diff --git a/4-Infrastructure/shim/core_equations_analysis.json b/4-Infrastructure/shim/core_equations_analysis.json
new file mode 100644
index 00000000..29b79b5c
--- /dev/null
+++ b/4-Infrastructure/shim/core_equations_analysis.json
@@ -0,0 +1,256 @@
+{
+  "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
+  }
+}
\ No newline at end of file
diff --git a/4-Infrastructure/shim/run_core_equations.py b/4-Infrastructure/shim/run_core_equations.py
new file mode 100644
index 00000000..13a0e4a4
--- /dev/null
+++ b/4-Infrastructure/shim/run_core_equations.py
@@ -0,0 +1,241 @@
+#!/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()