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

#!/usr/bin/env python3
"""
Manifold Shape Visualizer for Research Stack
Maps PIST/SVQF/FAMM structures from quaternion/braid formalism.
"""

import numpy as np
import sys
from pathlib import Path

# Add infrastructure paths
sys.path.insert(0, str(Path("/home/allaun/Documents/Research Stack/4-Infrastructure/shims")))

from dataclasses import dataclass
from typing import Tuple, List
import json


@dataclass
class QuaternionField:
    """S³ manifold point with quaternion coordinates."""
    w: float
    x: float
    y: float
    z: float
    
    def normalize(self):
        norm = np.sqrt(self.w**2 + self.x**2 + self.y**2 + self.z**2)
        return QuaternionField(self.w/norm, self.x/norm, self.y/norm, self.z/norm)
    
    def to_cartesian(self) -> Tuple[float, float, float]:
        """Stereographic projection to R³."""
        return (
            self.x / (1 - self.w + 1e-10),
            self.y / (1 - self.w + 1e-10),
            self.z / (1 - self.w + 1e-10)
        )


class ManifoldMapper:
    """
    Maps high-dimensional search space to visualizable manifold.
    Uses quaternion sieve + braid bracket topology.
    """
    
    def __init__(self, resolution: int = 64):
        self.resolution = resolution
        self.points: List[QuaternionField] = []
        self.trajectories: List[List[QuaternionField]] = []
    
    def generate_pist_shell(self, k: int, t: int, mass: int) -> np.ndarray:
        """
        Generate PIST shell coordinates.
        PIST: Perfectly Imperfect Square Theory
        Shell index: (k, t, mass=a*b)
        """
        # Integer-based shell as per NES-compatible fixed-point design
        a = int(np.sqrt(mass)) if mass > 0 else 1
        b = mass // a if a > 0 else 1
        
        theta = 2 * np.pi * k / self.resolution
        phi = np.pi * t / self.resolution
        
        # Quaternion from spherical coordinates
        w = np.cos(theta/2) * np.cos(phi/2)
        x = np.sin(theta/2) * np.cos(phi/2)
        y = np.sin(theta/2) * np.sin(phi/2)
        z = np.cos(theta/2) * np.sin(phi/2)
        
        return np.array([w, x, y, z])
    
    def sieve_filter(self, points: np.ndarray, threshold: float = 0.5) -> np.ndarray:
        """
        Quaternion sieve: counter-rotation band-pass filter.
        Only points with specific phase alignment survive.
        """
        # Apply counter-rotation filter (q at layer N, q⁻¹ at layer N-1)
        phases = np.arctan2(points[:, 2], points[:, 1])  # y/x phase
        aligned = np.abs(np.sin(phases * 2)) > threshold
        return points[aligned]
    
    def compute_frustration(self, point: np.ndarray, neighbors: np.ndarray) -> float:
        """
        FAMM frustration calculation on stress tensor.
        Φ > 1 regions are discarded (pruned search space).
        """
        if len(neighbors) == 0:
            return 0.0
        
        # Stress tensor: deviation from local manifold smoothness
        center = point[:3] / (point[0] + 1e-10)  # Stereographic
        neigh_centers = neighbors[:, :3] / (neighbors[:, 0:1] + 1e-10)
        
        deltas = neigh_centers - center
        stress = np.mean(np.linalg.norm(deltas, axis=1))
        
        # Frustration metric Φ
        phi = stress / (np.linalg.norm(center) + 1e-10)
        return float(phi)
    
    def map_manifold(self, output_path: str = None) -> dict:
        """Generate complete manifold map with all layers."""
        print("Generating manifold shape map...")
        
        all_points = []
        
        # Layer 0: Core PIST shells
        for k in range(self.resolution):
            for t in range(self.resolution//2):
                mass = (k + 1) * (t + 1)
                q = self.generate_pist_shell(k, t, mass)
                all_points.append(q)
        
        points_array = np.array(all_points)
        
        # Layer 1: Quaternion sieve (band-pass)
        filtered = self.sieve_filter(points_array, threshold=0.3)
        
        # Layer 2: FAMM frustration pruning
        survivors = []
        for i, pt in enumerate(filtered[:1000]):  # Sample for performance
            neighbors = filtered[max(0, i-5):min(len(filtered), i+5)]
            frustration = self.compute_frustration(pt, neighbors)
            if frustration <= 1.0:  # Keep only low-frustration regions
                survivors.append(pt)
        
        result = {
            "total_points": len(all_points),
            "post_sieve": len(filtered),
            "post_famm": len(survivors),
            "resolution": self.resolution,
            "manifold_type": "S3_quaternion_braid",
            "compression_ratio": len(survivors) / len(all_points) if all_points else 0,
            "sample_points": [p.tolist() for p in survivors[:20]]
        }
        
        if output_path:
            Path(output_path).parent.mkdir(parents=True, exist_ok=True)
            with open(output_path, 'w') as f:
                json.dump(result, f, indent=2)
            print(f"Manifold map saved to {output_path}")
        
        print(f"  Total: {result['total_points']}")
        print(f"  Post-sieve: {result['post_sieve']}")
        print(f"  Post-FAMM: {result['post_famm']}")
        print(f"  Compression: {result['compression_ratio']:.3f}")
        
        return result


def main():
    mapper = ManifoldMapper(resolution=32)
    
    output = "/home/allaun/Documents/Research Stack/shared-data/manifold_map.json"
    result = mapper.map_manifold(output)
    
    print("\nManifold shape mapping complete.")
    print("Use with: jupyter notebook 5-Applications/scripts/manifold_viz.ipynb")


if __name__ == "__main__":
    main()