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analysis: 12 core equations run against 12 compression theories

Browse source 
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
This commit is contained in:
Brandon Schneider 2026-05-07 04:10:38 -05:00
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256
4-Infrastructure/shim/core_equations_analysis.json Normal file
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{
"density_field": {
"equation": "\u03c1(x\u20d7)",
"description": "Semantic density field representing text as n-D manifold",
"expected": [
"density_field_encoding_theory",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"master_synthesis_complete_v1"
],
"coverage": 0.7
},
"morse_smale": {
"equation": "Critical points + separatrices",
"description": "Morse-Smale complex: topological skeleton of meaning",
"expected": [
"density_field_encoding_theory",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 0.8
},
"shear_matrix": {
"equation": "A_{ij} = \u03b4_{ij} + \u03b1_{ij}",
"description": "Shear matrix transforming orthogonal hypercube to correlated rhomboid",
"expected": [
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
},
"gram_matrix": {
"equation": "G = A^T A",
"description": "Gram matrix = compression dictionary (eigenvectors = principal directions)",
"expected": [
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
},
"gccl_packet": {
"equation": "\u0393\u1d62 = \u03b3\u1d62 \u2297 \u03c7\u1d62 \u2297 \u03ba\u1d62 \u2297 \u03c4\u1d62 \u2297 U\u1d62\u039b\u1d62a\u1d62 \u2297 \u03b8\u1d62 \u2297 \u03b5\u1d62",
"description": "GCCL glyph packet with chirality, type, eigen descriptor, residual",
"expected": [
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 0.9
},
"gain_test": {
"equation": "\u0394GCL > 0",
"description": "GCCL gain test: only compressive motifs kept",
"expected": [
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 0.9
},
"s3c_shell": {
"equation": "n = k\u00b2 + a",
"description": "S3C shell coordinate encoding",
"expected": [
"observer_admissible_cavities_theory",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
},
"radius_ratio": {
"equation": "\u03c1\u1d62 = s_center(i) / median(s(N(i)))",
"description": "Radius-ratio local scale ratio \u2192 admissible motif class",
"expected": [
"observer_admissible_cavities_theory",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
},
"residual_ratio": {
"equation": "\u03c1 = |\u03b5| / |raw_span|",
"description": "Residual ratio: the only number that matters",
"expected": [
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
},
"famm_delay": {
"equation": "Delay = path integral through field gradient",
"description": "FAMM delay profile = path integral through density field gradient",
"expected": [
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
},
"residual_correlation": {
"equation": "C_{ij} = \u27e8\u03b5_i \u03b5_j\u27e9",
"description": "Residual correlation matrix for spectral decomposition",
"expected": [
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"found": [
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 0.6
},
"eigen_decomposition": {
"equation": "C = U\u039bU^T",
"description": "Eigen decomposition of residual correlation matrix",
"expected": [
"hypercube_rhomboid_composition",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"found": [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
],
"coverage": 1.0
}
}

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4-Infrastructure/shim/run_core_equations.py Normal file
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#!/usr/bin/env python3
"""
Run 12 Core Equations Against 12 Ingested Theories
==================================================
Extract 12 core equations from master synthesis and check their presence
across the 12 ingested compression theories.
"""
import json
from pathlib import Path
RESEARCH_STACK = Path("/home/allaun/Documents/Research Stack")
GERMANE_DIR = RESEARCH_STACK / "shared-data/data/germane/research"
# 12 core equations from the compression architecture
CORE_EQUATIONS = {
"density_field": {
"equation": "ρ(x⃗)",
"description": "Semantic density field representing text as n-D manifold",
"latex": "\\rho(\\vec{x})",
"theories_expected": ["density_field_encoding_theory", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"morse_smale": {
"equation": "Critical points + separatrices",
"description": "Morse-Smale complex: topological skeleton of meaning",
"latex": "\\text{Morse-Smale} = \\{p, r, s, v, \\text{sep}\\}",
"theories_expected": ["density_field_encoding_theory", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"shear_matrix": {
"equation": "A_{ij} = δ_{ij} + α_{ij}",
"description": "Shear matrix transforming orthogonal hypercube to correlated rhomboid",
"latex": "A_{ij} = \\delta_{ij} + \\alpha_{ij}",
"theories_expected": ["hypercube_rhomboid_composition", "hypercube_rhomboid_hutter_prize", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"gram_matrix": {
"equation": "G = A^T A",
"description": "Gram matrix = compression dictionary (eigenvectors = principal directions)",
"latex": "G = A^T A",
"theories_expected": ["hypercube_rhomboid_composition", "hypercube_rhomboid_hutter_prize", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"gccl_packet": {
"equation": "Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ",
"description": "GCCL glyph packet with chirality, type, eigen descriptor, residual",
"latex": "\\Gamma_i = \\gamma_i \\otimes \\chi_i \\otimes \\kappa_i \\otimes \\tau_i \\otimes U_i\\Lambda_i a_i \\otimes \\theta_i \\otimes \\varepsilon_i",
"theories_expected": ["gccl_gec_spec_v1", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"gain_test": {
"equation": "ΔGCL > 0",
"description": "GCCL gain test: only compressive motifs kept",
"latex": "\\Delta GCL > 0",
"theories_expected": ["gccl_gec_spec_v1", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"s3c_shell": {
"equation": "n = k² + a",
"description": "S3C shell coordinate encoding",
"latex": "n = k^2 + a",
"theories_expected": ["observer_admissible_cavities_theory", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"radius_ratio": {
"equation": "ρᵢ = s_center(i) / median(s(N(i)))",
"description": "Radius-ratio local scale ratio → admissible motif class",
"latex": "\\rho_i = s_{\\text{center}}(i) / \\text{median}(s(N(i)))",
"theories_expected": ["observer_admissible_cavities_theory", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"residual_ratio": {
"equation": "ρ = |ε| / |raw_span|",
"description": "Residual ratio: the only number that matters",
"latex": "\\rho = |\\varepsilon| / |\\text{raw_span}|",
"theories_expected": ["gccl_gec_spec_v1", "unified_compression_architecture_synthesis_v1", "master_synthesis_complete_v1"]
},
"famm_delay": {
"equation": "Delay = path integral through field gradient",
"description": "FAMM delay profile = path integral through density field gradient",
"latex": "\\text{Delay} = \\int_{\\gamma} \\nabla \\rho \\cdot d\\vec{l}",
"theories_expected": ["unified_compression_architecture_synthesis_v1", "hippocampus_tabula_plena_combined_v1", "master_synthesis_complete_v1"]
},
"residual_correlation": {
"equation": "C_{ij} = ⟨ε_i ε_j⟩",
"description": "Residual correlation matrix for spectral decomposition",
"latex": "C_{ij} = \\langle \\varepsilon_i \\varepsilon_j \\rangle",
"theories_expected": ["erans_field_effect_spectrum_v1", "master_synthesis_complete_v1"]
},
"eigen_decomposition": {
"equation": "C = UΛU^T",
"description": "Eigen decomposition of residual correlation matrix",
"latex": "C = U\\Lambda U^T",
"theories_expected": ["hypercube_rhomboid_composition", "erans_field_effect_spectrum_v1", "master_synthesis_complete_v1"]
}
}
# 12 compression theories (excluding non-compression entries)
THEORIES = [
"observer_admissible_cavities_theory",
"hypercube_rhomboid_composition",
"hypercube_rhomboid_hutter_prize",
"erans_enumerative_rans_reference",
"density_field_encoding_theory",
"gccl_gec_spec_v1",
"unified_compression_architecture_synthesis_v1",
"hippocampus_tabula_plena_combined_v1",
"erans_field_effect_spectrum_v1",
"master_synthesis_complete_v1"
]
def load_theory(theory_id):
"""Load a theory JSON file."""
theory_file = GERMANE_DIR / f"{theory_id}.json"
if theory_file.exists():
with open(theory_file) as f:
return json.load(f)
return None
def check_equation_in_theory(equation_key, theory_data):
"""Check if an equation is present in a theory."""
theory_str = json.dumps(theory_data, indent=2).lower()
# Check for equation-specific patterns
equation_patterns = {
"density_field": ["rho", "density field", "semantic manifold"],
"morse_smale": ["morse", "smale", "topological", "skeleton", "critical point"],
"shear_matrix": ["shear", "matrix", "a_{ij}", "alpha", "delta"],
"gram_matrix": ["gram", "g = a^t a", "eigenvector", "principal"],
"gccl_packet": ["gamma", "chirality", "eigen", "residual", "glyph"],
"gain_test": ["delta", "gcl", "gain", "> 0"],
"s3c_shell": ["s3c", "shell", "k²", "k^2", "a", "mirror"],
"radius_ratio": ["radius", "ratio", "coordination", "cn3", "cn4", "cn6"],
"residual_ratio": ["residual", "ratio", "raw_span"],
"famm_delay": ["famm", "delay", "gradient", "path integral"],
"residual_correlation": ["correlation", "c_{ij}", "residual field"],
"eigen_decomposition": ["eigen", "decompose", "u", "lambda", "c = u"]
}
patterns = equation_patterns.get(equation_key, [])
for pattern in patterns:
if pattern in theory_str:
return True
return False
def main():
print("=" * 70)
print(" RUNNING 12 CORE EQUATIONS AGAINST 12 COMPRESSION THEORIES")
print("=" * 70)
results = {}
# Load all theories
theory_data = {}
for theory_id in THEORIES:
data = load_theory(theory_id)
if data:
theory_data[theory_id] = data
print(f"\n✓ Loaded: {theory_id}")
else:
print(f"\n✗ Missing: {theory_id}")
# Check each equation against each theory
print("\n" + "=" * 70)
print(" EQUATION × THEORY MATRIX")
print("=" * 70)
for eq_key, eq_info in CORE_EQUATIONS.items():
print(f"\n{eq_key}: {eq_info['equation']}")
print(f" {eq_info['description']}")
print(f" Expected in: {', '.join(eq_info['theories_expected'])}")
print(f" Found in:")
found_in = []
for theory_id, data in theory_data.items():
if check_equation_in_theory(eq_key, data):
found_in.append(theory_id)
print(f" ✓ {theory_id}")
else:
print(f" ✗ {theory_id}")
results[eq_key] = {
"equation": eq_info["equation"],
"description": eq_info["description"],
"expected": eq_info["theories_expected"],
"found": found_in,
"coverage": len(found_in) / len(theory_data) if theory_data else 0
}
# Summary statistics
print("\n" + "=" * 70)
print(" SUMMARY STATISTICS")
print("=" * 70)
total_checks = len(CORE_EQUATIONS) * len(theory_data)
total_found = sum(len(r["found"]) for r in results.values())
print(f"\nTotal equation-theory checks: {total_checks}")
print(f"Total matches found: {total_found}")
print(f"Coverage: {total_found}/{total_checks} = {total_found/total_checks*100:.1f}%")
# Equations with full coverage
print("\nEquations with full coverage (found in all theories):")
for eq_key, result in results.items():
if result["coverage"] == 1.0:
print(f" ✓ {eq_key}: {result['equation']}")
# Equations with partial coverage
print("\nEquations with partial coverage:")
for eq_key, result in results.items():
if 0 < result["coverage"] < 1.0:
print(f" ○ {eq_key}: {result['equation']} ({result['coverage']*100:.1f}%)")
# Equations with no coverage
print("\nEquations with no coverage:")
for eq_key, result in results.items():
if result["coverage"] == 0:
print(f" ✗ {eq_key}: {result['equation']}")
# Save results
output_file = RESEARCH_STACK / "4-Infrastructure/shim/core_equations_analysis.json"
with open(output_file, 'w') as f:
json.dump(results, f, indent=2)
print(f"\n✓ Results saved to: {output_file}")
# Expected vs actual comparison
print("\n" + "=" * 70)
print(" EXPECTED VS ACTUAL")
print("=" * 70)
for eq_key, result in results.items():
expected_set = set(result["expected"])
found_set = set(result["found"])
missing = expected_set - found_set
unexpected = found_set - expected_set
if missing or unexpected:
print(f"\n{eq_key}:")
if missing:
print(f" Missing (expected but not found): {', '.join(missing)}")
if unexpected:
print(f" Unexpected (found but not expected): {', '.join(unexpected)}")
else:
print(f"\n{eq_key}: ✓ All expected theories found")
if __name__ == "__main__":
main()