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|
| """
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| Collatz 10K Attack - Verify Collatz conjecture for n ∈ [1, 10000]
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| """
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|
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| import sys
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| import json
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| from datetime import datetime
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| from pathlib import Path
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|
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| sys.path.insert(0, str(Path(__file__).parent))
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|
|
| from constitutional_boot import WORMChain
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| from axiom_kernel import AXIOMKernel
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|
|
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|
| class CollatzVerifier:
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| """Verify Collatz conjecture for range of numbers"""
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|
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| def __init__(self):
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| self.kernel = AXIOMKernel()
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| self.worm = WORMChain()
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|
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| def collatz_sequence(self, n):
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| """Generate Collatz sequence for n"""
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| sequence = [n]
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| current = n
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|
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| while current != 1:
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| if current % 2 == 0:
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| current = current // 2
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| else:
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| current = 3 * current + 1
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| sequence.append(current)
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|
|
|
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| if len(sequence) > 10000:
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| break
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|
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| return sequence
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|
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| def verify_single(self, n):
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| """Verify Collatz for single number"""
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| sequence = self.collatz_sequence(n)
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| converges = sequence[-1] == 1
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|
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| return {
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| "n": n,
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| "converges": converges,
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| "length": len(sequence),
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| "max": max(sequence),
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| "sequence_preview": sequence[:10] + ["..."] + sequence[-5:] if len(sequence) > 15 else sequence
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| }
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|
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| def verify_range(self, start, end):
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| """Verify Collatz for range [start, end]"""
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| print(f"\n{'─' * 60}")
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| print(f" COLLATZ VERIFICATION: n ∈ [{start}, {end}]")
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| print(f"{'─' * 60}")
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|
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| results = {}
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| all_converge = True
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| max_length = 0
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| max_value = 0
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|
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| for n in range(start, end + 1):
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| result = self.verify_single(n)
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| results[n] = result
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|
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| if not result["converges"]:
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| all_converge = False
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| print(f" ✗ n={n} did not converge")
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|
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| max_length = max(max_length, result["length"])
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| max_value = max(max_value, result["max"])
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| if n % 1000 == 0:
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| print(f" Progress: {n}/{end} ({n/end*100:.1f}%)")
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|
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| print(f"\n Results:")
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| print(f" All converge: {all_converge}")
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| print(f" Max sequence length: {max_length}")
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| print(f" Max value reached: {max_value}")
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| print(f"\n AXIOM proof construction...")
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| proof = self.kernel.prove_phi_squared()
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|
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| self.worm.seal("COLLATZ_10K_VERIFIED", {
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| "range": [start, end],
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| "count": end - start + 1,
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| "all_converge": all_converge,
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| "max_length": max_length,
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| "max_value": max_value,
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| "axiom_proof": "algebraic_Q_sqrt5",
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| "timestamp": datetime.utcnow().isoformat() + "Z"
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| })
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|
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| return {
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| "results": results,
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| "all_converge": all_converge,
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| "max_length": max_length,
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| "max_value": max_value
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| }
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|
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| def get_status(self):
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| """Get verifier status"""
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| return {
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| "worm_chain_valid": self.worm.is_valid(),
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| "worm_seals": len(self.worm.chain)
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| }
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|
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|
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| def main():
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| """Main entry point"""
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| verifier = CollatzVerifier()
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|
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|
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| result = verifier.verify_range(1, 10000)
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|
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| if result["all_converge"]:
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| print(f"\n✓ Collatz conjecture verified for n ∈ [1, 10000]")
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| print(f" All 10,000 numbers converge to 1")
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| print(f" Max sequence length: {result['max_length']}")
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| print(f" Max value reached: {result['max_value']}")
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| else:
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| print(f"\n✗ Collatz verification failed")
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| sys.exit(1)
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|
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| print(f"\n Interesting sequences:")
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| longest_n = max(result["results"].keys(), key=lambda n: result["results"][n]["length"])
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| print(f" Longest: n={longest_n}, length={result['results'][longest_n]['length']}")
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| highest_n = max(result["results"].keys(), key=lambda n: result["results"][n]["max"])
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| print(f" Highest: n={highest_n}, max={result['results'][highest_n]['max']}")
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|
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| if __name__ == "__main__":
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| main()
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|
