#!/usr/bin/env python3 """ COUCH Equation Forest Analysis Applies the Equation Forest framework to COUCH equation. Maps COUCH to 12 foundation kernels, 5 core streets, 8 bridges, and Genome18 address space. Equation Forest: - 12 Foundation Kernels (F01-F12) - 5 Core Streets - 8 Bridge Nodes - 18-bit Genome18 ISA (262,144 states) """ import numpy as np from typing import Dict, List, Tuple, Any from dataclasses import dataclass from enum import Enum import json class FoundationKernel(Enum): """12 Foundation Kernels (Exact Solver Basis Vectors).""" F01 = "Shannon_Entropy_Calculation" F02 = "Information_Content_Measurement" F03 = "Hierarchical_Entropy_Decomposition" F04 = "Thermodynamic_Efficiency_Limit" F05 = "Computation_Energy_Bound" F06 = "Energy_Balance_Threshold" F07 = "Maxwell_Demon_Recovery" F08 = "Riemannian_Distance_Calculation" F09 = "Geodesic_Connection_Coefficients" F10 = "Single_Step_Geodesic_Integration" F11 = "Aggregate_Load_Combination" F12 = "Intrinsic_to_Total_Ratio" class CoreStreet(Enum): """5 Core Streets (Graph Collapse).""" ENTROPY_COMPRESSION = "Entropy/Compression (F01-F03)" THERMODYNAMIC = "Thermodynamic Admissibility (F04-F07)" GEOMETRIC_MOTION = "Geometric Motion (F08-F10)" COGNITIVE_ROUTING = "Cognitive/Routing Load (F11-F12)" DIAT_AVMR_S3C = "DIAT/AVMR/S3C Bridge" class BridgeNode(Enum): """8 Bridge Nodes.""" B1 = "Entropy ↔ Load" B2 = "Entropy ↔ Landauer" B3 = "Energy ↔ Routing" B4 = "Geometry ↔ Routing" B5 = "DIAT ↔ Geometry" B6 = "AVMR ↔ Entropy" B7 = "S3C ↔ Codec" B8 = "PIST ↔ Surface" @dataclass class Genome18Bin: """Genome18 3-bit bin (6 bins total = 18 bits).""" muBin: int # mutation/drift (routing load) - 3 bits rhoBin: int # verification pressure (routing efficiency) - 3 bits cBin: int # connectance (geometry/route neighborhood) - 3 bits mBin: int # compression residue (entropy) - 3 bits neBin: int # effective sample (entropy) - 3 bits sigmaBin: int # fitness proxy (entropy) - 3 bits @dataclass class KernelSignature: """Kernel signature for COUCH equation.""" f01_shannon_entropy: float f02_information_content: float f03_hierarchical_entropy: float f04_thermodynamic_efficiency: float f05_computation_energy: float f06_energy_balance: float f07_maxwell_demon: float f08_riemannian_distance: float f09_geodesic_connection: float f10_geodesic_integration: float f11_aggregate_load: float f12_intrinsic_ratio: float class COUCHForestMapper: """ Maps COUCH equation to Equation Forest. Pipeline: raw equation → F01-F12 kernel signature → street/bridge assignment → Genome18 bins → 18-bit ISA address → PIST/witness audit """ def __init__(self): self.kernels = list(FoundationKernel) self.streets = list(CoreStreet) self.bridges = list(BridgeNode) def calculate_couch_kernel_signature(self, couch_state: Dict[str, Any]) -> KernelSignature: """ Calculate F01-F12 kernel signature for COUCH equation. COUCH: ẍ_i + γẋ_i + ω_i²x_i + Σ_j κ_ij(x_i - x_j) = F(t) """ position = np.array(couch_state["position"]) velocity = np.array(couch_state["velocity"]) damping = couch_state["damping"] forcing = couch_state["forcing"] coupling = np.array(couch_state["coupling"]) # F01: Shannon Entropy Calculation # Based on oscillator state distribution state_prob = np.abs(position) / np.sum(np.abs(position)) f01 = -np.sum(state_prob * np.log2(state_prob + 1e-10)) # F02: Information Content Measurement # Based on hysteresis memory f02 = np.sum(np.abs(velocity)) * damping # F03: Hierarchical Entropy Decomposition # Based on coupling structure coupling_entropy = np.linalg.svd(coupling, compute_uv=False) f03 = np.sum(coupling_entropy) # F04: Thermodynamic Efficiency Limit # Based on energy dissipation (Carnot) f04 = damping / (damping + forcing) # F05: Computation Energy Bound # Based on kinetic energy f05 = 0.5 * np.sum(velocity**2) # F06: Energy Balance Threshold # Based on potential energy f06 = 0.5 * np.sum(position**2 * 2.0**2) # F07: Maxwell Demon Recovery # Based on coupling work f07 = np.sum(np.abs(coupling)) # F08: Riemannian Distance Calculation # Distance from equilibrium f08 = np.linalg.norm(position) # F09: Geodesic Connection Coefficients # Based on phase space curvature f09 = np.linalg.norm(np.cross(position, velocity)) # F10: Single Step Geodesic Integration # Based on state evolution f10 = np.linalg.norm(velocity) / (np.linalg.norm(position) + 1e-10) # F11: Aggregate Load Combination # Based on total system energy f11 = f05 + f06 # F12: Intrinsic to Total Ratio # Based on dimensionality f12 = len(position) / (len(position) + len(coupling.flatten())) return KernelSignature( f01_shannon_entropy=f01, f02_information_content=f02, f03_hierarchical_entropy=f03, f04_thermodynamic_efficiency=f04, f05_computation_energy=f05, f06_energy_balance=f06, f07_maxwell_demon=f07, f08_riemannian_distance=f08, f09_geodesic_connection=f09, f10_geodesic_integration=f10, f11_aggregate_load=f11, f12_intrinsic_ratio=f12 ) def assign_street(self, signature: KernelSignature) -> CoreStreet: """ Assign COUCH to a core street based on kernel signature. Analyze which kernel set dominates the signature. """ # Calculate street scores entropy_score = signature.f01_shannon_entropy + signature.f02_information_content + signature.f03_hierarchical_entropy thermodynamic_score = signature.f04_thermodynamic_efficiency + signature.f05_computation_energy + signature.f06_energy_balance + signature.f07_maxwell_demon geometric_score = signature.f08_riemannian_distance + signature.f09_geodesic_connection + signature.f10_geodesic_integration cognitive_score = signature.f11_aggregate_load + signature.f12_intrinsic_ratio scores = { CoreStreet.ENTROPY_COMPRESSION: entropy_score, CoreStreet.THERMODYNAMIC: thermodynamic_score, CoreStreet.GEOMETRIC_MOTION: geometric_score, CoreStreet.COGNITIVE_ROUTING: cognitive_score } # Assign to highest-scoring street assigned_street = max(scores, key=scores.get) return assigned_street def assign_bridges(self, signature: KernelSignature, street: CoreStreet) -> List[BridgeNode]: """ Assign COUCH to bridge nodes based on signature and street. """ bridges = [] # Bridge assignments based on signature analysis if signature.f01_shannon_entropy > 0.5: bridges.append(BridgeNode.B1) # Entropy ↔ Load if signature.f04_thermodynamic_efficiency > 0.5: bridges.append(BridgeNode.B2) # Entropy ↔ Landauer if signature.f05_computation_energy > 0.5: bridges.append(BridgeNode.B3) # Energy ↔ Routing if signature.f08_riemannian_distance > 0.5: bridges.append(BridgeNode.B4) # Geometry ↔ Routing if street == CoreStreet.GEOMETRIC_MOTION: bridges.append(BridgeNode.B5) # DIAT ↔ Geometry if signature.f01_shannon_entropy > 0.3: bridges.append(BridgeNode.B6) # AVMR ↔ Entropy if signature.f03_hierarchical_entropy > 0.3: bridges.append(BridgeNode.B7) # S3C ↔ Codec # PIST ↔ Surface (always for COUCH due to hysteresis) bridges.append(BridgeNode.B8) return bridges def calculate_genome18_bins(self, signature: KernelSignature) -> Genome18Bin: """ Calculate Genome18 bins from kernel signature. 6 bins × 3 bits = 18 bits (262,144 states) Kernel to bin mapping: - F01-F03 → mBin, neBin, sigmaBin - F04-F07 → cost/failure mask - F08-F10 → cBin - F11-F12 → muBin, rhoBin """ # Normalize signature values to 0-7 range (3 bits) def to_3bit(value: float) -> int: return int(np.clip(value * 7 / 10, 0, 7)) # F01-F03 → mBin, neBin, sigmaBin (entropy bins) mBin = to_3bit(signature.f01_shannon_entropy) neBin = to_3bit(signature.f02_information_content) sigmaBin = to_3bit(signature.f03_hierarchical_entropy) # F04-F07 → cost/failure mask (not directly mapped, use thermodynamic average) thermodynamic_avg = (signature.f04_thermodynamic_efficiency + signature.f05_computation_energy + signature.f06_energy_balance + signature.f07_maxwell_demon) / 4 # F08-F10 → cBin (geometry bin) cBin = to_3bit(signature.f08_riemannian_distance + signature.f09_geodesic_connection + signature.f10_geodesic_integration) # F11-F12 → muBin, rhoBin (cognitive/routing bins) muBin = to_3bit(signature.f11_aggregate_load) rhoBin = to_3bit(signature.f12_intrinsic_ratio) return Genome18Bin( muBin=muBin, rhoBin=rhoBin, cBin=cBin, mBin=mBin, neBin=neBin, sigmaBin=sigmaBin ) def calculate_genome18_address(self, bins: Genome18Bin) -> int: """ Calculate 18-bit ISA address from Genome18 bins. Address calculation: addr = muBin * 32768 + rhoBin * 4096 + cBin * 512 + mBin * 64 + neBin * 8 + sigmaBin """ addr = (bins.muBin * 32768 + bins.rhoBin * 4096 + bins.cBin * 512 + bins.mBin * 64 + bins.neBin * 8 + bins.sigmaBin) return addr def calculate_pist_witness_surface(self, signature: KernelSignature) -> Dict[str, Any]: """ Calculate PIST witness surface for COUCH equation. PIST witness surface = topological constraint enforcement """ # PIST shell coordinates k = int(signature.f08_riemannian_distance * 10) t = int(signature.f10_geodesic_integration * 10) h = signature.f02_information_content # hysteresis # FAMM frustration a = float(k % 3) b = float((k + 1) - (k % 3)) c = float(k) mass = a * b * c if (a * b * c) > 0 else 1.0 stress = np.array([ [signature.f08_riemannian_distance, signature.f10_geodesic_integration, signature.f09_geodesic_connection], [signature.f10_geodesic_integration, signature.f08_riemannian_distance, signature.f09_geodesic_connection], [signature.f09_geodesic_connection, signature.f08_riemannian_distance, signature.f10_geodesic_integration] ]) phi = np.trace(stress) / mass return { "shell_coordinates": {"k": k, "t": t, "h": h}, "famm_frustration": phi, "is_admissible": phi <= 1.0, "mass": mass } def analyze_forest_position(self, address: int) -> Dict[str, Any]: """ Analyze COUCH position in the 262,144-state Genome18 space. """ total_states = 262144 position_pct = address / total_states # Calculate which "region" of the forest if position_pct < 0.25: region = "Entropy-Dominant Region" elif position_pct < 0.5: region = "Thermodynamic-Dominant Region" elif position_pct < 0.75: region = "Geometric-Dominant Region" else: region = "Cognitive-Dominant Region" return { "address": address, "total_states": total_states, "position_percent": position_pct, "region": region, "binary_representation": format(address, '018b') } def main(): """Run COUCH Equation Forest analysis.""" print("=" * 70) print("COUCH EQUATION FOREST ANALYSIS") print("=" * 70) print("\n[*] Applying Equation Forest framework to COUCH equation") print("[*] 12 Foundation Kernels → 5 Core Streets → 8 Bridges → Genome18") # Initialize mapper mapper = COUCHForestMapper() # Define COUCH state couch_state = { "position": [0.24835708, -0.06913215, 0.32384427], "velocity": [0.45690896, -0.07024601, -0.07024109], "damping": 0.5, "forcing": 1.0, "coupling": [ [0.1, 0.05, 0.02], [0.05, 0.1, 0.05], [0.02, 0.05, 0.1] ] } # Calculate kernel signature print(f"\n[*] Calculating F01-F12 kernel signature...") signature = mapper.calculate_couch_kernel_signature(couch_state) print(f"\n[*] Kernel Signature:") print(f" F01 (Shannon Entropy): {signature.f01_shannon_entropy:.4f}") print(f" F02 (Information Content): {signature.f02_information_content:.4f}") print(f" F03 (Hierarchical Entropy): {signature.f03_hierarchical_entropy:.4f}") print(f" F04 (Thermodynamic Efficiency): {signature.f04_thermodynamic_efficiency:.4f}") print(f" F05 (Computation Energy): {signature.f05_computation_energy:.4f}") print(f" F06 (Energy Balance): {signature.f06_energy_balance:.4f}") print(f" F07 (Maxwell Demon): {signature.f07_maxwell_demon:.4f}") print(f" F08 (Riemannian Distance): {signature.f08_riemannian_distance:.4f}") print(f" F09 (Geodesic Connection): {signature.f09_geodesic_connection:.4f}") print(f" F10 (Geodesic Integration): {signature.f10_geodesic_integration:.4f}") print(f" F11 (Aggregate Load): {signature.f11_aggregate_load:.4f}") print(f" F12 (Intrinsic Ratio): {signature.f12_intrinsic_ratio:.4f}") # Assign street print(f"\n[*] Assigning to core street...") street = mapper.assign_street(signature) print(f" Assigned street: {street.value}") # Assign bridges print(f"\n[*] Assigning bridge nodes...") bridges = mapper.assign_bridges(signature, street) print(f" Assigned bridges: {[b.value for b in bridges]}") # Calculate Genome18 bins print(f"\n[*] Calculating Genome18 bins...") bins = mapper.calculate_genome18_bins(signature) print(f" muBin (mutation/drift): {bins.muBin} (routing load)") print(f" rhoBin (verification pressure): {bins.rhoBin} (routing efficiency)") print(f" cBin (connectance): {bins.cBin} (geometry/route neighborhood)") print(f" mBin (compression residue): {bins.mBin} (entropy)") print(f" neBin (effective sample): {bins.neBin} (entropy)") print(f" sigmaBin (fitness proxy): {bins.sigmaBin} (entropy)") # Calculate Genome18 address print(f"\n[*] Calculating 18-bit ISA address...") address = mapper.calculate_genome18_address(bins) print(f" Genome18 address: {address} / 262,144") print(f" Binary: {format(address, '018b')}") # Analyze forest position print(f"\n[*] Analyzing forest position...") position = mapper.analyze_forest_position(address) print(f" Position: {position['position_percent']:.2%}") print(f" Region: {position['region']}") # Calculate PIST witness surface print(f"\n[*] Calculating PIST witness surface...") pist_surface = mapper.calculate_pist_witness_surface(signature) print(f" Shell coordinates: {pist_surface['shell_coordinates']}") print(f" FAMM frustration (Φ): {pist_surface['famm_frustration']:.4f}") print(f" Is admissible: {pist_surface['is_admissible']}") # Save results (convert numpy types to native Python) def convert_to_native(obj): """Convert numpy types to native Python types for JSON serialization.""" if isinstance(obj, np.ndarray): return obj.tolist() elif isinstance(obj, np.integer): return int(obj) elif isinstance(obj, np.floating): return float(obj) elif isinstance(obj, np.bool_): return bool(obj) elif isinstance(obj, dict): return {k: convert_to_native(v) for k, v in obj.items()} elif isinstance(obj, list): return [convert_to_native(item) for item in obj] else: return obj results = { "couch_state": couch_state, "kernel_signature": { "f01": signature.f01_shannon_entropy, "f02": signature.f02_information_content, "f03": signature.f03_hierarchical_entropy, "f04": signature.f04_thermodynamic_efficiency, "f05": signature.f05_computation_energy, "f06": signature.f06_energy_balance, "f07": signature.f07_maxwell_demon, "f08": signature.f08_riemannian_distance, "f09": signature.f09_geodesic_connection, "f10": signature.f10_geodesic_integration, "f11": signature.f11_aggregate_load, "f12": signature.f12_intrinsic_ratio }, "street_assignment": street.value, "bridge_assignments": [b.value for b in bridges], "genome18_bins": { "muBin": bins.muBin, "rhoBin": bins.rhoBin, "cBin": bins.cBin, "mBin": bins.mBin, "neBin": bins.neBin, "sigmaBin": bins.sigmaBin }, "genome18_address": address, "forest_position": position, "pist_witness_surface": convert_to_native(pist_surface) } output_path = "/home/allaun/Documents/Research Stack/data/couch_equation_forest_analysis.json" with open(output_path, 'w') as f: json.dump(results, f, indent=2) print(f"\n[*] Results saved to: {output_path}") print("\n" + "=" * 70) print("✅ COUCH EQUATION FOREST ANALYSIS COMPLETE") print("=" * 70) if __name__ == "__main__": main()