#!/usr/bin/env python3
"""
Waveprobe Manifold Generator + FAMM Map Preshaping
==================================================

Uses waveprobe to generate manifold shapes from eigenvalue spectra,
then preshapes FAMM (Frustrated Access Memory Module) delay-line maps
based on the eigenvalue-derived manifold geometry.

Pipeline:
1. Generate waveprobe diagnostic payload with manifold eigenvalues
2. Compute eigenvalue spectrum from simulated manifold Laplacian
3. Derive manifold shape from eigenvalue distribution
4. Preshape FAMM delay maps to match manifold curvature
5. Output FAMM-compatible delay-weight configuration

Integration: waveprobe → eigenvalue → manifold → FAMM preshape
"""

import numpy as np
import json
import hashlib
import time
from dataclasses import dataclass
from typing import List, Dict, Tuple, Optional
from pathlib import Path

RESEARCH_STACK = Path("/home/allaun/Documents/Research Stack")


@dataclass
class WaveprobeManifold:
    """Waveprobe-generated manifold with eigenvalue spectrum."""
    probe_id: str
    dimension: int
    eigenvalues: List[float]  # Laplacian eigenvalue spectrum
    eigenvectors: List[List[float]]  # Manifold embedding
    curvature_tensor: List[float]
    topology_valid: bool
    manifold_shape: str  # 'spherical', 'hyperbolic', 'flat', 'toroidal'


@dataclass
class FAMMDelayMap:
    """FAMM delay-line map preshaped by manifold geometry."""
    address: int
    data: float  # Q16.16 representation
    delay: float  # Delay time (shaped by eigenvalue)
    delay_mass: float  # Causal constraint mass
    delay_weight: float  # Shaped by eigenvector component
    curvature_aligned: bool  # Whether delay follows manifold curvature


class WaveprobeManifoldGenerator:
    """
    Generate manifold shapes from waveprobe diagnostic payloads.
    
    Uses simulated Laplacian eigenvalue spectra to define manifold geometry,
    then extracts topological invariants for FAMM preshaping.
    """
    
    def __init__(self, dimension: int = 4):
        self.dimension = dimension
        self.probe_types = ["manifold_topology", "eigenvalue_spectrum", "curvature_tensor"]
    
    def generate_laplacian_spectrum(self, n_modes: int = 16) -> Tuple[List[float], List[List[float]]]:
        """
        Generate Laplacian eigenvalue spectrum for manifold.
        
        For a d-dimensional manifold, Laplacian eigenvalues λ_k scale as:
        λ_k ∝ k^(2/d) for large k (Weyl law)
        
        Returns: (eigenvalues, eigenvectors)
        """
        # Simulate eigenvalue spectrum
        # λ_k = (k * π / L)² for Dirichlet boundary conditions
        L = 1.0  # Characteristic length
        eigenvalues = []
        eigenvectors = []
        
        for k in range(1, n_modes + 1):
            # Weyl law scaling: λ_k ∝ k^(2/d)
            if self.dimension > 0:
                lam = (np.pi * k / L) ** (2.0 / self.dimension)
            else:
                lam = (np.pi * k / L) ** 2
            
            eigenvalues.append(lam)
            
            # Generate corresponding eigenfunction (simplified)
            # φ_k(x) = sin(kπx/L) for 1D, product for higher D
            vec = [np.sin(k * np.pi * i / (n_modes + 1)) for i in range(1, n_modes + 1)]
            vec = [v / np.linalg.norm(vec) for v in vec]  # Normalize
            eigenvectors.append(vec)
        
        return eigenvalues, eigenvectors
    
    def classify_manifold_shape(self, eigenvalues: List[float]) -> str:
        """
        Classify manifold shape from eigenvalue distribution.
        
        - Spherical: eigenvalues cluster at low end (positive curvature)
        - Hyperbolic: eigenvalues spread out (negative curvature)  
        - Flat: uniform distribution (zero curvature)
        - Toroidal: periodic pattern
        """
        if len(eigenvalues) < 3:
            return 'unknown'
        
        # Compute eigenvalue gaps
        gaps = [eigenvalues[i+1] - eigenvalues[i] for i in range(len(eigenvalues)-1)]
        mean_gap = np.mean(gaps)
        std_gap = np.std(gaps)
        
        # Coefficient of variation
        cv = std_gap / mean_gap if mean_gap > 0 else 0
        
        # Classify based on gap distribution
        if cv < 0.3:
            return 'spherical'  # Low variation, clustered
        elif cv > 0.7:
            return 'hyperbolic'  # High variation, spread out
        elif any(g < 0.01 * mean_gap for g in gaps[:3]):
            return 'toroidal'  # Near-degenerate low modes
        else:
            return 'flat'
    
    def compute_curvature_tensor(self, eigenvalues: List[float]) -> List[float]:
        """
        Compute Ricci curvature tensor components from eigenvalues.
        
        Simplified: R_ii ∝ Σ(1/λ_k) for k > 0 (zeta function regularized)
        """
        # Regularized sum: exclude zero mode
        curvatures = []
        for i in range(min(4, self.dimension)):
            if len(eigenvalues) > 1:
                # Ricci curvature ~ sum of inverse eigenvalues
                ricci = sum(1.0 / lam for lam in eigenvalues[1:] if lam > 0.001)
                curvatures.append(ricci / len(eigenvalues))
            else:
                curvatures.append(0.0)
        
        return curvatures
    
    def generate_waveprobe(self, probe_type: str = "manifold_topology") -> WaveprobeManifold:
        """Generate waveprobe diagnostic payload with manifold data."""
        timestamp = time.time()
        probe_id = f"manifold_{hashlib.sha256(str(timestamp).encode()).hexdigest()[:12]}"
        
        # Generate eigenvalue spectrum
        eigenvalues, eigenvectors = self.generate_laplacian_spectrum(n_modes=16)
        
        # Classify manifold shape
        manifold_shape = self.classify_manifold_shape(eigenvalues)
        
        # Compute curvature
        curvature_tensor = self.compute_curvature_tensor(eigenvalues)
        
        # Topology validation
        topology_valid = all(ev > 0 for ev in eigenvalues[1:])  # Positive semi-definite Laplacian
        
        return WaveprobeManifold(
            probe_id=probe_id,
            dimension=self.dimension,
            eigenvalues=eigenvalues,
            eigenvectors=eigenvectors,
            curvature_tensor=curvature_tensor,
            topology_valid=topology_valid,
            manifold_shape=manifold_shape
        )


class FAMMPreshaper:
    """
    Preshape FAMM delay-line maps based on waveprobe manifold geometry.
    
    Maps manifold eigenvalues to FAMM delay parameters:
    - delay ∝ 1/√λ (lower eigenvalue = longer delay = lower frequency mode)
    - delay_weight ∝ eigenvector amplitude (stronger coupling for dominant modes)
    - delay_mass ∝ curvature (higher curvature = more causal constraint)
    """
    
    def __init__(self, bank_size: int = 256, max_delay: float = 32767.0):
        self.bank_size = bank_size
        self.max_delay = max_delay  # Q16.16 max
    
    def eigenvalue_to_delay(self, eigenvalue: float, scale: float = 1000.0) -> float:
        """
        Map Laplacian eigenvalue to FAMM delay time.
        
        Lower eigenvalue (lower frequency mode) → longer delay
        τ ∝ 1/√λ
        """
        if eigenvalue <= 0:
            return self.max_delay
        
        # Delay ∝ 1/√λ
        delay = scale / np.sqrt(eigenvalue)
        
        # Clamp to Q16.16 range
        return min(delay, self.max_delay)
    
    def eigenvector_to_weight(self, eigenvector_component: float) -> float:
        """
        Map eigenvector component to FAMM delay weight.
        
        Larger eigenvector amplitude → stronger delay weight
        w = |φ_k(x)|² (probability density interpretation)
        """
        weight = eigenvector_component ** 2
        return min(weight, 1.0)  # Normalized to [0,1]
    
    def curvature_to_mass(self, curvature: float, base_mass: float = 1.0) -> float:
        """
        Map manifold curvature to FAMM delay mass.
        
        Higher curvature → larger delay mass (more causal constraint)
        mass ∝ |R| (absolute Ricci curvature)
        """
        mass = base_mass * (1.0 + abs(curvature))
        return min(mass, self.max_delay / 10)  # Scale appropriately
    
    def preshape_famm_map(
        self,
        manifold: WaveprobeManifold,
        n_cells: Optional[int] = None
    ) -> List[FAMMDelayMap]:
        """
        Preshape FAMM delay-line map from waveprobe manifold.
        
        Distributes FAMM cells across manifold modes,
        assigning delays based on eigenvalue spectrum.
        """
        if n_cells is None:
            n_cells = self.bank_size
        
        famm_maps = []
        
        # Use top N eigenvalues for N cells
        n_modes = min(len(manifold.eigenvalues), n_cells)
        
        for i in range(n_cells):
            # Cycle through eigenmodes
            mode_idx = i % n_modes
            
            # Get eigenvalue and eigenvector for this mode
            eigenvalue = manifold.eigenvalues[mode_idx]
            eigenvector = manifold.eigenvectors[mode_idx]
            
            # Pick component from eigenvector (distribute across spatial positions)
            vec_idx = i % len(eigenvector)
            eigencomponent = eigenvector[vec_idx]
            
            # Compute curvature component
            curvature_idx = i % len(manifold.curvature_tensor)
            curvature = manifold.curvature_tensor[curvature_idx]
            
            # Map to FAMM parameters
            delay = self.eigenvalue_to_delay(eigenvalue)
            weight = self.eigenvector_to_weight(eigencomponent)
            mass = self.curvature_to_mass(curvature)
            
            # Data value (simulated Q16.16)
            data_val = eigencomponent * 32767.0  # Scale to Q16.16 range
            
            famm_maps.append(FAMMDelayMap(
                address=i,
                data=float(data_val),
                delay=float(delay),
                delay_mass=float(mass),
                delay_weight=float(weight),
                curvature_aligned=True
            ))
        
        return famm_maps


class WaveprobeFAMMIntegration:
    """
    Integrate waveprobe manifold generation with FAMM preshaping.
    
    Complete pipeline: waveprobe → eigenvalue → manifold → FAMM
    """
    
    def __init__(self, dimension: int = 4, bank_size: int = 256):
        self.waveprobe_gen = WaveprobeManifoldGenerator(dimension)
        self.famm_preshaper = FAMMPreshaper(bank_size)
    
    def generate_preshaped_famm(
        self,
        probe_type: str = "manifold_topology",
        output_format: str = "lean"
    ) -> Dict:
        """
        Generate complete waveprobe → FAMM preshaped configuration.
        
        Returns configuration in specified format (lean, json, or python).
        """
        # Step 1: Generate waveprobe manifold
        manifold = self.waveprobe_gen.generate_waveprobe(probe_type)
        
        # Step 2: Preshape FAMM map
        famm_maps = self.famm_preshaper.preshape_famm_map(manifold)
        
        # Step 3: Format output
        if output_format == "lean":
            return self._to_lean_format(manifold, famm_maps)
        elif output_format == "json":
            return self._to_json_format(manifold, famm_maps)
        else:
            return self._to_python_format(manifold, famm_maps)
    
    def _to_lean_format(
        self,
        manifold: WaveprobeManifold,
        famm_maps: List[FAMMDelayMap]
    ) -> Dict:
        """Convert to Lean 4 FAMM initialization format."""
        lean_cells = []
        for m in famm_maps:
            # Convert to Q16.16 hex representation
            data_hex = f"0x{int(m.data) & 0xFFFF:04X}"
            delay_hex = f"0x{int(m.delay) & 0xFFFF:04X}"
            mass_hex = f"0x{int(m.delay_mass) & 0xFFFF:04X}"
            weight_hex = f"0x{int(m.delay_weight * 65535) & 0xFFFF:04X}"
            
            lean_cells.append({
                "data": data_hex,
                "delay": delay_hex,
                "delayMass": mass_hex,
                "delayWeight": weight_hex
            })
        
        return {
            "manifold": {
                "probe_id": manifold.probe_id,
                "dimension": manifold.dimension,
                "shape": manifold.manifold_shape,
                "eigenvalues": [f"{ev:.6f}" for ev in manifold.eigenvalues[:8]],  # Top 8
                "curvature": [f"{c:.6f}" for c in manifold.curvature_tensor],
                "topology_valid": manifold.topology_valid
            },
            "famm_bank": {
                "size": len(famm_maps),
                "maxDelay": f"0x{int(self.famm_preshaper.max_delay):04X}",
                "cells": lean_cells[:16]  # First 16 for demo
            },
            "generation_timestamp": time.time()
        }
    
    def _to_json_format(
        self,
        manifold: WaveprobeManifold,
        famm_maps: List[FAMMDelayMap]
    ) -> Dict:
        """Convert to JSON format for external tools."""
        return {
            "waveprobe": {
                "probe_id": manifold.probe_id,
                "dimension": manifold.dimension,
                "manifold_shape": manifold.manifold_shape,
                "eigenvalue_spectrum": manifold.eigenvalues,
                "curvature_tensor": manifold.curvature_tensor,
                "topology_valid": manifold.topology_valid
            },
            "famm_delay_map": [
                {
                    "address": m.address,
                    "delay_ms": m.delay,
                    "delay_mass": m.delay_mass,
                    "delay_weight": m.delay_weight,
                    "data": m.data,
                    "curvature_aligned": m.curvature_aligned
                }
                for m in famm_maps
            ]
        }
    
    def _to_python_format(
        self,
        manifold: WaveprobeManifold,
        famm_maps: List[FAMMDelayMap]
    ) -> Dict:
        """Convert to Python-compatible format."""
        return {
            "manifold": manifold,
            "famm_maps": famm_maps,
            "summary": {
                "shape": manifold.manifold_shape,
                "n_cells": len(famm_maps),
                "mean_delay": np.mean([m.delay for m in famm_maps]),
                "mean_weight": np.mean([m.delay_weight for m in famm_maps])
            }
        }


def main():
    """Generate waveprobe manifold and preshape FAMM maps."""
    print("=" * 70)
    print("Waveprobe Manifold Generator + FAMM Map Preshaper")
    print("=" * 70)
    
    # Initialize integration
    integration = WaveprobeFAMMIntegration(dimension=4, bank_size=256)
    
    print("\n[1] Generating waveprobe manifold with eigenvalue spectrum...")
    
    # Generate preshaped FAMM
    result = integration.generate_preshaped_famm(
        probe_type="manifold_topology",
        output_format="lean"
    )
    
    print(f"  Probe ID: {result['manifold']['probe_id']}")
    print(f"  Dimension: {result['manifold']['dimension']}")
    print(f"  Manifold Shape: {result['manifold']['shape']}")
    print(f"  Topology Valid: {result['manifold']['topology_valid']}")
    
    print("\n[2] Eigenvalue Spectrum (top 8):")
    for i, ev in enumerate(result['manifold']['eigenvalues'][:8]):
        print(f"  λ_{i+1} = {ev}")
    
    print("\n[3] Curvature Tensor:")
    for i, c in enumerate(result['manifold']['curvature']):
        print(f"  R_{i} = {c}")
    
    print(f"\n[4] FAMM Bank Configuration:")
    print(f"  Size: {result['famm_bank']['size']} cells")
    print(f"  Max Delay: {result['famm_bank']['maxDelay']} (Q16.16)")
    
    print(f"\n[5] Sample FAMM Cells (first 4):")
    for i, cell in enumerate(result['famm_bank']['cells'][:4]):
        print(f"  Cell[{i}]: data={cell['data']}, delay={cell['delay']}, "
              f"mass={cell['delayMass']}, weight={cell['delayWeight']}")
    
    # Save output
    output_path = RESEARCH_STACK / "4-Infrastructure/shim/waveprobe_famm_output.json"
    with open(output_path, 'w') as f:
        json.dump(result, f, indent=2)
    
    print(f"\n[6] Output saved to: {output_path}")
    
    print("\n" + "=" * 70)
    print("Integration Complete")
    print("Waveprobe eigenvalue spectrum → Manifold shape → FAMM delay map preshape")
    print("=" * 70)
    
    return result


if __name__ == "__main__":
    main()