Research-Stack/5-Applications/scripts/couch_equation_forest_analysis.py

#!/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()