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allaun
f1a050277b
48 test points across K=1..4 and 12 label sets (Sidon power sets, Sidon constructions, dense non-Sidon, prime-based). Results: K=1: ρ=-0.85 (products→SLOS), ρ=-0.94 (SLOS↔tensor) K=2: ρ=-0.88 (products→SLOS), ρ=-0.94 (SLOS↔tensor) K=3: ρ=-0.93 (products→SLOS), ρ=-0.98 (SLOS↔tensor) K=4: ρ=-0.93 (products→SLOS), tensor N/A (K>3) Key: all Spearman correlations are negative and strengthen with K. Sidon sets produce 1.5-2.3× higher KL divergence than same-size non-Sidon. Primes are intermediate: partially Sidon-like but weaker. DAG: 192 nodes, 96 edges, all individually checkpointed for resume. Resume with: python3 scripts/perceval_slos_verify.py --resume Receipt: docs/research/SLOS_SIDON_VERIFICATION_RECEIPT.md Build: N/A (Python/perceval verification, no Lean build)
8 lines
2 KiB
JSON
8 lines
2 KiB
JSON
{"module": "T1", "severity": "CRITICAL", "claim": "K=1: Spearman \u03c1=-0.846 (n=12), lower distinct_ratio\u2192higher KL CONFIRMED \u2014 Sidon structure predicts SLOS concentration ordering", "verdict": "PASS", "details": {"k": 1, "spearman_rho": -0.846, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=1: SLOS vs tensor \u03c1=-0.944 (n=12), METHODS AGREE on ordering", "verdict": "PASS", "details": {"k": 1, "spearman_rho_tensor_vs_slos": -0.5315, "spearman_rho_tensor_ratio_vs_slos_kl": -0.9441, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=2: Spearman \u03c1=-0.880 (n=12), lower distinct_ratio\u2192higher KL CONFIRMED \u2014 Sidon structure predicts SLOS concentration ordering", "verdict": "PASS", "details": {"k": 2, "spearman_rho": -0.8795, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=2: SLOS vs tensor \u03c1=-0.937 (n=12), METHODS AGREE on ordering", "verdict": "PASS", "details": {"k": 2, "spearman_rho_tensor_vs_slos": -0.5035, "spearman_rho_tensor_ratio_vs_slos_kl": -0.9371, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=3: Spearman \u03c1=-0.930 (n=12), lower distinct_ratio\u2192higher KL CONFIRMED \u2014 Sidon structure predicts SLOS concentration ordering", "verdict": "PASS", "details": {"k": 3, "spearman_rho": -0.9298, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=3: SLOS vs tensor \u03c1=-0.979 (n=12), METHODS AGREE on ordering", "verdict": "PASS", "details": {"k": 3, "spearman_rho_tensor_vs_slos": -0.3077, "spearman_rho_tensor_ratio_vs_slos_kl": -0.979, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=4: Spearman \u03c1=-0.930 (n=12), lower distinct_ratio\u2192higher KL CONFIRMED \u2014 Sidon structure predicts SLOS concentration ordering", "verdict": "PASS", "details": {"k": 4, "spearman_rho": -0.9298, "n": 12}}
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{"module": "T1", "severity": "CRITICAL", "claim": "K=4: insufficient data for tensor vs SLOS", "verdict": "FAIL", "details": {"k": 4, "reason": "insufficient tensor results"}}
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