectral Theory (math.SP) +
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Description

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H = −Δ + V on L²(ℝⁿ). Essential and discrete spectrum, boundedness from below, and eigenvalue asymptotics. Applications to quantum mechanics.

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Dependency Flowchart

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+graph TD + D1["D1 Schrödinger operator H\nH = −Δ + V on L²"] + D2["D2 Relative compactness\nV(−Δ+1)^{-1} compact"] + D3["D3 Discrete spectrum σ_d\nIsolated eigenvalues of finite multiplicity"] + D4["D4 Essential spectrum σ_ess\nσ(H) \ σ_d"] + + T1["T1 Kato-Rellich\nV Kato-small ⇒ H self-adjoint on D(−Δ)"] + T2["T2 Weyl theorem\nσ_ess(−Δ+V) = [0,∞) for V → 0 at ∞"] + T3["T3 HVZ theorem\nσ_ess for N-body = ⋃ clusters"] + T4["T4 Cwikel-Lieb-Rosenbljum\nN_0(V) ≤ C ∫ V_-^{n/2} for n ≥ 3"] + T5["T5 Lieb-Thirring\n∑|λ_j|^γ ≤ L_γ ∫ V_-^{γ+n/2}"] + + D1 --> D2 + D1 --> D3 + D1 --> D4 + D1 --> T1 + D2 --> T2 + D3 --> T4 + D4 --> T2 + D4 --> T3 + D3 --> T5 + T1 --> T2 + T2 --> T3 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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Info

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    +
  • Subcategory: spectral_theory
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  • Keywords: Schrödinger operator, Weyl theorem, Kato-Rellich, CLR, Lieb-Thirring
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  • Research frontier: arXiv math.SP
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+ + + diff --git a/processes/spectral_theory/spectral_theory-selfadjoint.html b/processes/spectral_theory/spectral_theory-selfadjoint.html new file mode 100644 index 0000000000000000000000000000000000000000..8ba288dcc2b8c3223866b17d77d8d7df358ece83 --- /dev/null +++ b/processes/spectral_theory/spectral_theory-selfadjoint.html @@ -0,0 +1,108 @@ + + + + + + Self-Adjoint Operators - Mathematics Process + + + + +
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Self-Adjoint Operators

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+ Spectral Theory + Mathematics +
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+ ← Back to Mathematics Index + Spectral Theory Index + arXiv: Spectral Theory (math.SP) +
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Description

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Symmetric and self-adjoint operators on Hilbert spaces. Spectrum real, spectral theorem, and functional calculus.

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Dependency Flowchart

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+graph TD + D1["D1 Symmetric operator T\n⟨Tx,y⟩ = ⟨x,Ty⟩ on D(T)"] + D2["D2 Self-adjoint T = T*\nD(T) = D(T*), T = T* on D(T)"] + D3["D3 Essential self-adjointness\nClosure of T is self-adjoint"] + D4["D4 Spectral measure E\nProjection-valued measure for T"] + + T1["T1 Spectrum real\nSelf-adjoint ⇒ σ(T) ⊂ R"] + T2["T2 Spectral theorem\nT = ∫ λ dE(λ) for self-adjoint T"] + T3["T3 von Neumann criterion\nT symmetric, ran(T±i) = H ⇒ self-adjoint"] + T4["T4 Functional calculus\nf(T) = ∫ f(λ) dE(λ) for Borel f"] + T5["T5 Stone theorem\n−iT generator of unitary group ⇔ T self-adjoint"] + + D1 --> D2 + D2 --> D3 + D2 --> D4 + D2 --> T1 + D4 --> T2 + D2 --> T3 + D4 --> T4 + D2 --> T5 + T2 --> T4 + T1 --> T2 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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Info

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  • Subcategory: spectral_theory
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  • Keywords: self-adjoint, spectral theorem, functional calculus, Stone theorem
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  • Research frontier: arXiv math.SP
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+ + + diff --git a/processes/spectral_theory/spectral_theory-spectrum.html b/processes/spectral_theory/spectral_theory-spectrum.html new file mode 100644 index 0000000000000000000000000000000000000000..20f81c38160bad494712c9e4cd15cb7fac561a6c --- /dev/null +++ b/processes/spectral_theory/spectral_theory-spectrum.html @@ -0,0 +1,108 @@ + + + + + + Spectrum of Operators - Mathematics Process + + + + +
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Spectrum of Operators

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+ Spectral Theory + Mathematics +
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+ ← Back to Mathematics Index + Spectral Theory Index + arXiv: Spectral Theory (math.SP) +
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Description

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Point spectrum, continuous spectrum, residual spectrum. Resolvent set and spectral radius. Foundation for spectral decomposition.

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Dependency Flowchart

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+graph TD + D1["D1 Spectrum σ(T)\nλ such that T − λI not invertible"] + D2["D2 Resolvent set ρ(T)\nComplement of spectrum; (T − λI)^{-1} bounded"] + D3["D3 Point / continuous / residual\nEigenvalues vs approximate eigenvalues vs rest"] + D4["D4 Spectral radius r(T)\nlim ||T^n||^{1/n} = sup |σ(T)|"] + + T1["T1 Spectrum nonempty\nFor T on complex Banach space, T ≠ 0"] + T2["T2 Gelfand formula\nr(T) = lim ||T^n||^{1/n}"] + T3["T3 Spectral mapping\np(σ(T)) = σ(p(T)) for polynomials"] + T4["T4 Compact ⇒ 0 in spectrum\nOr T finite rank"] + T5["T5 Resolvent identity\nR_λ − R_μ = (λ−μ) R_λ R_μ"] + + D1 --> D2 + D1 --> D3 + D1 --> D4 + D2 --> T5 + D4 --> T2 + D1 --> T1 + D1 --> T3 + D4 --> T3 + D1 --> T4 + D2 --> T5 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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Info

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  • Subcategory: spectral_theory
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  • Keywords: spectrum, resolvent, spectral radius, Gelfand, Banach algebra
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  • Research frontier: arXiv math.SP
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+ + + diff --git a/processes/symplectic_geometry/symplectic_geometry-darboux.html b/processes/symplectic_geometry/symplectic_geometry-darboux.html new file mode 100644 index 0000000000000000000000000000000000000000..e075aaf13f8935d21c9509817361af1a3141494c --- /dev/null +++ b/processes/symplectic_geometry/symplectic_geometry-darboux.html @@ -0,0 +1,108 @@ + + + + + + Darboux Theorem - Mathematics Process + + + + +
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Darboux Theorem and Canonical Coordinates

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+ Symplectic Geometry + Mathematics +
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+ ← Back to Mathematics Index + Symplectic Geometry Index + arXiv: Symplectic Geometry (math.SG) +
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+

Description

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Darboux theorem: locally all symplectic manifolds look like (ℝ²ⁿ, ω₀). Canonical coordinates (q,p), Moser trick, and Weinstein Lagrangian neighborhoods.

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Dependency Flowchart

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+graph TD + D1["D1 Standard symplectic ω_0\nω_0 = Σ dp_i ∧ dq_i on R^{2n}"] + D2["D2 Darboux chart\nLocal coords (q,p) with ω = Σ dp_i ∧ dq_i"] + D3["D3 Lagrangian submanifold L\ndim L = n, ω|_L = 0"] + D4["D4 Isotopy\nSmooth 1-parameter family of diffeomorphisms"] + + T1["T1 Darboux theorem\n(M,ω) locally ≅ (R^{2n}, ω_0)"] + T2["T2 Moser trick\nIsotopy of symplectic forms via Moser vector field"] + T3["T3 Weinstein Lagrangian\nNhd of L symplectomorphic to T*L"] + T4["T4 Symplectic embedding\nB^{2n}(r) → (M,ω) for small r"] + T5["T5 Relative Darboux\nTwo forms agree on L ⇒ differ by exact near L"] + + D1 --> D2 + D1 --> T1 + D2 --> T1 + D3 --> T3 + D4 --> T2 + D1 --> T2 + T2 --> T1 + D3 --> T4 + T1 --> T3 + T2 --> T5 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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Info

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    +
  • Subcategory: symplectic_geometry
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  • Keywords: Darboux, Moser, Lagrangian, Weinstein, canonical coordinates
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  • Research frontier: arXiv math.SG
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+ + + diff --git a/processes/symplectic_geometry/symplectic_geometry-form.html b/processes/symplectic_geometry/symplectic_geometry-form.html new file mode 100644 index 0000000000000000000000000000000000000000..b2022d8af304e286cc65902496f2e5e6c53592dc --- /dev/null +++ b/processes/symplectic_geometry/symplectic_geometry-form.html @@ -0,0 +1,108 @@ + + + + + + Symplectic Form - Mathematics Process + + + + +
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Symplectic Form

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+ Symplectic Geometry + Mathematics +
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+ ← Back to Mathematics Index + Symplectic Geometry Index + arXiv: Symplectic Geometry (math.SG) +
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Description

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Symplectic manifold (M, ω): nondegenerate closed 2-form. Dimension even, ω^n volume form. Linear symplectic algebra and Darboux basis.

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Dependency Flowchart

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+graph TD + D1["D1 Symplectic form ω\nClosed, nondegenerate 2-form"] + D2["D2 Nondegeneracy\nω^n ≠ 0; ω^∧: TM → T*M iso"] + D3["D3 Symplectic vector space\n(V, ω) with dim V even"] + D4["D4 Symplectomorphism\nφ*ω = ω, preserves form"] + + T1["T1 Dimension even\ndim M = 2n for symplectic M"] + T2["T2 ω^n is volume form\nOriented manifold"] + T3["T3 Linear Darboux\n(V,ω) ≅ (R^{2n}, ω_0) standard"] + T4["T4 Darboux theorem\nLocally (M,ω) ≅ (R^{2n}, ω_0)"] + T5["T5 Symplectic quotient\nM // G inherits symplectic structure"] + + D1 --> D2 + D1 --> D3 + D1 --> D4 + D2 --> T1 + D2 --> T2 + D3 --> T3 + D1 --> T4 + D4 --> T5 + T3 --> T4 + T1 --> T2 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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+

Info

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    +
  • Subcategory: symplectic_geometry
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  • Keywords: symplectic form, Darboux, nondegenerate, symplectomorphism
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  • Research frontier: arXiv math.SG
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+ + + diff --git a/processes/symplectic_geometry/symplectic_geometry-hamiltonian.html b/processes/symplectic_geometry/symplectic_geometry-hamiltonian.html new file mode 100644 index 0000000000000000000000000000000000000000..901879d90b298cf62ea4ae917d2f9e547a050f43 --- /dev/null +++ b/processes/symplectic_geometry/symplectic_geometry-hamiltonian.html @@ -0,0 +1,108 @@ + + + + + + Hamiltonian Vector Fields - Mathematics Process + + + + +
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Hamiltonian Vector Fields

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+ Symplectic Geometry + Mathematics +
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+ ← Back to Mathematics Index + Symplectic Geometry Index + arXiv: Symplectic Geometry (math.SG) +
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+

Description

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Hamiltonian H, Hamiltonian vector field X_H via ι_{X_H}ω = dH. Flow preserves ω. Poisson bracket and Liouville theorem.

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Dependency Flowchart

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+graph TD + D1["D1 Hamiltonian vector field X_H\nι_{X_H} ω = dH"] + D2["D2 Poisson bracket {f,g}\nω(X_f, X_g) = df(X_g)"] + D3["D3 Hamiltonian flow φ_t\nGenerated by X_H, dφ_t/dt = X_H ∘ φ_t"] + D4["D4 Liouville form\nα on cotangent bundle, dα = ω"] + + T1["T1 Flow preserves ω\nφ_t* ω = ω"] + T2["T2 Liouville theorem\nHamiltonian flow preserves volume ω^n"] + T3["T3 {f,g} = X_f(g)\nPoisson = Lie derivative of g along X_f"] + T4["T4 Arnold-Liouville\nn integrals in involution ⇒ tori, action-angle"] + T5["T5 Darboux on cotangent\nT*Q has canonical (q,p) with ω = dp∧dq"] + + D1 --> D2 + D1 --> D3 + D4 --> D1 + D3 --> T1 + D3 --> T2 + D2 --> T3 + D2 --> T4 + D4 --> T5 + T1 --> T2 + D1 --> T3 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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+

Info

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  • Subcategory: symplectic_geometry
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  • Keywords: Hamiltonian, Poisson bracket, Liouville, Arnold, action-angle
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  • Research frontier: arXiv math.SG
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+ + + diff --git a/processes/symplectic_geometry/symplectic_geometry-index.html b/processes/symplectic_geometry/symplectic_geometry-index.html new file mode 100644 index 0000000000000000000000000000000000000000..6610156945b1d7ea5543112386a6ababcefb53b2 --- /dev/null +++ b/processes/symplectic_geometry/symplectic_geometry-index.html @@ -0,0 +1,37 @@ + + + + + + Symplectic Geometry - Mathematics Processes + + + +
+
+ ← Back to Mathematics Index + arXiv math.SG +
+

Symplectic Geometry

+

Dependency graphs for symplectic forms, Hamiltonian flows, Darboux theorem, and Poisson structures.

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+ + diff --git a/processes/symplectic_geometry/symplectic_geometry-poisson.html b/processes/symplectic_geometry/symplectic_geometry-poisson.html new file mode 100644 index 0000000000000000000000000000000000000000..ccea29c2cbfbfb4e2d34f5ab1178d3f840588b9e --- /dev/null +++ b/processes/symplectic_geometry/symplectic_geometry-poisson.html @@ -0,0 +1,108 @@ + + + + + + Poisson Structures - Mathematics Process + + + + +
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+

Poisson Structures

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+ Symplectic Geometry + Mathematics +
+
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+ ← Back to Mathematics Index + Symplectic Geometry Index + arXiv: Symplectic Geometry (math.SG) +
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+
+

Description

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Poisson manifold: bracket {·,·} satisfying Leibniz and Jacobi. Symplectic leaves, Casimirs, and deformation quantization.

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Dependency Flowchart

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+graph TD + D1["D1 Poisson bracket π\nSkew-symmetric, Leibniz, Jacobi identity"] + D2["D2 Poisson manifold (M, π)\nBivector field with [π,π] = 0"] + D3["D3 Symplectic leaf\nMaximal integral submanifold of π#(T*M)"] + D4["D4 Casimir function C\n{C, f} = 0 for all f"] + + T1["T1 ω symplectic ⇒ {f,g} = ω(X_f,X_g)\nDefines Poisson"] + T2["T2 Symplectic foliation\n(M,π) union of symplectic leaves"] + T3["T3 Darboux-Weinstein\nLocal splitting: symplectic × cosymplectic"] + T4["T4 Kostant-Souriau\nPrequantization of integral ω"] + T5["T5 Kontsevich formality\nDeformation quantization exists"] + + D1 --> D2 + D2 --> D3 + D2 --> D4 + D1 --> T1 + D3 --> T2 + D2 --> T3 + D4 --> T2 + T1 --> D2 + T2 --> T3 + T3 --> T5 + + classDef definition fill:#3498db,color:#fff,stroke:#2980b9 + classDef theorem fill:#1abc9c,color:#fff,stroke:#16a085 + class D1,D2,D3,D4 definition + class T1,T2,T3,T4,T5 theorem +
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Color Scheme

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Blue
Definitions (D1–D4)
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Teal
Theorems (T1–T5)
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+

Info

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    +
  • Subcategory: symplectic_geometry
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  • Keywords: Poisson bracket, symplectic leaf, Casimir, Kontsevich, deformation quantization
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  • Research frontier: arXiv math.SG
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+ + + diff --git a/catalytic_hydrogenation_optimization.html b/validation_flowcharts/catalytic_hydrogenation_optimization.html similarity index 100% rename from catalytic_hydrogenation_optimization.html rename to validation_flowcharts/catalytic_hydrogenation_optimization.html diff --git a/electrochemical_oxygen_reduction.html b/validation_flowcharts/electrochemical_oxygen_reduction.html similarity index 100% rename from electrochemical_oxygen_reduction.html rename to validation_flowcharts/electrochemical_oxygen_reduction.html diff --git a/quantum_chemistry_calculation.html b/validation_flowcharts/quantum_chemistry_calculation.html similarity index 100% rename from quantum_chemistry_calculation.html rename to validation_flowcharts/quantum_chemistry_calculation.html diff --git a/raft_polymerization_mechanism.html b/validation_flowcharts/raft_polymerization_mechanism.html similarity index 100% rename from raft_polymerization_mechanism.html rename to validation_flowcharts/raft_polymerization_mechanism.html diff --git a/surface_catalysis_mechanism.html b/validation_flowcharts/surface_catalysis_mechanism.html similarity index 100% rename from surface_catalysis_mechanism.html rename to validation_flowcharts/surface_catalysis_mechanism.html