MODERN_EO_11110.md

# 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}")