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95 lines
3 KiB
Python
95 lines
3 KiB
Python
#!/usr/bin/env python3
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"""
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entropic_collision_prober.py — Entropic Collision debt calculation for Sidon sets
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Computes the sumset entropy of a candidate set A:
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H_sum(A) = - sum (p(s) * log2(p(s))) where s = a + b for a, b in A, a <= b
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Checks for entropy/compression spoofing by verifying if:
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|H_sum(A) - predicted_entropy| < epsilon
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"""
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from __future__ import annotations
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import argparse
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import json
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import math
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from typing import Dict, List, Tuple
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def compute_sumset_entropy(A: List[int]) -> Tuple[float, int, Dict[int, int]]:
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"""Compute the exact sumset entropy and pair-sum frequency map.
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All calculations are done with precise frequency maps.
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Returns:
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entropy: Shannons entropy (in bits)
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collisions: number of duplicate pair-sums (C_B2 collision debt)
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sums: dictionary of pair sums and their counts
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"""
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n = len(A)
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sums = {}
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total_pairs = 0
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for i in range(n):
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for j in range(i, n):
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s = A[i] + A[j]
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sums[s] = sums.get(s, 0) + 1
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total_pairs += 1
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# Calculate Shannon entropy
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entropy = 0.0
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collisions = 0
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for s, count in sums.items():
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if count > 1:
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collisions += (count - 1)
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p = count / total_pairs
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entropy -= p * math.log2(p)
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return entropy, collisions, sums
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def main() -> int:
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parser = argparse.ArgumentParser(description="Entropic Collision Prober")
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parser.add_argument("--set", type=int, nargs="+", default=[1, 3, 7, 12, 20, 30, 44, 65],
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help="The candidate set (integer elements)")
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parser.add_argument("--output", default="entropic_collision_receipt.json", help="Output receipt path")
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args = parser.parse_args()
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A = sorted(list(set(args.set)))
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n = len(A)
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if n < 2:
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print("[-] Error: Candidate set must have at least 2 distinct elements.")
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return 1
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entropy, collisions, sums = compute_sumset_entropy(A)
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# Maximum possible entropy is when all pair-sums are distinct (true Sidon set)
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total_pairs = n * (n + 1) // 2
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max_possible_entropy = math.log2(total_pairs)
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# Deviation metric (entropy spoof check)
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entropy_deficit = max_possible_entropy - entropy
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res = {
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"candidate_set": A,
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"set_size": n,
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"total_pairs": total_pairs,
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"unique_sums": len(sums),
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"collisions_debt": collisions,
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"observed_entropy": entropy,
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"max_possible_entropy": max_possible_entropy,
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"entropy_deficit": entropy_deficit,
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"is_sidon": collisions == 0,
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"claim_boundary": "entropic-collision-debt-only"
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}
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with open(args.output, "w") as f:
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json.dump(res, f, indent=2)
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print(f"[+] Observed Entropy: {entropy:.6f} bits (Max: {max_possible_entropy:.6f} bits)")
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print(f"[+] Deficit: {entropy_deficit:.6f} bits | Collisions: {collisions}")
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print(f"[+] Entropic collision receipt saved to: {args.output}")
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return 0
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if __name__ == "__main__":
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import sys
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sys.exit(main())
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