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}")