mirror of
https://github.com/allaunthefox/Research-Stack.git
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84b3c4ce7e
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
256 lines
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8.6 KiB
JSON
256 lines
No EOL
8.6 KiB
JSON
{
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"density_field": {
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"equation": "\u03c1(x\u20d7)",
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"description": "Semantic density field representing text as n-D manifold",
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"expected": [
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"density_field_encoding_theory",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 0.7
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},
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"morse_smale": {
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"equation": "Critical points + separatrices",
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"description": "Morse-Smale complex: topological skeleton of meaning",
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"expected": [
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"density_field_encoding_theory",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 0.8
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},
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"shear_matrix": {
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"equation": "A_{ij} = \u03b4_{ij} + \u03b1_{ij}",
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"description": "Shear matrix transforming orthogonal hypercube to correlated rhomboid",
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"expected": [
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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},
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"gram_matrix": {
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"equation": "G = A^T A",
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"description": "Gram matrix = compression dictionary (eigenvectors = principal directions)",
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"expected": [
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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},
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"gccl_packet": {
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"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",
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"description": "GCCL glyph packet with chirality, type, eigen descriptor, residual",
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"expected": [
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 0.9
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},
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"gain_test": {
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"equation": "\u0394GCL > 0",
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"description": "GCCL gain test: only compressive motifs kept",
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"expected": [
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 0.9
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},
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"s3c_shell": {
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"equation": "n = k\u00b2 + a",
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"description": "S3C shell coordinate encoding",
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"expected": [
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"observer_admissible_cavities_theory",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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},
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"radius_ratio": {
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"equation": "\u03c1\u1d62 = s_center(i) / median(s(N(i)))",
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"description": "Radius-ratio local scale ratio \u2192 admissible motif class",
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"expected": [
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"observer_admissible_cavities_theory",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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},
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"residual_ratio": {
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"equation": "\u03c1 = |\u03b5| / |raw_span|",
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"description": "Residual ratio: the only number that matters",
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"expected": [
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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},
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"famm_delay": {
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"equation": "Delay = path integral through field gradient",
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"description": "FAMM delay profile = path integral through density field gradient",
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"expected": [
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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},
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"residual_correlation": {
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"equation": "C_{ij} = \u27e8\u03b5_i \u03b5_j\u27e9",
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"description": "Residual correlation matrix for spectral decomposition",
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"expected": [
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 0.6
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},
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"eigen_decomposition": {
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"equation": "C = U\u039bU^T",
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"description": "Eigen decomposition of residual correlation matrix",
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"expected": [
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"hypercube_rhomboid_composition",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"found": [
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"observer_admissible_cavities_theory",
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"hypercube_rhomboid_composition",
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"hypercube_rhomboid_hutter_prize",
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"erans_enumerative_rans_reference",
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"density_field_encoding_theory",
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"gccl_gec_spec_v1",
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"unified_compression_architecture_synthesis_v1",
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"hippocampus_tabula_plena_combined_v1",
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"erans_field_effect_spectrum_v1",
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"master_synthesis_complete_v1"
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],
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"coverage": 1.0
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}
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} |