04_Genesis_Protocol/src/python/proof.py

import argparse
import numpy as np

def get_dictionary(dim, dictionary_size, seed):
    """Procedurally generate a normalized dictionary matrix using deterministic PRNG seed."""
    rng = np.random.RandomState(seed)
    dict_mat = rng.standard_normal((dim, dictionary_size)).astype(np.float32)
    norms = np.linalg.norm(dict_mat, axis=0, keepdims=True) + 1e-9
    return dict_mat / norms

def sparse_matching_pursuit(W, u_dict, v_dict, rank):
    """Compresses W by projecting onto u_dict and v_dict up to a given rank."""
    W_residual = W.copy()
    projections = []
    
    for r in range(rank):
        # Calculate projection search space
        # Find dictionary columns (u_i, v_j) that maximize projection correlation
        # correlation(i, j) = u_i^T * W_residual * v_j
        corr_matrix = np.dot(u_dict.T, np.dot(W_residual, v_dict))
        
        # Locate indices of maximum absolute correlation
        idx_u, idx_v = np.unravel_index(np.argmax(np.abs(corr_matrix)), corr_matrix.shape)
        coeff = corr_matrix[idx_u, idx_v]
        
        # Capture indices and coefficient
        projections.append((idx_u, idx_v, coeff))
        
        # Update residual: subtract the rank-1 component
        outer_prod = np.outer(u_dict[:, idx_u], v_dict[:, idx_v])
        W_residual -= coeff * outer_prod
        
    return projections

def reconstruct_matrix(projections, u_dict, v_dict, m, n):
    """Reconstructs the weight matrix from sparse projections and dictionaries."""
    W_rec = np.zeros((m, n), dtype=np.float32)
    for idx_u, idx_v, coeff in projections:
        W_rec += coeff * np.outer(u_dict[:, idx_u], v_dict[:, idx_v])
    return W_rec

def run_proof():
    print("======================================================================")
    print("ZYMATICA | Genesis Protocol: Procedural Seed Reconstruction Proof")
    print("======================================================================\n")

    M, N = 64, 64
    DICT_SIZE = 128
    RANK = 4
    MASTER_SEED = 42

    print(f"[1] Generating Mock Layer Weight Matrix W ({M}x{N} floats)...")
    # Generate structured weights (like low-rank patterns in neural networks)
    rng = np.random.RandomState(MASTER_SEED)
    W_true = rng.standard_normal((M, N)).astype(np.float32)
    # enforce structure by making it low-rank plus noise
    U_true = rng.standard_normal((M, 4))
    V_true = rng.standard_normal((N, 4))
    W_true = np.dot(U_true, V_true.T) + 0.1 * rng.standard_normal((M, N))
    
    raw_size_bytes = W_true.nbytes
    print(f"  -> Size of raw weights matrix W: {raw_size_bytes} bytes ({raw_size_bytes / 1024:.2f} KB)")

    print(f"\n[2] Instantiating Procedural Dictionaries (Seed={MASTER_SEED}, DictSize={DICT_SIZE})...")
    u_dict = get_dictionary(M, DICT_SIZE, MASTER_SEED)
    v_dict = get_dictionary(N, DICT_SIZE, MASTER_SEED + 500)
    print(f"  -> Generated U_dict shape: {u_dict.shape}")
    print(f"  -> Generated V_dict shape: {v_dict.shape}")

    print(f"\n[3] Compiling Weight Matrix into Sparse Trajectories (Rank={RANK})...")
    projections = sparse_matching_pursuit(W_true, u_dict, v_dict, RANK)
    
    # Calculate compressed size: each projection has 1-byte U idx, 1-byte V idx, 2-byte coefficient (float16)
    # Total = 4 bytes per rank.
    compressed_bytes = RANK * 4
    compression_ratio = raw_size_bytes / compressed_bytes
    print(f"  Sparse Projections:")
    for r, (iu, iv, val) in enumerate(projections):
        print(f"    Rank {r+1}: U_idx={iu:3d}, V_idx={iv:3d}, Coefficient={val:.4f}")
    print(f"  -> Compressed Payload Size: {compressed_bytes} bytes")
    print(f"  -> Compression Ratio:        {compression_ratio:.2f}x")

    print("\n[4] Executing Edge Reconstructor (Procedural Inflation)...")
    W_rec = reconstruct_matrix(projections, u_dict, v_dict, M, N)
    
    mse = np.mean((W_true - W_rec) ** 2)
    cosine_sim = np.dot(W_true.flatten(), W_rec.flatten()) / (np.linalg.norm(W_true) * np.linalg.norm(W_rec) + 1e-9)
    
    print(f"  - Reconstruction Mean Squared Error (MSE): {mse:.6f}")
    print(f"  - Cosine Similarity (Fidelity Index):      {cosine_sim * 100:.2f}%")
    
    print("\n[VERIFICATION] Deterministic procedural morphogenesis completed successfully.")

if __name__ == "__main__":
    parser = argparse.ArgumentParser(description="Zymatica Genesis Protocol Proof")
    parser.add_argument("--test", action="store_true", help="Run test mode")
    args = parser.parse_args()
    run_proof()