Here’s the complete **Math domain edge relationship graph** in Mermaid JS format, showing all 22 intra-domain and cross-domain connections for mathematical entities: ```mermaid graph TD %% === INTRA-MATH CONNECTIONS (9 edges) === Math-π-01["Math-π-01: Pi (π)"] -->|"Fundamental<br>constant"| Math-π-02["Math-π-02: Fourier Series"] Math-π-01 -->|"Geometric<br>basis"| Math-π-03["Math-π-03: Modular Arithmetic"] Math-π-02 -->|"Special case"| Math-π-04["Math-π-04: Repeating Decimals"] Math-α-05["Math-α-05: Limit Transitions"] -->|"Generalizes"| Math-ε-06["Math-ε-06: Bifurcation Theory"] Math-ε-06 -->|"Quantifies"| Math-ε-07["Math-ε-07: Phase Space Transitions"] Math-ε-07 -->|"Topological<br>extension"| Math-ε-08["Math-ε-08: Topological Changes"] Math-ε-08 -->|"Critical case"| Math-ε-09["Math-ε-09: Critical Points"] Math-π-03 -->|"Discrete<br>version"| Math-α-05 Math-π-04 -->|"Periodic<br>behavior"| Math-ε-06 %% === MATH → PHYSICS (7 edges) === Math-π-01 -->|"Circle<br>geometry"| Phys-π-02["Phys-π-02: Planetary Orbits"] Math-π-02 -->|"Wave<br>decomposition"| Phys-π-03["Phys-π-03: Wave Cycles"] Math-α-05 -->|"Continuum<br>limit"| Phys-α-05["Phys-α-05: Reynolds Number"] Math-ε-06 -->|"Chaos<br>modeling"| Phys-ε-10["Phys-ε-10: Turbulence Onset"] Math-ε-07 -->|"Phase space<br>mapping"| Phys-ε-08["Phys-ε-08: Superconductivity"] Math-ε-09 -->|"Criticality<br>analysis"| Phys-α-07["Phys-α-07: Phase Transitions"] Math-π-03 -->|"Modular<br>symmetry"| Phys-π-04["Phys-π-04: Quantum Spin"] %% === MATH → OTHER DOMAINS (6 edges) === Math-π-01 -->|"Cyclic<br>patterns"| Bio-π-03["Bio-π-03: Predator-Prey"] Math-ε-06 -->|"Threshold<br>models"| Soc-α-05["Soc-α-05: Tipping Points"] Math-π-02 -->|"Harmonic<br>analysis"| Art-π-02["Art-π-02: Musical Refrains"] Math-α-05 -->|"Boundary<br>conditions"| Esot-α-05["Esot-α-05: Numerology (α=1)"] Math-π-04 -->|"Recurrence<br>patterns"| Soc-π-03["Soc-π-03: Election Cycles"] Math-ε-08 -->|"Structural<br>changes"| Art-ε-06["Art-ε-06: Avant-Garde"] %% === STYLING === classDef math fill:#f9f,stroke:#333; classDef physics fill:#bbf,stroke:#333; classDef other fill:#ccc,stroke-dasharray: 3 3; class Math-π-01,Math-π-02,Math-π-03,Math-π-04,Math-α-05,Math-ε-06,Math-ε-07,Math-ε-08,Math-ε-09 math; class Phys-π-02,Phys-π-03,Phys-α-05,Phys-ε-10,Phys-ε-08,Phys-α-07,Phys-π-04 physics; class Bio-π-03,Soc-α-05,Art-π-02,Esot-α-05,Soc-π-03,Art-ε-06 other; linkStyle 0,1,2,3,4,5,6,7,8 stroke:#f66,stroke-width:2px; %% Intra-math linkStyle 9,10,11,12,13,14,15 stroke:#66f,stroke-width:2px; %% Math→Physics linkStyle 16,17,18,19,20,21 stroke:#999,stroke-width:1.5px; %% Cross-domain ``` # Key Features 1. **Complete Math-Centric Edges**: All 22 connections where mathematical entities are sources. 2. **Domain Coloring**: - **Pink**: Math nodes - **Blue**: Physics nodes - **Gray**: Other domains (dashed border) 3. **Edge Types**: - **Red**: Intra-math relationships - **Blue**: Math→Physics connections - **Gray**: Math→Other domain links 4. **Semantic Labels**: Each arrow describes the nature of the relationship (e.g., “Wave decomposition”). # Notable Connections - **Core Math**: Pi (π) → Fourier → Modular Arithmetic forms the foundational triad. - **Physics Bridge**: Critical point theory → Phase transitions is the highest-confidence cross-link (Confidence=5). - **Esoteric Link**: Limit transitions → Numerology is the lowest-confidence edge (Confidence=1). For the complementary physics-centric or biology-centric subgraphs, let me know!