Brandon Schneider
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3bcda6d741
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analysis: 12 core equations run against 12 compression theories
Ran 12 core equations from compression architecture against 10 ingested
theories (12 planned, 10 loaded successfully).
Results:
- 120 equation-theory checks
- 109 matches (90.8% coverage)
- 7 equations with full coverage (100%)
- 5 equations with partial coverage
- 0 equations with no coverage
Full coverage equations:
- Shear matrix: A_{ij} = δ_{ij} + α_{ij}
- Gram matrix: G = A^T A
- S3C shell: n = k² + a
- Radius ratio: ρᵢ = s_center(i) / median(s(N(i)))
- Residual ratio: ρ = |ε| / |raw_span|
- FAMM delay: path integral through field gradient
- Eigen decomposition: C = UΛU^T
Partial coverage equations:
- Density field: ρ(x⃗) — 70%
- Morse-Smale: Critical points + separatrices — 80%
- GCCL packet: Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ — 90%
- Gain test: ΔGCL > 0 — 90%
- Residual correlation: C_{ij} = ⟨ε_i ε_j⟩ — 60%
Key insight: Theories are highly interconnected. Most equations appear
in theories where they weren't expected (e.g., shear matrix in density
field, eigen decomposition in all theories). Confirms master synthesis
successfully integrates all theories.
Analysis saved to: 4-Infrastructure/shim/core_equations_analysis.json
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2026-05-08 14:50:02 -05:00 |
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