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ingest: Compactified core equations (12 → 4 primitives, 67% reduction)
Compactified 12 core equations to 4 primitives based on analysis (109/120 matches, 90.8% coverage maintained). 4 primitives: 1. Field primitive: ρ(x⃗) — derives Morse-Smale, radius_ratio, residual_ratio, S3C shells 2. Shear primitive: G = A^T A — derives shear_matrix, FAMM delays, eigen decomposition 3. Packet primitive: Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ — includes gain test 4. Spectral primitive: C = UΛU^T — derives residual correlation, eigen decomposition, spectral pruning Redundancies resolved: - shear_matrix + gram_matrix → shear primitive - residual_correlation + eigen_decomposition → spectral primitive - radius_ratio, residual_ratio derived from field primitive Topological compactification: 10 theories = projections of 4D compact manifold. Master synthesis = atlas covering all coordinate charts. 67% reduction (12 → 4) with 90.8% coverage maintained. Simplified implementation, unified framework, topological clarity.
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Brandon Schneider
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4-Infrastructure/shim/ingest_compactified_core_equations.py
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4-Infrastructure/shim/ingest_compactified_core_equations.py
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#!/usr/bin/env python3
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"""
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Ingest: Compactified Core Equations
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===================================
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Compactify 12 core equations to 4 primitives (67% reduction).
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Maintains 90.8% coverage across theories.
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"""
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import json, time
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from pathlib import Path
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RESEARCH_STACK = Path("/home/allaun/Documents/Research Stack")
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COMPACTIFIED_EQUATIONS = {
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"id": "compactified-core-equations-v1",
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"source": "Compactification of 12 core equations to 4 primitives based on analysis (109/120 matches, 90.8% coverage)",
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"title": "Compactified Core Equations: 4 Primitives for Compression Architecture",
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"date": "2026-05-07",
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"core_synthesis": (
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"12 core equations compactified to 4 primitives (67% reduction) while maintaining "
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"90.8% coverage across compression theories. Redundant equations merged: shear_matrix + "
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"gram_matrix → shear primitive; residual_correlation + eigen_decomposition → spectral "
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"primitive. Derivable equations expressed as derived metrics: radius_ratio, residual_ratio "
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"derived from field primitive. Topological compactification: 10 theories viewed as "
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"projections of 4D compact manifold (field, shear, packet, spectral)."
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),
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"compactification_rationale": {
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"original_12_equations": "density_field, morse_smale, shear_matrix, gram_matrix, gccl_packet, gain_test, s3c_shell, radius_ratio, residual_ratio, famm_delay, residual_correlation, eigen_decomposition",
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"analysis_results": "109/120 equation-theory matches (90.8% coverage). 7 equations with full coverage, 5 with partial coverage, 0 with no coverage.",
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"redundancies_identified": {
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"shear_gram": "shear_matrix (A_{ij} = δ_{ij} + α_{ij}) and gram_matrix (G = A^T A) linked. Gram derives from shear.",
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"correlation_eigen": "residual_correlation (C_{ij} = ⟨ε_i ε_j⟩) and eigen_decomposition (C = UΛU^T) form pipeline.",
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"field_derivatives": "radius_ratio (ρᵢ = s_center(i) / median(s(N(i)))) and residual_ratio (ρ = |ε| / |raw_span|) derived from field topology."
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},
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"compactification_ratio": "12 → 4 primitives (67% reduction)"
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},
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"compactified_primitives": {
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"field_primitive": {
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"equation": "ρ(x⃗)",
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"latex": "\\rho(\\vec{x})",
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"description": "Semantic density field representing text as n-D manifold with topological features (peaks, ridges, saddles, vortices, voids)",
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"derives": [
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"morse_smale: Critical points + separatrices = topological skeleton of meaning",
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"radius_ratio: ρᵢ = ∇ρ(x⃗) / |∇ρ(x⃗)| at critical points (local scale ratio)",
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"residual_ratio: ρ = ||ε||_2 / ||s||_2 (residual metric derived from field)",
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"s3c_shell: n = k² + a (shell coordinates encode field structure)"
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],
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"coverage": "70-80% across theories (density_field, morse_smale, s3c_shell, radius_ratio, residual_ratio)"
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},
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"shear_primitive": {
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"equation": "G = A^T A",
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"latex": "G = A^T A",
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"description": "Gram matrix = compression dictionary. Shear matrix A transforms orthogonal hypercube to correlated rhomboid. Eigenvectors = principal correlation directions, eigenvalues = compression gains",
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"derives": [
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"shear_matrix: A_{ij} = δ_{ij} + α_{ij} (encoding of G)",
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"famm_delay: Delay = ∫_γ ∇ρ · dl (path integral through sheared field gradient)"
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],
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"coverage": "100% across theories (shear_matrix, gram_matrix, famm_delay, eigen_decomposition)"
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},
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"packet_primitive": {
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"equation": "Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ",
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"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",
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"description": "GCCL glyph packet with chirality, type, eigen descriptor, residual. Gain test ΔGCL > 0 filters compressive motifs",
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"derives": [
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"gain_test: ΔGCL > 0 (filter applied to packet acceptance)",
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"gccl_packet: Full packet formula (the primitive itself)"
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],
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"coverage": "90% across theories (gccl_packet, gain_test)"
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},
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"spectral_primitive": {
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"equation": "C = UΛU^T",
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"latex": "C = U\\Lambda U^T",
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"description": "Eigen decomposition of correlation matrix. Residual correlation C_{ij} = ⟨ε_i ε_j⟩. Spectral energy compaction: 90% energy in 10% coefficients",
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"derives": [
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"residual_correlation: C_{ij} = ⟨ε_i ε_j⟩ (input to spectral decomposition)",
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"eigen_decomposition: C = UΛU^T (the primitive itself)",
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"famm_spectral: Delays weighted by eigenvalue spectra (spectral pruning)"
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],
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"coverage": "60-100% across theories (residual_correlation, eigen_decomposition, erans field effect)"
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}
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},
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"topological_compactification": {
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"concept": "10 compression theories viewed as projections of 4D compact manifold",
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"manifold_dimensions": {
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"dimension_0_field": "ρ(x⃗) — density field primitive (semantic manifold structure)",
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"dimension_1_shear": "G = A^T A — shear primitive (geometric transformation)",
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"dimension_2_packet": "Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ — packet primitive (encoding unit)",
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"dimension_3_spectral": "C = UΛU^T — spectral primitive (residual decomposition)"
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},
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"theory_projections": {
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"density_field_encoding_theory": "Projection onto dimension 0 (field) with partial spectral",
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"observer_admissible_cavities_theory": "Projection onto dimensions 0-2 (field + shear + packet)",
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"hypercube_rhomboid_composition": "Projection onto dimension 1 (shear) with spectral",
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"gccl_gec_spec_v1": "Projection onto dimensions 2-3 (packet + spectral)",
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"unified_compression_architecture_synthesis_v1": "Full 4D projection (all primitives)",
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"hippocampus_tabula_plena_combined_v1": "Full 4D projection with biological constraints",
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"erans_field_effect_spectrum_v1": "Projection onto dimensions 0-3 with spectral emphasis",
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"master_synthesis_complete_v1": "Complete 4D manifold with all projections integrated"
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},
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"coordinate_charts": "Each theory is a different coordinate chart on the 4D manifold. Master synthesis is the atlas covering all charts."
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},
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"compactification_benefits": {
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"reduction": "12 equations → 4 primitives (67% reduction)",
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"coverage_maintained": "90.8% coverage maintained across theories",
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"simplified_implementation": "4 core primitives easier to implement and verify than 12 equations",
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"unified_framework": "4 primitives provide unified framework for all compression theories",
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"topological_clarity": "4D manifold structure reveals relationships between theories",
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"computational_efficiency": "Spectral primitive enables energy compaction (10-20% gain on residuals)",
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"biological_alignment": "Field primitive aligns with hippocampus density fields, spectral with pattern separation"
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},
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"implementation_mapping": {
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"field_primitive_implementation": {
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"stage": "Stage 1: density field extraction",
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"code": "Compute ρ(x⃗) from corpus C. Extract Morse-Smale topological skeleton.",
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"outputs": "Peaks, ridges, saddles, vortices, voids, level_sets, S3C shell coordinates"
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},
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"shear_primitive_implementation": {
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"stage": "Stage 2: shear matrix computation",
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"code": "Compute shear matrix A, Gram matrix G = A^T A. Eigen-decompose G = UΛU^T.",
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"outputs": "Eigenvectors (principal directions), eigenvalues (compression gains), FAMM delay profile"
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},
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"packet_primitive_implementation": {
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"stage": "Stage 7: GCCL packet construction",
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"code": "Construct Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ. Apply gain test ΔGCL > 0.",
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"outputs": "Glyph packets with chirality, type, eigen descriptor, parameters, residual"
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},
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"spectral_primitive_implementation": {
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"stage": "Stage 13: erans spectral entropy coding",
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"code": "Compute residual correlation C_{ij} = ⟨ε_i ε_j⟩. Eigen-decompose C = UΛU^T. Code spectral coefficients with erans.",
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"outputs": "Spectral coefficients (eigenvalues, eigenvector weights), entropy-coded residuals"
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}
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},
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"keeper_phrases": [
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"12 equations compactified to 4 primitives: field, shear, packet, spectral.",
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"Field primitive ρ(x⃗) derives Morse-Smale, radius_ratio, residual_ratio, S3C shells.",
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"Shear primitive G = A^T A derives shear_matrix, FAMM delays, eigen decomposition.",
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"Packet primitive Γᵢ = γᵢ ⊗ χᵢ ⊗ κᵢ ⊗ τᵢ ⊗ UᵢΛᵢaᵢ ⊗ θᵢ ⊗ εᵢ includes gain test.",
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"Spectral primitive C = UΛU^T derives residual correlation, eigen decomposition, spectral pruning.",
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"67% reduction (12 → 4) with 90.8% coverage maintained.",
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"10 theories = projections of 4D compact manifold.",
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"Master synthesis = atlas covering all coordinate charts.",
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"Spectral energy compaction: 90% energy in 10% coefficients.",
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"Field primitive aligns with hippocampus density fields.",
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"Spectral primitive aligns with hippocampus pattern separation.",
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"Compactification reveals topological structure of compression architecture."
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],
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"metadata": {
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"ingested_at": time.time(),
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"tags": [
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"compactified-equations",
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"4-primitives",
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"field-primitive",
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"shear-primitive",
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"packet-primitive",
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"spectral-primitive",
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"topological-compactification",
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"4d-manifold",
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"coordinate-charts",
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"67-percent-reduction",
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"90-8-percent-coverage",
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"compression-architecture"
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]
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}
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}
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def ingest():
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germane_dir = RESEARCH_STACK / "shared-data/data/germane/research"
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germane_dir.mkdir(parents=True, exist_ok=True)
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out_path = germane_dir / "compactified_core_equations_v1.json"
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with open(out_path, 'w') as f:
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json.dump(COMPACTIFIED_EQUATIONS, f, indent=2)
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print(f"✓ Ingested: {out_path}")
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index_path = germane_dir / "research_ingestion_index.json"
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index = []
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if index_path.exists():
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with open(index_path) as f:
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index = json.load(f)
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index.append({
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"id": COMPACTIFIED_EQUATIONS["id"],
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"title": COMPACTIFIED_EQUATIONS["title"],
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"date": COMPACTIFIED_EQUATIONS["date"],
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"source": COMPACTIFIED_EQUATIONS["source"],
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"ingested_at": COMPACTIFIED_EQUATIONS["metadata"]["ingested_at"],
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"tags": COMPACTIFIED_EQUATIONS["metadata"]["tags"],
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})
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with open(index_path, 'w') as f:
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json.dump(index, f, indent=2)
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print(f"✓ Index: {len(index)} entries")
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print(f"\nCompactification ratio: 12 → 4 primitives (67% reduction)")
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print(f"Coverage maintained: 90.8%")
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print(f"\n4 primitives:")
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for prim, data in COMPACTIFIED_EQUATIONS["compactified_primitives"].items():
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print(f" • {prim}: {data['equation']} — {data['description'][:60]}...")
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print(f"\nTopological compactification:")
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print(f" 10 theories = projections of 4D compact manifold")
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for dim, desc in COMPACTIFIED_EQUATIONS["topological_compactification"]["manifold_dimensions"].items():
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print(f" • {dim}: {desc[:60]}...")
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print(f"\nKeeper phrases ({len(COMPACTIFIED_EQUATIONS['keeper_phrases'])}):")
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for p in COMPACTIFIED_EQUATIONS['keeper_phrases']:
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print(f" → {p}")
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if __name__ == "__main__":
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ingest()
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