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From Sacred Geometry to Silicon
Reverse-Engineering Computational Constraints from Ancient Numerical Systems to Topological Cryptography
A Forge Tournament Research Paper — SnapKitty West / SNAPKITTYWEST — 2026
Summary
25-section, ~30-page LaTeX research paper investigating the thesis that radically different computational traditions can be compared through their treatment of constraints, state, transformation, and representation.
Tournament Contestants
| Contestant | Domain |
|---|---|
| A: Ancient Numerical Systems | Babylonian base-60, accounting, astronomy |
| B: SUBLEQ | Single-instruction universality |
| C: Lambda Calculus | Symbolic substitution |
| D: Turing Machine | State + tape + transition |
| E: DAG Execution | Dependency ordering, deterministic scheduling |
| F: Formal Verification | Lean 4, SMT, zero-sorry proofs |
| G: Topological Computation | Braid groups, Yang-Baxter, anyons |
| H: Mobius Bridge | Experimental topological crypto framework |
Winner: Formal Verification (highest scores on precision, constraint transparency, cryptographic relevance)
Central Thesis
The connection between ancient geometry, minimal machines, formal computation, and cryptography is methodological:
- Represent the structure
- Identify the constraints
- Transform the representation
- Execute the transformation
- Verify the result
- Measure what actually happened
Evidence Standard
All claims are classified by evidence level (1=Conjecture through 7=Replicated). No cryptographic breaks are claimed without reproducible demonstration. Failed experiments are reported as valid results.
Key Tables
- Computational paradigms comparison (8 paradigms x 5 properties)
- Mathematical concept to cybersecurity translation (15 concepts)
- RSA security assumptions
- ECDLP security assumptions
- Mobius Bridge component evidence classification
- Forge Tournament scoring (11 criteria x 8 contestants)
- Evidence classification (7 levels)
- Experimental reproducibility requirements
Source
GitHub: https://github.com/SNAPKITTYWEST/forge-tournament-paper
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