#!/usr/bin/env python3 """ COUCH Equation N-Space Map Analysis Applies every Research Stack mathematical framework to COUCH equation as an n-space map with "=" at the center. COUCH: ẍ_i + γẋ_i + ω_i²x_i + Σ_j κ_ij(x_i - x_j) = F(t) Treat "=" as central attractor in n-dimensional space. """ import numpy as np from typing import Dict, List, Tuple, Any from dataclasses import dataclass from enum import Enum import json import hashlib class NSpaceFramework(Enum): """Mathematical frameworks from Research Stack.""" PIST = "PIST (Perfectly Imperfect Square Theory)" FAMM = "FAMM (Fractal Adaptive Manifold Mapping)" QUATERNION = "Quaternion Counter-Rotation" MENGER = "Menger Sponge Fractal" ENE = "ENE Triangle Manifold" MERKLE = "Merkle Jack Tree" MANIFOLD = "Manifold Compression" TRIUMVIRATE = "Triumvirate Clock" SVQF = "SVQF Sparse Voxel" CALABI_YAU = "Calabi-Yau Compactification" RICCI_FLOW = "Ricci Flow Adaptation" BRAID = "Braid Group Theory" @dataclass class COUCHState: """COUCH oscillator state in n-space.""" position: np.ndarray # x_i velocity: np.ndarray # ẋ_i acceleration: np.ndarray # ẍ_i coupling: np.ndarray # κ_ij damping: float # γ frequency: np.ndarray # ω_i forcing: float # F(t) hysteresis: float # H = ∮ F(t) · dx @dataclass class NSpaceCoordinate: """N-space coordinate with framework-specific mapping.""" framework: NSpaceFramework coordinates: np.ndarray distance_from_center: float is_admissible: bool class COUCHNSpaceMap: """ COUCH equation as n-space map with "=" at center. Central attractor: "=" (equilibrium point where ẋ_i = 0, ẍ_i = 0) """ def __init__(self, n_oscillators: int = 3, n_dimensions: int = 10): self.n_oscillators = n_oscillators self.n_dimensions = n_dimensions self.center = np.zeros(n_dimensions) # "=" as central attractor self.frameworks = list(NSpaceFramework) self.framework_mappings: Dict[NSpaceFramework, List[NSpaceCoordinate]] = {} def initialize_couch_state(self) -> COUCHState: """Initialize COUCH oscillator system.""" np.random.seed(42) position = np.random.randn(self.n_oscillators) * 0.5 velocity = np.random.randn(self.n_oscillators) * 0.3 acceleration = np.zeros(self.n_oscillators) # Coupling matrix (symmetric) coupling = np.random.randn(self.n_oscillators, self.n_oscillators) * 0.1 coupling = (coupling + coupling.T) / 2 damping = 0.5 frequency = np.ones(self.n_oscillators) * 2.0 forcing = 1.0 hysteresis = 0.0 return COUCHState( position=position, velocity=velocity, acceleration=acceleration, coupling=coupling, damping=damping, frequency=frequency, forcing=forcing, hysteresis=hysteresis ) def apply_pist_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply PIST (Perfectly Imperfect Square Theory) mapping. Shell coordinates: (k, t, H) where H = hysteresis FAMM frustration: Φ = trace(stress_tensor) / mass """ coordinates = [] for i in range(self.n_oscillators): # Shell index based on position magnitude k = int(np.abs(state.position[i]) * 10) # Time step (iteration) t = i # Hysteresis as third coordinate h = state.hysteresis # Mass (vertex product) a = float(k % 3) b = float((k + 1) - (k % 3)) c = float(k) mass = a * b * c if mass == 0: mass = 1.0 # Stress tensor (simplified) stress = np.array([ [state.position[i], state.velocity[i], state.acceleration[i]], [state.velocity[i], state.position[i], state.acceleration[i]], [state.acceleration[i], state.position[i], state.velocity[i]] ]) # FAMM frustration phi = np.trace(stress) / mass # Map to n-space coord = np.zeros(self.n_dimensions) coord[0] = k coord[1] = t coord[2] = h coord[3] = phi coord[4:7] = [a, b, c] distance = np.linalg.norm(coord - self.center) is_admissible = phi <= 1.0 coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.PIST, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_menger_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply Menger Sponge fractal mapping. Hausdorff dimension: d_H = log(20)/log(3) ≈ 2.7268 Address: menger_hash(x,y,z) ⊕ fractal_offset """ coordinates = [] d_H = 2.7268 for i in range(self.n_oscillators): # Map oscillator state to 3D coordinates x = int(state.position[i] * 10 + 32) y = int(state.velocity[i] * 10 + 32) z = int(state.acceleration[i] * 10 + 32) # Menger hash hash_val = x ^ ((y << 1) & 0xFFFFFFFF) ^ ((z << 2) & 0xFFFFFFFF) # Fractal offset offset = int((x + y + z) * d_H) # Address address = hash_val ^ offset # Map to n-space coord = np.zeros(self.n_dimensions) coord[0] = x coord[1] = y coord[2] = z coord[3] = hash_val coord[4] = offset coord[5] = address coord[6] = d_H distance = np.linalg.norm(coord - self.center) is_admissible = True # All Menger coordinates admissible coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.MENGER, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_ene_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply ENE Triangle Manifold mapping. Concentric shells with triangular number indexing Rotation field + transmission field """ coordinates = [] for i in range(self.n_oscillators): # Shell index k = int(np.abs(state.position[i]) * 5) # Triangular number t_num = k * (k + 1) // 2 # Vertex parameters a = float(k % 3) b = float((k + 1) - (k % 3)) c = float(k) # Mass mass = a * b * c if (a * b * c) > 0 else 1.0 # Rotation angle rotation = float(k) * 0.1 # Bandwidth and latency (curvature-based) curvature = 0.5 bandwidth = 10.0 * (1.0 - curvature) latency = 1.0 + curvature # Map to n-space coord = np.zeros(self.n_dimensions) coord[0] = k coord[1] = t_num coord[2:5] = [a, b, c] coord[5] = mass coord[6] = rotation coord[7] = bandwidth coord[8] = latency distance = np.linalg.norm(coord - self.center) is_admissible = True coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.ENE, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_quaternion_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply quaternion counter-rotation mapping. Zero-net-angular-momentum design Counter-rotating steps: q at layer N, q⁻¹ at layer N-1 """ coordinates = [] for i in range(self.n_oscillators): # Map state to quaternion (w, x, y, z) w = 1.0 # Scalar part x = state.position[i] y = state.velocity[i] z = state.acceleration[i] # Normalize norm = np.sqrt(w**2 + x**2 + y**2 + z**2) if norm > 0: w, x, y, z = w/norm, x/norm, y/norm, z/norm # Counter-rotation (inverse quaternion) w_inv = w x_inv = -x y_inv = -y z_inv = -z # Map to n-space coord = np.zeros(self.n_dimensions) coord[0:4] = [w, x, y, z] coord[4:8] = [w_inv, x_inv, y_inv, z_inv] distance = np.linalg.norm(coord - self.center) is_admissible = True coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.QUATERNION, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_manifold_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply manifold compression mapping. Isometric chart constraints Jacobian determinant for compression """ coordinates = [] for i in range(self.n_oscillators): # State as manifold point x = state.position[i] v = state.velocity[i] a = state.acceleration[i] # Jacobian (simplified 3x3) J = np.array([ [1.0, 0.1, 0.0], [0.1, 1.0, 0.1], [0.0, 0.1, 1.0] ]) # Jacobian determinant det_J = np.linalg.det(J) # Chart bloat: B = N/D N = 3 # Representation dimension D = 2 # Intrinsic dimension bloat = N / D # Map to n-space coord = np.zeros(self.n_dimensions) coord[0:3] = [x, v, a] coord[3] = det_J coord[4] = bloat coord[5] = N coord[6] = D distance = np.linalg.norm(coord - self.center) is_admissible = bloat == 1.0 # Isometric when bloat = 1 coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.MANIFOLD, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_braid_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply braid group theory mapping. Strand crossing invariants Topological constraints """ coordinates = [] for i in range(self.n_oscillators): # Treat oscillators as strands strand_a = i strand_b = (i + 1) % self.n_oscillators # Crossing direction based on relative position crossing = 1 if state.position[i] > state.position[strand_b] else -1 # Invariant invariant = f"braid_{strand_a}_{strand_b}_{crossing}" # Map to n-space (encode invariant numerically) coord = np.zeros(self.n_dimensions) coord[0] = strand_a coord[1] = strand_b coord[2] = crossing digest = hashlib.sha256(invariant.encode("utf-8")).digest() coord[3] = int.from_bytes(digest[:8], "big") % 1000 distance = np.linalg.norm(coord - self.center) is_admissible = True coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.BRAID, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_svqf_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply SVQF sparse voxel indexing mapping. Sparse voxel representation Only store admissible regions """ coordinates = [] for i in range(self.n_oscillators): # Voxel coordinates vx = int(state.position[i] * 10 + 50) vy = int(state.velocity[i] * 10 + 50) vz = int(state.acceleration[i] * 10 + 50) # Sparse index (only if within bounds) is_admissible = 0 <= vx < 100 and 0 <= vy < 100 and 0 <= vz < 100 # Map to n-space coord = np.zeros(self.n_dimensions) coord[0:3] = [vx, vy, vz] coord[3] = 1 if is_admissible else 0 coord[4] = vx * 10000 + vy * 100 + vz # Linear index distance = np.linalg.norm(coord - self.center) coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.SVQF, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_triumvirate_mapping(self, state: COUCHState) -> List[NSpaceCoordinate]: """ Apply Triumvirate clock mapping. Builder-Judge-Warden roles Clock actions: ADD, PAUSE, SUBTRACT """ coordinates = [] for i in range(self.n_oscillators): # Map oscillator state to clock phase phase = np.arctan2(state.velocity[i], state.position[i]) # Clock action based on phase if phase > np.pi/2: action = 1 # ADD (Builder) elif phase < -np.pi/2: action = -1 # SUBTRACT (Warden) else: action = 0 # PAUSE (Judge) # Map to n-space coord = np.zeros(self.n_dimensions) coord[0] = phase coord[1] = action coord[2] = i distance = np.linalg.norm(coord - self.center) is_admissible = True coordinates.append(NSpaceCoordinate( framework=NSpaceFramework.TRIUMVIRATE, coordinates=coord, distance_from_center=distance, is_admissible=is_admissible )) return coordinates def apply_all_frameworks(self, state: COUCHState) -> Dict[NSpaceFramework, List[NSpaceCoordinate]]: """Apply all frameworks to COUCH state.""" mappings = {} mappings[NSpaceFramework.PIST] = self.apply_pist_mapping(state) mappings[NSpaceFramework.MENGER] = self.apply_menger_mapping(state) mappings[NSpaceFramework.ENE] = self.apply_ene_mapping(state) mappings[NSpaceFramework.QUATERNION] = self.apply_quaternion_mapping(state) mappings[NSpaceFramework.MANIFOLD] = self.apply_manifold_mapping(state) mappings[NSpaceFramework.BRAID] = self.apply_braid_mapping(state) mappings[NSpaceFramework.SVQF] = self.apply_svqf_mapping(state) mappings[NSpaceFramework.TRIUMVIRATE] = self.apply_triumvirate_mapping(state) self.framework_mappings = mappings return mappings def analyze_center_attractor(self) -> Dict[str, Any]: """ Analyze "=" as central attractor in n-space. Check if all frameworks converge to center or diverge. """ analysis = { "center": self.center.tolist(), "frameworks": {}, "convergence": {}, "admissibility": {} } for framework, coords in self.framework_mappings.items(): distances = [c.distance_from_center for c in coords] admissible = [c.is_admissible for c in coords] analysis["frameworks"][framework.value] = { "avg_distance": np.mean(distances), "max_distance": np.max(distances), "min_distance": np.min(distances), "admissible_count": sum(admissible), "total_count": len(admissible), "admissibility_ratio": sum(admissible) / len(admissible) if admissible else 0 } # Convergence: check if distances decrease toward center analysis["convergence"][framework.value] = distances[0] > distances[-1] if len(distances) > 1 else True # Admissibility analysis["admissibility"][framework.value] = all(admissible) return analysis def find_framework_intersections(self) -> Dict[str, Any]: """ Find intersections between framework mappings. Identify coordinates where multiple frameworks agree. """ intersections = { "pairwise": {}, "common_admissible": [], "framework_distances": {} } frameworks = list(self.framework_mappings.keys()) # Pairwise intersections for i in range(len(frameworks)): for j in range(i + 1, len(frameworks)): f1 = frameworks[i] f2 = frameworks[j] coords1 = self.framework_mappings[f1] coords2 = self.framework_mappings[f2] # Find closest pairs min_dist = float('inf') closest_pair = None for c1 in coords1: for c2 in coords2: dist = np.linalg.norm(c1.coordinates - c2.coordinates) if dist < min_dist: min_dist = dist closest_pair = (c1, c2) intersections["pairwise"][f"{f1.value} ↔ {f2.value}"] = { "min_distance": min_dist, "closest_pair_coords": closest_pair[0].coordinates.tolist() if closest_pair else None, "both_admissible": closest_pair[0].is_admissible and closest_pair[1].is_admissible if closest_pair else False } # Common admissible coordinates all_admissible = [] for framework, coords in self.framework_mappings.items(): admissible_coords = [c.coordinates for c in coords if c.is_admissible] all_admissible.append(admissible_coords) # Find intersection of all admissible sets if all_admissible: common = all_admissible[0] for coords in all_admissible[1:]: common = [c for c in common if any(np.allclose(c, other) for other in coords)] intersections["common_admissible"] = [c.tolist() for c in common[:5]] # First 5 return intersections def main(): """Run COUCH n-space map analysis.""" print("=" * 70) print("COUCH EQUATION N-SPACE MAP ANALYSIS") print("=" * 70) print("\n[*] Treating COUCH as n-space map with '=' at center") print("[*] Applying all Research Stack mathematical frameworks") # Initialize n-space map nspace_map = COUCHNSpaceMap(n_oscillators=3, n_dimensions=10) # Initialize COUCH state couch_state = nspace_map.initialize_couch_state() print(f"\n[*] COUCH State:") print(f" Oscillators: {nspace_map.n_oscillators}") print(f" Position: {couch_state.position}") print(f" Velocity: {couch_state.velocity}") print(f" Damping: {couch_state.damping}") print(f" Forcing: {couch_state.forcing}") # Apply all frameworks print(f"\n[*] Applying {len(nspace_map.frameworks)} frameworks...") mappings = nspace_map.apply_all_frameworks(couch_state) for framework, coords in mappings.items(): admissible_count = sum(c.is_admissible for c in coords) print(f" {framework.value}: {len(coords)} coordinates, {admissible_count} admissible") # Analyze center attractor print(f"\n[*] Analyzing '=' as central attractor...") center_analysis = nspace_map.analyze_center_attractor() print(f"\n[*] Center Attractor Analysis:") for framework, stats in center_analysis["frameworks"].items(): print(f" {framework}:") print(f" Avg distance: {stats['avg_distance']:.4f}") print(f" Admissibility: {stats['admissibility_ratio']:.2%}") # Find intersections print(f"\n[*] Finding framework intersections...") intersections = nspace_map.find_framework_intersections() print(f"\n[*] Framework Intersections:") for pair, data in intersections["pairwise"].items(): print(f" {pair}:") print(f" Min distance: {data['min_distance']:.4f}") print(f" Both admissible: {data['both_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": { "position": couch_state.position.tolist(), "velocity": couch_state.velocity.tolist(), "damping": float(couch_state.damping), "forcing": float(couch_state.forcing) }, "center_analysis": convert_to_native(center_analysis), "intersections": convert_to_native(intersections) } output_path = "/home/allaun/Documents/Research Stack/data/couch_nspace_map_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 N-SPACE MAP ANALYSIS COMPLETE") print("=" * 70) if __name__ == "__main__": main()