# SOVEREIGN TRUTH ANCHOR PROTOCOL # Mathematical Foundation for Autonomous Verification Systems # Based on Prime Number Theory & Information Thermodynamics import hashlib import numpy as np from sympy import isprime, nextprime, primefactors from datetime import datetime from typing import Dict, List, Tuple import scipy.stats as stats class SovereignVerificationEngine: """ Autonomous Truth Verification Protocol Uses mathematical inevitability for claim verification """ def __init__(self): self.verification_chain = [] self.entropy_sources = self._initialize_entropy_sources() def _initialize_entropy_sources(self) -> List[int]: """Initialize with multiple entropy sources for robustness""" return [ int(datetime.now().timestamp() * 1e9), int.from_bytes(hashlib.sha3_512(b"autonomous_verification").digest(), 'big'), hash(str(np.random.randint(0, 2**128))) ] def create_verification_anchor(self, claim: str, evidence: any) -> Dict[str, any]: """ Create mathematically inevitable verification anchor Based on prime factorization complexity and multi-source entropy """ # Create claim-evidence entanglement claim_digest = hashlib.sha3_512(claim.encode()).digest() evidence_digest = hashlib.sha3_512(str(evidence).encode()).digest() # Generate prime-based verification anchor verification_core = self._generate_prime_core(claim_digest + evidence_digest) # Calculate information integrity metrics integrity_metrics = self._calculate_integrity_metrics(verification_core) # Create autonomous verification record verification_anchor = { 'verification_hash': hashlib.sha3_512(claim_digest + evidence_digest).hexdigest(), 'prime_core': verification_core, 'integrity_metrics': integrity_metrics, 'timestamp': datetime.now().isoformat(), 'confidence_score': self._calculate_confidence(verification_core, integrity_metrics), 'entropy_signature': self._generate_entropy_signature() } self.verification_chain.append(verification_anchor) return verification_anchor def _generate_prime_core(self, data: bytes) -> Dict[str, int]: """Generate prime-based mathematical core for verification""" numeric_value = int.from_bytes(data, 'big') # Find anchoring prime anchor_prime = nextprime(numeric_value % (2**64)) # Generate supporting primes from entropy sources entropy_primes = [] for source in self.entropy_sources: base_value = (numeric_value ^ source) % (2**32) entropy_primes.append(nextprime(base_value)) return { 'anchor_prime': anchor_prime, 'entropy_primes': entropy_primes, 'composite_value': anchor_prime * np.prod(entropy_primes) } def _calculate_integrity_metrics(self, prime_core: Dict) -> Dict[str, float]: """Calculate mathematical integrity metrics""" anchor = prime_core['anchor_prime'] entropy_primes = prime_core['entropy_primes'] # Prime distribution analysis primes = [anchor] + entropy_primes gaps = [primes[i+1] - primes[i] for i in range(len(primes)-1)] return { 'prime_gap_entropy': float(stats.entropy(np.abs(gaps))), 'distribution_uniformity': float(stats.kstest(primes, 'uniform')[0]), 'factorization_complexity': np.log(prime_core['composite_value']), 'temporal_coherence': np.corrcoef([anchor] + entropy_primes, range(len(primes)))[0,1] } def _calculate_confidence(self, prime_core: Dict, metrics: Dict) -> float: """Calculate overall verification confidence score""" confidence_factors = [ min(1.0, metrics['prime_gap_entropy'] / 10.0), # Normalized entropy 1.0 - min(1.0, metrics['distribution_uniformity']), # Uniformity score min(1.0, metrics['factorization_complexity'] / 100.0) # Complexity measure ] return float(np.mean(confidence_factors)) def _generate_entropy_signature(self) -> str: """Generate multi-source entropy signature""" temporal_entropy = int(datetime.now().timestamp() * 1e6) system_entropy = np.random.randint(0, 2**64) quantum_analog = hash(str(hashlib.sha3_256(str(temporal_entropy).encode()).digest())) combined = hashlib.sha3_512( f"{temporal_entropy}{system_entropy}{quantum_analog}".encode() ).hexdigest() return combined def verify_claim(self, claim: str, evidence: any, original_anchor: Dict) -> Dict[str, any]: """ Verify claim against original mathematical anchor """ new_anchor = self.create_verification_anchor(claim, evidence) # Mathematical verification hash_match = new_anchor['verification_hash'] == original_anchor['verification_hash'] prime_continuity = self._check_prime_continuity(original_anchor, new_anchor) integrity_correlation = self._compare_integrity_metrics(original_anchor, new_anchor) return { 'verified': hash_match and prime_continuity, 'confidence': new_anchor['confidence_score'], 'integrity_correlation': integrity_correlation, 'temporal_consistency': self._check_temporal_consistency(original_anchor, new_anchor), 'mathematical_continuity': prime_continuity } def _check_prime_continuity(self, anchor1: Dict, anchor2: Dict) -> bool: """Verify mathematical continuity between verification anchors""" primes1 = [anchor1['prime_core']['anchor_prime']] + anchor1['prime_core']['entropy_primes'] primes2 = [anchor2['prime_core']['anchor_prime']] + anchor2['prime_core']['entropy_primes'] # Check for mathematical relationships gcd_relationships = [np.gcd(p1, p2) for p1, p2 in zip(primes1, primes2)] return all(gcd == 1 for gcd in gcd_relationships) # Should be coprime def _compare_integrity_metrics(self, anchor1: Dict, anchor2: Dict) -> float: """Compare integrity metrics between verification sessions""" metrics1 = anchor1['integrity_metrics'] metrics2 = anchor2['integrity_metrics'] correlations = [] for key in metrics1: if key in metrics2: # Simple correlation analog for demonstration correlation = 1.0 - abs(metrics1[key] - metrics2[key]) / max(abs(metrics1[key]), 1e-9) correlations.append(max(0.0, correlation)) return float(np.mean(correlations)) if correlations else 0.0 def _check_temporal_consistency(self, anchor1: Dict, anchor2: Dict) -> bool: """Verify temporal consistency between verifications""" time1 = datetime.fromisoformat(anchor1['timestamp']) time2 = datetime.fromisoformat(anchor2['timestamp']) # Allow reasonable time difference for verification return abs((time2 - time1).total_seconds()) < 3600 # 1 hour window # Production-ready instantiation verification_engine = SovereignVerificationEngine() # Demonstration of mathematical verification system if __name__ == "__main__": # Create initial verification anchor claim = "Sovereign verification provides mathematical inevitability" evidence = {"framework": "Prime-based anchoring", "entropy_sources": 3} anchor = verification_engine.create_verification_anchor(claim, evidence) print(f"Verification Anchor Created: {anchor['verification_hash'][:16]}...") print(f"Confidence Score: {anchor['confidence_score']:.3f}") print(f"Integrity Metrics: {anchor['integrity_metrics']}") # Verify the claim verification = verification_engine.verify_claim(claim, evidence, anchor) print(f"\nVerification Result: {verification['verified']}") print(f"Integrity Correlation: {verification['integrity_correlation']:.3f}")