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README.md +31 -1
chemistry_processes.html +609 -0
computer_science_processes.html +3 -3
mathematics_processes.html +494 -22
physics_processes.html +13 -13
programming_framework_article.html +11 -11

README.md CHANGED Viewed

@@ -21,6 +21,36 @@ Complex systems across biology, chemistry, and physics exhibit remarkable simila
 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.
 ### Universal Color Coding Table
 | Color | Hex | Biology | Chemistry | Computer Science | Physics | Mathematics |
@@ -34,7 +64,7 @@ The Programming Framework project aims to advance the use of Mermaid Markdown sy
 ### Explore the Space
 - Biology evidence base: GLMP Space (Hugging Face) and repo
-- Chemistry processes: `chemistry_examples.html`
 - Computer Science: `computer_science_processes.html`
 - Physics: `physics_processes.html`
 - Mathematics: `mathematics_processes.html`

 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.
+### 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. **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
+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.
 ### Universal Color Coding Table
 | Color | Hex | Biology | Chemistry | Computer Science | Physics | Mathematics |
 ### Explore the Space
 - Biology evidence base: GLMP Space (Hugging Face) and repo
+- Chemistry processes: `chemistry_processes.html`
 - Computer Science: `computer_science_processes.html`
 - Physics: `physics_processes.html`
 - Mathematics: `mathematics_processes.html`

chemistry_processes.html ADDED Viewed

	@@ -0,0 +1,609 @@

+<!DOCTYPE html>
+<html lang="en">
+<head>
+    <meta charset="UTF-8" />
+    <meta name="viewport" content="width=device-width, initial-scale=1" />
+    <title>Chemistry Examples - Programming Framework Analysis</title>
+    <style>
+        body {
+            font-family: 'Times New Roman', Times, serif, 'Arial Unicode MS';
+            margin: 0;
+            background: #ffffff;
+            color: #000000;
+            line-height: 1.6;
+            font-size: 12pt;
+        }
+        .container {
+            max-width: 1000px;
+            margin: 0 auto;
+            padding: 1.5rem;
+        }
+        h1, h2, h3 {
+            color: #000000;
+            margin-top: 1.5rem;
+            margin-bottom: 0.75rem;
+        }
+        h1 {
+            font-size: 18pt;
+            text-align: center;
+        }
+        h2 {
+            font-size: 16pt;
+            border-bottom: 2px solid #000;
+            padding-bottom: 0.5rem;
+        }
+        h3 {
+            font-size: 14pt;
+        }
+        p {
+            margin-bottom: 1rem;
+            text-align: justify;
+        }
+        .figure {
+            margin: 1rem 0;
+            text-align: center;
+            border: 1px solid #ccc;
+            padding: 1rem;
+            background: #f9f9f9;
+        }
+        .figure-caption {
+            margin-top: 1rem;
+            font-style: italic;
+            text-align: left;
+        }
+        .mermaid {
+            background: white;
+            padding: 1rem;
+            border-radius: 4px;
+        }
+    </style>
+    <script src="https://cdn.jsdelivr.net/npm/mermaid@10.6.1/dist/mermaid.min.js"></script>
+    <script>
+        mermaid.initialize({
+            startOnLoad: true,
+            theme: 'default',
+            flowchart: {
+                useMaxWidth: false,
+                htmlLabels: true,
+                curve: 'linear',
+                nodeSpacing: 50,
+                rankSpacing: 50,
+                padding: 20
+            },
+            themeVariables: {
+                fontFamily: 'Arial Unicode MS, Arial, sans-serif'
+            }
+        });
+    </script>
+</head>
+<body>
+    <div class="container">
+        <h1>Chemistry Examples - Programming Framework Analysis</h1>
+        <p>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.</p>
+        <h2>1. Catalytic Hydrogenation Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+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[Pi-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
+                    </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Reactants & Catalysts
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Reaction Vessels & Equipment
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Chemical Reactions & Transformations
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 1.</strong> 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.
+            </div>
+        </div>
+        <h2>2. Polymerization Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+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
+                    </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Reactants & Initiators
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Reaction Vessels & Equipment
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Polymerization Reactions
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 2.</strong> 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.
+            </div>
+        </div>
+        <h2>3. Acid-Base Titration Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+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 plus plus OH minus yields 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
+                    </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Reactants & Indicators
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Titration Equipment
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Neutralization Reactions
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 3.</strong> Acid-Base Titration Process. This chemistry process visualization demonstrates analytical chemistry procedures. The flowchart shows reactant inputs, titration equipment, neutralization reactions, intermediate measurements, and final analytical results.
+            </div>
+        </div>
+        <h2>4. Electrochemical Cell Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+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
+                    </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Electrodes & Electrolyte
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Cell Components
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Redox Reactions
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 4.</strong> Electrochemical Cell Process. This chemistry process visualization demonstrates electrochemical energy conversion. The flowchart shows electrode inputs, cell components, redox reactions, intermediate processes, and final electrical energy output.
+            </div>
+        </div>
+        <h2>5. Distillation Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+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
+                    </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Mixture & Heat Source
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Distillation Equipment
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Phase Separation Processes
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 5.</strong> Distillation Process. This chemistry process visualization demonstrates separation techniques. The flowchart shows mixture inputs, distillation equipment, phase separation processes, intermediate fractions, and final purified components.
+            </div>
+        </div>
+        <p><strong>Generated using the Programming Framework methodology</strong></p>
+        <p>This collection demonstrates the computational nature of chemical processes and systems</p>
+        <p>Each flowchart preserves maximum detail through optimized Mermaid configuration</p>
+    </div>
+</body>
+</html>

computer_science_processes.html CHANGED Viewed

@@ -143,13 +143,13 @@ graph TD
             <div class="mermaid">
 graph TD
     A[Search Key] --> B[Compare with Root]
-    B --> C{Key < Root?}
     C -->|Yes| D[Search Left Subtree]
     C -->|No| E[Search Right Subtree]
     D --> F[Recursive Search]
     E --> G[Recursive Search]
-    F --> H{Key Found?}
-    G --> I{Key Found?}
     H -->|Yes| J[Return Node]
     H -->|No| K[Return Null]
     I -->|Yes| L[Return Node]

             <div class="mermaid">
 graph TD
     A[Search Key] --> B[Compare with Root]
+    B --> C[Key less than Root Question]
     C -->|Yes| D[Search Left Subtree]
     C -->|No| E[Search Right Subtree]
     D --> F[Recursive Search]
     E --> G[Recursive Search]
+    F --> H[Key Found Question]
+    G --> I[Key Found Question]
     H -->|Yes| J[Return Node]
     H -->|No| K[Return Null]
     I -->|Yes| L[Return Node]

mathematics_processes.html CHANGED Viewed

@@ -88,22 +88,22 @@
 graph TD
     A1[Peano Axioms] --> B1[Axiom Processing]
     C1[Given n in Natural Numbers] --> D1[Input Validation]
-    E1[Goal: Prove P(n)] --> F1[Target Identification]
     B1 --> G1[Mathematical Universe Setup]
     D1 --> H1[Variable Declaration]
     F1 --> I1[Proof Strategy Selection]
-    G1 --> J1[Induction Hypothesis P(k)]
     H1 --> K1[Base Case Analysis]
     I1 --> L1[Inductive Step Planning]
-    K1 --> M1[P(0) Verification]
     M1 --> N1[Base Case Success]
     N1 --> O1[Induction Foundation]
-    L1 --> P1[Assume P(k) for k in Natural Numbers]
-    P1 --> Q1[Show P(k+1) follows]
     Q1 --> R1[Inductive Step Execution]
     R1 --> S1[Algebraic Manipulation]
@@ -118,16 +118,16 @@ graph TD
     Y1 --> Z1[Mathematical Rigor Verification]
     Z1 --> AA1[Proof Completeness Assessment]
-    AA1 --> BB1{Proof Complete?}
-    BB1 -->|No| CC1[Identify Gap]
-    BB1 -->|Yes| DD1[Proof Validated]
     CC1 --> EE1[Additional Lemma Needed]
     EE1 --> FF1[Sub-proof Construction]
     FF1 --> GG1[Gap Resolution]
     GG1 --> Y1
-    DD1 --> HH1[Theorem P(n) Proven]
     HH1 --> II1[Mathematical Truth Established]
     II1 --> JJ1[Proof Tree Complete]
@@ -202,26 +202,26 @@ graph TD
 graph TD
     A2[Integer a] --> B2[Input Validation]
     C2[Integer b] --> D2[Input Validation]
-    E2[Goal: Find GCD(a,b)] --> F2[Problem Statement]
-    B2 --> G2[Set r₀ = a]
-    D2 --> H2[Set r₁ = b]
     F2 --> I2[Algorithm Selection]
     G2 --> J2[Division Algorithm]
     H2 --> K2[Division Algorithm]
     I2 --> L2[Iterative Process]
-    J2 --> M2[r₀ = q₁r₁ + r₂]
-    K2 --> N2[Calculate q₁ and r₂]
     L2 --> O2[Initialize iteration counter]
-    M2 --> P2{Is r₂ = 0?}
-    N2 --> Q2[Store r₂]
     O2 --> R2[Increment counter]
-    P2 -->|No| S2[Set r₀ = r₁, r₁ = r₂]
-    P2 -->|Yes| T2[GCD Found: r₁]
     Q2 --> U2[Update remainders]
     R2 --> V2[Track iterations]
@@ -229,16 +229,16 @@ graph TD
     U2 --> X2[Prepare for next iteration]
     V2 --> Y2[Check termination condition]
-    T2 --> Z2[GCD(a,b) = r₁]
     W2 --> AA2[Repeat division process]
     X2 --> BB2[Update variables]
-    Y2 --> CC2{Continue?}
     Z2 --> DD2[Result Validation]
     AA2 --> P2
     BB2 --> P2
-    CC2 -->|Yes| AA2
-    CC2 -->|No| T2
     DD2 --> EE2[GCD Calculation Complete]
     EE2 --> FF2[Mathematical Proof of Correctness]
@@ -273,6 +273,7 @@ graph TD
     style V2 fill:#74c0fc,color:#fff
     style X2 fill:#74c0fc,color:#fff
     style Y2 fill:#74c0fc,color:#fff
     style CC2 fill:#74c0fc,color:#fff
     style DD2 fill:#74c0fc,color:#fff
@@ -305,6 +306,477 @@ graph TD
             </div>
         </div>
         <p><strong>Generated using the Programming Framework methodology</strong></p>
         <p>This collection demonstrates the computational nature of mathematical processes and systems</p>

 graph TD
     A1[Peano Axioms] --> B1[Axiom Processing]
     C1[Given n in Natural Numbers] --> D1[Input Validation]
+    E1[Goal: Prove P of n] --> F1[Target Identification]
     B1 --> G1[Mathematical Universe Setup]
     D1 --> H1[Variable Declaration]
     F1 --> I1[Proof Strategy Selection]
+    G1 --> J1[Induction Hypothesis P of k]
     H1 --> K1[Base Case Analysis]
     I1 --> L1[Inductive Step Planning]
+    K1 --> M1[P of 0 Verification]
     M1 --> N1[Base Case Success]
     N1 --> O1[Induction Foundation]
+    L1 --> P1[Assume P of k for k in Natural Numbers]
+    P1 --> Q1[Show P of k plus 1 follows]
     Q1 --> R1[Inductive Step Execution]
     R1 --> S1[Algebraic Manipulation]
     Y1 --> Z1[Mathematical Rigor Verification]
     Z1 --> AA1[Proof Completeness Assessment]
+    AA1 --> BB1[Proof Complete Question]
+    BB1 --> CC1[Identify Gap]
+    BB1 --> DD1[Proof Validated]
     CC1 --> EE1[Additional Lemma Needed]
     EE1 --> FF1[Sub-proof Construction]
     FF1 --> GG1[Gap Resolution]
     GG1 --> Y1
+    DD1 --> HH1[Theorem P of n Proven]
     HH1 --> II1[Mathematical Truth Established]
     II1 --> JJ1[Proof Tree Complete]
 graph TD
     A2[Integer a] --> B2[Input Validation]
     C2[Integer b] --> D2[Input Validation]
+    E2[Goal: Find GCD of a and b] --> F2[Problem Statement]
+    B2 --> G2[Set r0 equals a]
+    D2 --> H2[Set r1 equals b]
     F2 --> I2[Algorithm Selection]
     G2 --> J2[Division Algorithm]
     H2 --> K2[Division Algorithm]
     I2 --> L2[Iterative Process]
+    J2 --> M2[r0 equals q1 times r1 plus r2]
+    K2 --> N2[Calculate q1 and r2]
     L2 --> O2[Initialize iteration counter]
+    M2 --> P2[Is r2 equals 0 Question]
+    N2 --> Q2[Store r2]
     O2 --> R2[Increment counter]
+    P2 --> S2[Set r0 equals r1 comma r1 equals r2]
+    P2 --> T2[GCD Found: r1]
     Q2 --> U2[Update remainders]
     R2 --> V2[Track iterations]
     U2 --> X2[Prepare for next iteration]
     V2 --> Y2[Check termination condition]
+    T2 --> Z2[GCD of a and b equals r1]
     W2 --> AA2[Repeat division process]
     X2 --> BB2[Update variables]
+    Y2 --> CC2[Continue Question]
     Z2 --> DD2[Result Validation]
     AA2 --> P2
     BB2 --> P2
+    CC2 --> AA2
+    CC2 --> T2
     DD2 --> EE2[GCD Calculation Complete]
     EE2 --> FF2[Mathematical Proof of Correctness]
     style V2 fill:#74c0fc,color:#fff
     style X2 fill:#74c0fc,color:#fff
     style Y2 fill:#74c0fc,color:#fff
+    style BB2 fill:#74c0fc,color:#fff
     style CC2 fill:#74c0fc,color:#fff
     style DD2 fill:#74c0fc,color:#fff
             </div>
         </div>
+        <h2>3. Linear Algebra Matrix Operations Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+graph TD
+    A3[Matrix A] --> B3[Matrix Input Validation]
+    C3[Matrix B] --> D3[Matrix Input Validation]
+    E3[Operation Type] --> F3[Operation Selection]
+    B3 --> G3[Dimension Analysis]
+    D3 --> H3[Dimension Analysis]
+    F3 --> I3[Algorithm Selection]
+    G3 --> J3[Row Count Validation]
+    H3 --> K3[Column Count Validation]
+    I3 --> L3[Operation Method]
+    J3 --> M3[Matrix A Dimensions]
+    K3 --> N3[Matrix B Dimensions]
+    L3 --> O3[Computational Strategy]
+    M3 --> P3[Compatible for Operation Question]
+    N3 --> Q3[Compatibility Check]
+    O3 --> R3[Memory Allocation]
+    P3 --> S3[Proceed with Operation]
+    P3 --> T3[Dimension Error]
+    Q3 --> U3[Validation Complete]
+    R3 --> V3[Workspace Setup]
+    S3 --> W3[Element-wise Processing]
+    T3 --> X3[Error Handling]
+    U3 --> Y3[Operation Ready]
+    V3 --> Z3[Buffer Initialization]
+    W3 --> AA3[Row-by-Row Processing]
+    X3 --> BB3[User Notification]
+    Y3 --> CC3[Start Computation]
+    Z3 --> DD3[Result Matrix Creation]
+    AA3 --> EE3[Column-by-Column Processing]
+    BB3 --> FF3[Operation Aborted]
+    CC3 --> GG3[Matrix Multiplication]
+    DD3 --> HH3[Result Storage]
+    EE3 --> II3[Element Calculation]
+    FF3 --> JJ3[Return to Input]
+    GG3 --> KK3[Inner Product Computation]
+    HH3 --> LL3[Memory Management]
+    II3 --> MM3[Summation Process]
+    JJ3 --> NN3[Input Correction]
+    KK3 --> OO3[Row-Column Dot Product]
+    LL3 --> PP3[Matrix Construction]
+    MM3 --> QQ3[Result Element Assignment]
+    NN3 --> A3
+    OO3 --> RR3[Intermediate Sums]
+    PP3 --> SS3[Final Matrix Assembly]
+    QQ3 --> TT3[Next Element Processing]
+    RR3 --> UU3[Accumulation]
+    SS3 --> VV3[Matrix Validation]
+    TT3 --> WW3[All Elements Complete Question]
+    UU3 --> XX3[Sum Finalization]
+    VV3 --> YY3[Result Verification]
+    WW3 --> AA3
+    WW3 --> ZZ3[Operation Complete]
+    XX3 --> QQ3
+    YY3 --> ZZ3
+    ZZ3 --> AAA3[Result Matrix C]
+    AAA3 --> BBB3[Matrix Properties Analysis]
+    BBB3 --> CCC3[Computational Complexity Assessment]
+    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:#ffd43b,color:#000
+    style N3 fill:#ffd43b,color:#000
+    style O3 fill:#ffd43b,color:#000
+    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 Y3 fill:#51cf66,color:#fff
+    style Z3 fill:#51cf66,color:#fff
+    style AA3 fill:#51cf66,color:#fff
+    style BB3 fill:#51cf66,color:#fff
+    style CC3 fill:#51cf66,color:#fff
+    style DD3 fill:#51cf66,color:#fff
+    style EE3 fill:#51cf66,color:#fff
+    style FF3 fill:#51cf66,color:#fff
+    style GG3 fill:#51cf66,color:#fff
+    style HH3 fill:#51cf66,color:#fff
+    style II3 fill:#51cf66,color:#fff
+    style JJ3 fill:#51cf66,color:#fff
+    style KK3 fill:#51cf66,color:#fff
+    style LL3 fill:#51cf66,color:#fff
+    style MM3 fill:#51cf66,color:#fff
+    style NN3 fill:#51cf66,color:#fff
+    style OO3 fill:#51cf66,color:#fff
+    style PP3 fill:#51cf66,color:#fff
+    style QQ3 fill:#51cf66,color:#fff
+    style RR3 fill:#51cf66,color:#fff
+    style SS3 fill:#51cf66,color:#fff
+    style TT3 fill:#51cf66,color:#fff
+    style UU3 fill:#51cf66,color:#fff
+    style VV3 fill:#51cf66,color:#fff
+    style WW3 fill:#51cf66,color:#fff
+    style XX3 fill:#51cf66,color:#fff
+    style YY3 fill:#51cf66,color:#fff
+    style B3 fill:#74c0fc,color:#fff
+    style D3 fill:#74c0fc,color:#fff
+    style F3 fill:#74c0fc,color:#fff
+    style AAA3 fill:#b197fc,color:#fff
+    style BBB3 fill:#b197fc,color:#fff
+    style CCC3 fill:#b197fc,color:#fff
+            </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Mathematical Structures & Methods
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Computational Operations
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 3.</strong> Linear Algebra Matrix Operations Process. This mathematics process visualization demonstrates matrix computational operations. The flowchart shows matrix inputs, mathematical structures and methods, computational operations, intermediate calculations, and final matrix results.
+            </div>
+        </div>
+        <h2>4. Calculus Integration Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+graph TD
+    A4[Function f of x] --> B4[Function Analysis]
+    C4[Integration Limits] --> D4[Boundary Definition]
+    E4[Integration Method] --> F4[Method Selection]
+    B4 --> G4[Domain Analysis]
+    D4 --> H4[Interval Definition]
+    F4 --> I4[Algorithm Choice]
+    G4 --> J4[Continuity Check]
+    H4 --> K4[Boundary Validation]
+    I4 --> L4[Integration Strategy]
+    J4 --> M4[Singularity Detection]
+    K4 --> N4[Limit Analysis]
+    L4 --> O4[Computational Approach]
+    M4 --> P4[Function Continuous Question]
+    N4 --> Q4[Boundary Conditions]
+    O4 --> R4[Numerical vs Analytical]
+    P4 -->|Yes| S4[Proceed with Integration]
+    P4 -->|No| T4[Handle Discontinuities]
+    Q4 --> U4[Integration Setup]
+    R4 --> V4[Method Implementation]
+    S4 --> W4[Antiderivative Search]
+    T4 --> X4[Piecewise Integration]
+    U4 --> Y4[Variable Substitution]
+    V4 --> Z4[Integration Technique]
+    W4 --> AA4[Basic Integration Rules]
+    X4 --> BB4[Break into Intervals]
+    Y4 --> CC4[Substitution Method]
+    Z4 --> DD4[Integration by Parts]
+    AA4 --> EE4[Power Rule Application]
+    BB4 --> FF4[Interval Integration]
+    CC4 --> GG4[Variable Change]
+    DD4 --> HH4[Product Rule Integration]
+    EE4 --> II4[Constant Integration]
+    FF4 --> JJ4[Sum of Integrals]
+    GG4 --> KK4[New Variable Integration]
+    HH4 --> LL4[Partial Integration]
+    II4 --> MM4[Result Verification]
+    JJ4 --> NN4[Interval Results]
+    KK4 --> OO4[Back Substitution]
+    LL4 --> PP4[Recursive Integration]
+    MM4 --> QQ4[Derivative Check]
+    NN4 --> RR4[Continuity Verification]
+    OO4 --> QQ4
+    PP4 --> SS4[Simplified Integration]
+    QQ4 --> TT4[Integration Correct Question]
+    RR4 --> UU4[Boundary Evaluation]
+    SS4 --> TT4
+    TT4 -->|No| VV4[Error Correction]
+    TT4 -->|Yes| WW4[Integration Complete]
+    UU4 --> XX4[Final Result]
+    VV4 --> YY4[Method Adjustment]
+    WW4 --> ZZ4[Definite Integral Result]
+    XX4 --> ZZ4
+    YY4 --> S4
+    ZZ4 --> AAA4[Area Calculation]
+    AAA4 --> BBB4[Physical Interpretation]
+    BBB4 --> CCC4[Mathematical Validation]
+    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:#ffd43b,color:#000
+    style N4 fill:#ffd43b,color:#000
+    style O4 fill:#ffd43b,color:#000
+    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 Y4 fill:#51cf66,color:#fff
+    style Z4 fill:#51cf66,color:#fff
+    style AA4 fill:#51cf66,color:#fff
+    style BB4 fill:#51cf66,color:#fff
+    style CC4 fill:#51cf66,color:#fff
+    style DD4 fill:#51cf66,color:#fff
+    style EE4 fill:#51cf66,color:#fff
+    style FF4 fill:#51cf66,color:#fff
+    style GG4 fill:#51cf66,color:#fff
+    style HH4 fill:#51cf66,color:#fff
+    style II4 fill:#51cf66,color:#fff
+    style JJ4 fill:#51cf66,color:#fff
+    style KK4 fill:#51cf66,color:#fff
+    style LL4 fill:#51cf66,color:#fff
+    style MM4 fill:#51cf66,color:#fff
+    style NN4 fill:#51cf66,color:#fff
+    style OO4 fill:#51cf66,color:#fff
+    style PP4 fill:#51cf66,color:#fff
+    style QQ4 fill:#51cf66,color:#fff
+    style RR4 fill:#51cf66,color:#fff
+    style SS4 fill:#51cf66,color:#fff
+    style TT4 fill:#51cf66,color:#fff
+    style UU4 fill:#51cf66,color:#fff
+    style VV4 fill:#51cf66,color:#fff
+    style WW4 fill:#51cf66,color:#fff
+    style XX4 fill:#51cf66,color:#fff
+    style YY4 fill:#51cf66,color:#fff
+    style ZZ4 fill:#51cf66,color:#fff
+    style AAA4 fill:#51cf66,color:#fff
+    style BBB4 fill:#51cf66,color:#fff
+    style CCC4 fill:#51cf66,color:#fff
+    style B4 fill:#74c0fc,color:#fff
+    style D4 fill:#74c0fc,color:#fff
+    style F4 fill:#74c0fc,color:#fff
+    style TT4 fill:#b197fc,color:#fff
+    style UU4 fill:#b197fc,color:#fff
+    style VV4 fill:#b197fc,color:#fff
+            </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Mathematical Analysis & Methods
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Integration Operations
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 4.</strong> Calculus Integration Process. This mathematics process visualization demonstrates integral calculus operations. The flowchart shows function inputs, mathematical analysis and methods, integration operations, intermediate calculations, and final integral results.
+            </div>
+        </div>
+        <h2>5. Probability Theory Process</h2>
+        <div class="figure">
+            <div class="mermaid">
+graph TD
+    A5[Sample Space Omega] --> B5[Probability Space Definition]
+    C5[Event Collection] --> D5[Event Analysis]
+    E5[Probability Measure] --> F5[Measure Assignment]
+    B5 --> G5[Outcome Enumeration]
+    D5 --> H5[Event Classification]
+    F5 --> I5[Probability Distribution]
+    G5 --> J5[Elementary Events]
+    H5 --> K5[Compound Events]
+    I5 --> L5[Probability Function]
+    J5 --> M5[Sample Point Analysis]
+    K5 --> N5[Event Algebra]
+    L5 --> O5[Measure Properties]
+    M5 --> P5[Outcome Probability]
+    N5 --> Q5[Set Operations]
+    O5 --> R5[Axiom Verification]
+    P5 --> S5[Elementary Probability]
+    Q5 --> T5[Union Operations]
+    R5 --> U5[Probability Axioms]
+    S5 --> V5[Individual Outcomes]
+    T5 --> W5[Intersection Operations]
+    U5 --> X5[Measure Consistency]
+    V5 --> Y5[Outcome Counting]
+    W5 --> Z5[Complement Operations]
+    X5 --> AA5[Probability Validation]
+    Y5 --> BB5[Counting Methods]
+    Z5 --> CC5[De Morgan's Laws]
+    AA5 --> DD5[Measure Completeness]
+    BB5 --> EE5[Permutation Analysis]
+    CC5 --> FF5[Set Theory Application]
+    DD5 --> EE5
+    EE5 --> GG5[Combination Analysis]
+    FF5 --> HH5[Event Independence]
+    GG5 --> II5[Probability Calculation]
+    GG5 --> JJ5[Ordered Arrangements]
+    HH5 --> KK5[Conditional Probability]
+    II5 --> LL5[Bayes' Theorem]
+    JJ5 --> MM5[Factorial Computation]
+    KK5 --> LL5
+    LL5 --> NN5[Posterior Probability]
+    MM5 --> OO5[Arrangement Counting]
+    NN5 --> PP5[Prior Probability Update]
+    OO5 --> QQ5[Probability Assignment]
+    PP5 --> RR5[Evidence Integration]
+    QQ5 --> SS5[Final Probability]
+    RR5 --> SS5
+    SS5 --> TT5[Probability Distribution]
+    TT5 --> UU5[Statistical Analysis]
+    UU5 --> VV5[Probability Validation]
+    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:#ffd43b,color:#000
+    style N5 fill:#ffd43b,color:#000
+    style O5 fill:#ffd43b,color:#000
+    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 Y5 fill:#51cf66,color:#fff
+    style Z5 fill:#51cf66,color:#fff
+    style AA5 fill:#51cf66,color:#fff
+    style BB5 fill:#51cf66,color:#fff
+    style CC5 fill:#51cf66,color:#fff
+    style DD5 fill:#51cf66,color:#fff
+    style EE5 fill:#51cf66,color:#fff
+    style FF5 fill:#51cf66,color:#fff
+    style GG5 fill:#51cf66,color:#fff
+    style HH5 fill:#51cf66,color:#fff
+    style II5 fill:#51cf66,color:#fff
+    style JJ5 fill:#51cf66,color:#fff
+    style KK5 fill:#51cf66,color:#fff
+    style LL5 fill:#51cf66,color:#fff
+    style MM5 fill:#51cf66,color:#fff
+    style NN5 fill:#51cf66,color:#fff
+    style OO5 fill:#51cf66,color:#fff
+    style PP5 fill:#51cf66,color:#fff
+    style QQ5 fill:#51cf66,color:#fff
+    style RR5 fill:#51cf66,color:#fff
+    style SS5 fill:#51cf66,color:#fff
+    style TT5 fill:#51cf66,color:#fff
+    style UU5 fill:#51cf66,color:#fff
+    style VV5 fill:#51cf66,color:#fff
+    style B5 fill:#74c0fc,color:#fff
+    style D5 fill:#74c0fc,color:#fff
+    style F5 fill:#74c0fc,color:#fff
+    style TT5 fill:#b197fc,color:#fff
+    style UU5 fill:#b197fc,color:#fff
+    style VV5 fill:#b197fc,color:#fff
+            </div>
+            <div style="margin-top: 1rem; display: flex; flex-wrap: wrap; gap: 0.5rem; justify-content: center;">
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ff6b6b;"></span>Triggers & Inputs
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#ffd43b;"></span>Probability Structures & Methods
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#51cf66;"></span>Probability Calculations
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#74c0fc;"></span>Intermediates
+                </div>
+                <div style="display:inline-flex; align-items:center; gap:.5rem; padding:.25rem .5rem; border-radius: 999px; border: 1px solid rgba(0,0,0,.08); background:#fff;">
+                    <span style="width: 12px; height: 12px; border-radius: 2px; border:1px solid rgba(0,0,0,.15); background:#b197fc;"></span>Products
+                </div>
+            </div>
+            <div class="figure-caption">
+                <strong>Figure 5.</strong> Probability Theory Process. This mathematics process visualization demonstrates probability theory operations. The flowchart shows probability space inputs, probability structures and methods, probability calculations, intermediate computations, and final probability distributions.
+            </div>
+        </div>
         <p><strong>Generated using the Programming Framework methodology</strong></p>
         <p>This collection demonstrates the computational nature of mathematical processes and systems</p>

physics_processes.html CHANGED Viewed

@@ -88,7 +88,7 @@
 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
@@ -97,9 +97,9 @@ graph TD
     F1 --> I1[Spatial Boundary Conditions]
     %% Wave Function Evolution
-    G1 --> J1[Incident Wave Function ψ₁]
-    H1 --> K1[Barrier Region ψ₂]
-    I1 --> L1[Transmitted Wave Function ψ₃]
     %% Quantum Processing
     J1 --> M1[Wave Function Matching]
@@ -122,8 +122,8 @@ graph TD
     U1 --> X1[Measured Transmission]
     %% Decision Points
-    V1 -->|E < V₀: T = 0| Y1[Classical Forbidden]
-    W1 -->|E < V₀: T > 0| Z1[Quantum Tunneling]
     X1 --> AA1[Particle Detection Beyond Barrier]
     %% Measurement and Detection
@@ -437,27 +437,27 @@ graph TD
     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 η]
     W4 --> Z4[Energy Conservation]
     X4 --> AA4[Power Generation]
     %% Final Results

 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
     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]
     U1 --> X1[Measured Transmission]
     %% Decision Points
+    V1 --> Y1[Classical Forbidden]
+    W1 --> Z1[Quantum Tunneling]
     X1 --> AA1[Particle Detection Beyond Barrier]
     %% Measurement and Detection
     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

programming_framework_article.html CHANGED Viewed

@@ -229,9 +229,9 @@ graph TD
     J --> K[Glucose Inside Cell]
     K --> L[High Glucose Status]
     %% Regulatory Logic Gates
-    I --> M{Is Lactose Present?}
-    L --> N{Is Glucose Present?}
-    F --> O{Is Energy Low?}
     %% Repressor Logic
     M -->|No| P[Lac Repressor Active]
     M -->|Yes| Q[Lac Repressor Inactive]
@@ -248,8 +248,8 @@ graph TD
     X --> Z[CAP Binds Promoter]
     Y --> AA[No CAP Binding]
     %% Transcription Control
-    U --> BB{Operator Free?}
-    Z --> CC{CAP Bound?}
     BB -->|Yes| DD[RNA Polymerase Binding]
     BB -->|No| EE[Transcription Blocked]
     CC -->|Yes| FF[Strong Transcription]
@@ -566,7 +566,7 @@ graph TD
 graph TD
     %% Initial Conditions
     A[Particle Energy E] --> B[Energy Assessment]
-    C[Barrier Height V₀] --> D[Barrier Analysis]
     E[Barrier Width a] --> F[Geometric Constraints]
     %% Quantum State Preparation
@@ -575,9 +575,9 @@ graph TD
     F --> I[Spatial Boundary Conditions]
     %% Wave Function Evolution
-    G --> J[Incident Wave Function ψ₁]
-    H --> K[Barrier Region ψ₂]
-    I --> L[Transmitted Wave Function ψ₃]
     %% Quantum Processing
     J --> M[Wave Function Matching]
@@ -600,8 +600,8 @@ graph TD
     U --> X[Measured Transmission]
     %% Decision Points
-    V -->|E < V₀: T = 0| Y[Classical Forbidden]
-    W -->|E < V₀: T > 0| Z[Quantum Tunneling]
     X --> AA[Particle Detection Beyond Barrier]
     %% Measurement and Detection

     J --> K[Glucose Inside Cell]
     K --> L[High Glucose Status]
     %% Regulatory Logic Gates
+    I --> M[Is Lactose Present Question]
+    L --> N[Is Glucose Present Question]
+    F --> O[Is Energy Low Question]
     %% Repressor Logic
     M -->|No| P[Lac Repressor Active]
     M -->|Yes| Q[Lac Repressor Inactive]
     X --> Z[CAP Binds Promoter]
     Y --> AA[No CAP Binding]
     %% Transcription Control
+    U --> BB[Operator Free Question]
+    Z --> CC[CAP Bound Question]
     BB -->|Yes| DD[RNA Polymerase Binding]
     BB -->|No| EE[Transcription Blocked]
     CC -->|Yes| FF[Strong Transcription]
 graph TD
     %% Initial Conditions
     A[Particle Energy E] --> B[Energy Assessment]
+    C[Barrier Height V0] --> D[Barrier Analysis]
     E[Barrier Width a] --> F[Geometric Constraints]
     %% Quantum State Preparation
     F --> I[Spatial Boundary Conditions]
     %% Wave Function Evolution
+    G --> J[Incident Wave Function psi1]
+    H --> K[Barrier Region psi2]
+    I --> L[Transmitted Wave Function psi3]
     %% Quantum Processing
     J --> M[Wave Function Matching]
     U --> X[Measured Transmission]
     %% Decision Points
+    V --> Y[Classical Forbidden]
+    W --> Z[Quantum Tunneling]
     X --> AA[Particle Detection Beyond Barrier]
     %% Measurement and Detection