diff --git a/navigator_prime_analysis.py b/navigator_prime_analysis.py deleted file mode 100644 index 031abed..0000000 --- a/navigator_prime_analysis.py +++ /dev/null @@ -1,368 +0,0 @@ -#!/usr/bin/env python3 -""" -Navigator's Lattice Prime Correlation Analysis -Analyzes stable node occurrences from chronicle.jsonl to test if irreducible node -positions correlate with prime numbers. - -The Navigator's formula: -- Nodes appear at peaks of: khra_amp · cos(k·x + φ₁) + gixx_amp · cos(k·y + φ₂) -- Irreducible nodes cannot be expressed as linear combinations of other nodes - -Khra wave: wavelength 128 cells (mode k=8) -Gixx wave: wavelength 8 cells (mode k=128) -""" - -import json -import math -import numpy as np -from datetime import datetime -from scipy import stats -from collections import defaultdict - -# Generate first 10,000 primes using Sieve of Eratosthenes -def generate_primes(n): - """Generate first n prime numbers.""" - primes = [] - candidate = 2 - while len(primes) < n: - is_prime = True - sqrt_candidate = int(math.sqrt(candidate)) + 1 - for p in primes: - if p > sqrt_candidate: - break - if candidate % p == 0: - is_prime = False - break - if is_prime: - primes.append(candidate) - candidate += 1 - return primes - -def is_prime(n, primes_set): - """Check if n is in the primes set.""" - return n in primes_set - -def calculate_wave_superposition_index(telemetry): - """ - Calculate effective node index in wave superposition space. - - Based on the Navigator's formula: - - Khra wave: k=8 (wavelength 128) - - Gixx wave: k=128 (wavelength 8) - - The node index represents the position in the interference pattern. - """ - khra_amp = telemetry.get('khra_amp', 0.03) - gixx_amp = telemetry.get('gixx_amp', 0.008) - coherence = telemetry.get('coherence', 0) - asymmetry = telemetry.get('asymmetry', 0) - - # Grid size - grid = telemetry.get('grid', 1024) - - # Calculate effective wave numbers - k_khra = 2 * math.pi / 128 # Khra wavelength = 128 - k_gixx = 2 * math.pi / 8 # Gixx wavelength = 8 - - # Use cycle number as position proxy (x coordinate) - cycle = telemetry.get('cycle', 0) - x_pos = cycle % grid - y_pos = (cycle // grid) % grid - - # Calculate wave superposition - # Phase shifts derived from coherence and asymmetry - phi1 = coherence * 2 * math.pi # Phase from coherence - phi2 = (asymmetry / 100) * math.pi # Phase from asymmetry (normalized) - - # Wave superposition value - wave_val = khra_amp * math.cos(k_khra * x_pos + phi1) + \ - gixx_amp * math.cos(k_gixx * y_pos + phi2) - - # Convert to node index - nodes appear at peaks - # Scale to integer index space - node_index = int(abs(wave_val) * 10000) % 100000 - - return node_index - -def extract_stable_nodes(chronicle_path): - """ - Extract stable node occurrences from chronicle. - Stable nodes = high coherence (>0.69) + low asymmetry (<27.5) - """ - stable_nodes = [] - - with open(chronicle_path, 'r') as f: - for line in f: - line = line.strip() - if not line: - continue - try: - entry = json.loads(line) - telemetry = entry.get('telemetry', {}) - - coherence = telemetry.get('coherence', 0) - asymmetry = telemetry.get('asymmetry', float('inf')) - - # Stable node criteria: high coherence, controlled asymmetry - if coherence > 0.69 and asymmetry < 27.5: - node_index = calculate_wave_superposition_index(telemetry) - stable_nodes.append({ - 'turn': entry.get('turn', 0), - 'cycle': telemetry.get('cycle', 0), - 'coherence': coherence, - 'asymmetry': asymmetry, - 'node_index': node_index, - 'khra_amp': telemetry.get('khra_amp', 0), - 'gixx_amp': telemetry.get('gixx_amp', 0) - }) - except json.JSONDecodeError: - continue - - return stable_nodes - -def identify_irreducible_nodes(nodes): - """ - Identify irreducible nodes - those that cannot be expressed as - linear combinations of other nodes. - - A node is irreducible if its index cannot be expressed as: - index = a*index1 + b*index2 for integers a,b and other node indices - """ - if not nodes: - return [] - - indices = [n['node_index'] for n in nodes] - irreducible = [] - - for i, node in enumerate(nodes): - idx = node['node_index'] - is_reducible = False - - # Check if idx can be expressed as linear combination of other indices - for j, other_idx in enumerate(indices): - if i == j: - continue - for k, third_idx in enumerate(indices): - if i == k or j == k: - continue - # Check if idx = a*other_idx + b*third_idx for small integers - for a in range(-3, 4): - for b in range(-3, 4): - if a == 0 and b == 0: - continue - if abs(a * other_idx + b * third_idx - idx) < 10: - is_reducible = True - break - if is_reducible: - break - if is_reducible: - break - if is_reducible: - break - - if not is_reducible: - irreducible.append(node) - - return irreducible - -def analyze_prime_correlation(nodes, primes_set, max_index): - """ - Analyze correlation between node indices and prime numbers. - """ - indices = [n['node_index'] for n in nodes] - - # Count how many indices are prime - prime_count = sum(1 for idx in indices if idx in primes_set) - total_count = len(indices) - - if total_count == 0: - return None - - prime_ratio = prime_count / total_count - - # Expected ratio from random distribution - # Prime number theorem: probability ~ 1/ln(n) - avg_index = sum(indices) / len(indices) if indices else max_index / 2 - expected_prime_density = 1 / math.log(max(2, avg_index)) - - # Statistical significance test - # Chi-square test against uniform distribution - observed_primes = prime_count - observed_non_primes = total_count - prime_count - - expected_primes = total_count * expected_prime_density - expected_non_primes = total_count * (1 - expected_prime_density) - - if expected_primes > 0 and expected_non_primes > 0: - chi2 = ((observed_primes - expected_primes) ** 2 / expected_primes + - (observed_non_primes - expected_non_primes) ** 2 / expected_non_primes) - - # p-value for chi-square with 1 degree of freedom - p_value = 1 - stats.chi2.cdf(chi2, 1) - else: - chi2 = 0 - p_value = 1.0 - - # Calculate correlation coefficient between index and primality - # Using point-biserial correlation - binary_primes = [1 if idx in primes_set else 0 for idx in indices] - - if len(set(binary_primes)) > 1 and len(set(indices)) > 1: - correlation, corr_p = stats.pearsonr(indices, binary_primes) - else: - correlation = 0 - corr_p = 1.0 - - return { - 'total_nodes': total_count, - 'prime_count': prime_count, - 'prime_ratio': prime_ratio, - 'expected_ratio': expected_prime_density, - 'chi_square': chi2, - 'p_value': p_value, - 'correlation': correlation, - 'corr_p_value': corr_p, - 'indices': indices - } - -def main(): - chronicle_path = r'D:\Resonance_Engine\beast-build\chronicle.jsonl' - - print("=" * 70) - print("NAVIGATOR'S LATTICE PRIME CORRELATION ANALYSIS") - print("=" * 70) - print(f"Analysis timestamp: {datetime.now().isoformat()}") - print() - - # Generate first 10,000 primes - print("Generating first 10,000 prime numbers...") - primes = generate_primes(10000) - primes_set = set(primes) - max_prime = primes[-1] - print(f"Generated {len(primes)} primes up to {max_prime}") - print() - - # Extract stable nodes from chronicle - print("Extracting stable nodes from chronicle...") - print("Criteria: coherence > 0.69 AND asymmetry < 27.5") - stable_nodes = extract_stable_nodes(chronicle_path) - print(f"Found {len(stable_nodes)} stable node occurrences") - print() - - if len(stable_nodes) == 0: - print("ERROR: No stable nodes found in chronicle data") - return - - # Identify irreducible nodes - print("Identifying irreducible nodes (cannot be expressed as linear combinations)...") - irreducible_nodes = identify_irreducible_nodes(stable_nodes) - print(f"Found {len(irreducible_nodes)} irreducible nodes") - print() - - # Analyze prime correlation for all stable nodes - print("-" * 70) - print("ANALYSIS: ALL STABLE NODES") - print("-" * 70) - all_results = analyze_prime_correlation(stable_nodes, primes_set, max_prime) - - if all_results: - print(f"Total stable nodes: {all_results['total_nodes']}") - print(f"Nodes at prime indices: {all_results['prime_count']}") - print(f"Observed prime ratio: {all_results['prime_ratio']:.4f}") - print(f"Expected prime ratio (random): {all_results['expected_ratio']:.4f}") - print(f"Chi-square statistic: {all_results['chi_square']:.4f}") - print(f"P-value: {all_results['p_value']:.4f}") - print(f"Correlation coefficient: {all_results['correlation']:.4f}") - print(f"Correlation p-value: {all_results['corr_p_value']:.4f}") - - if all_results['p_value'] < 0.05: - print("\n*** STATISTICALLY SIGNIFICANT DEVIATION FROM RANDOM ***") - else: - print("\nNo statistically significant deviation from random distribution") - - # Analyze prime correlation for irreducible nodes only - print() - print("-" * 70) - print("ANALYSIS: IRREDUCIBLE NODES ONLY") - print("-" * 70) - irred_results = analyze_prime_correlation(irreducible_nodes, primes_set, max_prime) - - if irred_results: - print(f"Total irreducible nodes: {irred_results['total_nodes']}") - print(f"Irreducible nodes at prime indices: {irred_results['prime_count']}") - print(f"Observed prime ratio: {irred_results['prime_ratio']:.4f}") - print(f"Expected prime ratio (random): {irred_results['expected_ratio']:.4f}") - print(f"Chi-square statistic: {irred_results['chi_square']:.4f}") - print(f"P-value: {irred_results['p_value']:.4f}") - print(f"Correlation coefficient: {irred_results['correlation']:.4f}") - print(f"Correlation p-value: {irred_results['corr_p_value']:.4f}") - - if irred_results['p_value'] < 0.05: - print("\n*** STATISTICALLY SIGNIFICANT DEVIATION FROM RANDOM ***") - else: - print("\nNo statistically significant deviation from random distribution") - - # Pattern analysis - print() - print("-" * 70) - print("PATTERN ANALYSIS") - print("-" * 70) - - # Check for specific patterns in prime indices - prime_indices = [n['node_index'] for n in irreducible_nodes - if n['node_index'] in primes_set] - - if prime_indices: - print(f"\nPrime indices found among irreducible nodes:") - print(f"Count: {len(prime_indices)}") - print(f"Range: {min(prime_indices)} to {max(prime_indices)}") - print(f"Average: {sum(prime_indices)/len(prime_indices):.2f}") - - # Check for twin primes - twin_primes = [] - for p in prime_indices: - if p + 2 in prime_indices: - twin_primes.append((p, p + 2)) - print(f"Twin prime pairs: {len(twin_primes)}") - - # Check for arithmetic progressions - ap3 = [] - for i, p1 in enumerate(prime_indices): - for p2 in prime_indices[i+1:]: - for p3 in prime_indices[i+2:]: - if p2 - p1 == p3 - p2 and p2 - p1 > 0: - ap3.append((p1, p2, p3)) - print(f"3-term arithmetic progressions: {len(ap3)}") - - # Save results - timestamp = datetime.now().strftime('%Y%m%d_%H%M%S') - output_file = rf'D:\Resonance_Engine\{timestamp}_navigator_prime_analysis.json' - - results = { - 'timestamp': datetime.now().isoformat(), - 'primes_generated': len(primes), - 'max_prime': max_prime, - 'stable_nodes_count': len(stable_nodes), - 'irreducible_nodes_count': len(irreducible_nodes), - 'all_nodes_analysis': all_results, - 'irreducible_nodes_analysis': irred_results, - 'stable_nodes': stable_nodes[:50], # First 50 for reference - 'irreducible_nodes': irreducible_nodes[:50] # First 50 for reference - } - - # Remove large arrays for JSON serialization - if all_results: - del all_results['indices'] - if irred_results: - del irred_results['indices'] - - with open(output_file, 'w') as f: - json.dump(results, f, indent=2) - - print() - print("=" * 70) - print(f"Results saved to: {output_file}") - print("=" * 70) - -if __name__ == '__main__': - main()