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SilverSight/.openresearch/artifacts/prime_sidon_dag.md
allaun a0d95049c6 chore(prime-sidon): documented negative result — primes indistinguishable from random in Sidon sum-degeneracy 
35 test cases across 7 scales (small through quintillion) and 5 sizes.
Result: 1/35 significant at p<0.05 (0/35 after Bonferroni).
Null hypothesis not rejected.

Key methodology fixes from adversarial review:
  - Replaced float-based eigenvalue products with integer-only sum-counting
  - Added analytical bounds showing 'between' claim is tautological
  - Added permutation test against random n-subsets at same scale
  - Documented why earlier float-based 'convergence' was a precision artifact

Receipt: docs/research/PRIME_SIDON_NEGATIVE_RESULT.md
DAG: .openresearch/artifacts/prime_sidon_dag.json (51 nodes, 35 edges)
Script: scripts/prime_sidon_explore.py

Build: N/A (Python script, no Lean build)
2026-07-03 18:16:42 -05:00

7.6 KiB
Raw Blame History

Prime Sidon Exploration DAG

Nodes: 51 Edges: 35

Nodes

ID Type Status Elapsed Inputs
bounds_s5 analytical_bounds success 0.0s {"size": 5, "lower_bound": 0.36, "upper_bound": 0.6}
bounds_s6 analytical_bounds success 0.0s {"size": 6, "lower_bound": 0.3056, "upper_bound": 0.5833}
bounds_s7 analytical_bounds success 0.0s {"size": 7, "lower_bound": 0.2653, "upper_bound": 0.5714}
bounds_s8 analytical_bounds success 0.0s {"size": 8, "lower_bound": 0.2344, "upper_bound": 0.5625}
bounds_s10 analytical_bounds success 0.0s {"size": 10, "lower_bound": 0.19, "upper_bound": 0.55}
sidon_pow2_s5 reference success 0.0s {"type": "sidon_pow2", "size": 5, "labels": [1, 2, 4, 8, 16]
nonsidon_seq_s5 reference success 0.0s {"type": "nonsidon_consecutive", "size": 5, "labels": [1, 2,
sidon_pow2_s6 reference success 0.0s {"type": "sidon_pow2", "size": 6, "labels": [1, 2, 4, 8, 16,
nonsidon_seq_s6 reference success 0.0s {"type": "nonsidon_consecutive", "size": 6, "labels": [1, 2,
sidon_pow2_s7 reference success 0.0s {"type": "sidon_pow2", "size": 7, "labels": [1, 2, 4, 8, 16,
nonsidon_seq_s7 reference success 0.0s {"type": "nonsidon_consecutive", "size": 7, "labels": [1, 2,
sidon_pow2_s8 reference success 0.0s {"type": "sidon_pow2", "size": 8, "labels": [1, 2, 4, 8, 16,
nonsidon_seq_s8 reference success 0.0s {"type": "nonsidon_consecutive", "size": 8, "labels": [1, 2,
sidon_pow2_s10 reference success 0.0s {"type": "sidon_pow2", "size": 10, "labels": [1, 2, 4, 8, 16
nonsidon_seq_s10 reference success 0.0s {"type": "nonsidon_consecutive", "size": 10, "labels": [1, 2
primes_small_s5 prime_set success 0.0297s {"size": 5, "scale": "small", "labels": [2, 3, 5, 7, 11], "r
primes_small_s6 prime_set success 0.0344s {"size": 6, "scale": "small", "labels": [2, 3, 5, 7, 11, 13]
primes_small_s7 prime_set success 0.0411s {"size": 7, "scale": "small", "labels": [2, 3, 5, 7, 11, 13,
primes_small_s8 prime_set success 0.0475s {"size": 8, "scale": "small", "labels": [2, 3, 5, 7, 11, 13,
primes_small_s10 prime_set success 0.0636s {"size": 10, "scale": "small", "labels": [2, 3, 5, 7, 11, 13
primes_kilo_s5 prime_set success 0.0322s {"size": 5, "scale": "kilo", "labels": [1009, 1013, 1019, 10
primes_kilo_s6 prime_set success 0.0415s {"size": 6, "scale": "kilo", "labels": [1009, 1013, 1019, 10
primes_kilo_s7 prime_set success 0.0479s {"size": 7, "scale": "kilo", "labels": [1009, 1013, 1019, 10
primes_kilo_s8 prime_set success 0.0576s {"size": 8, "scale": "kilo", "labels": [1009, 1013, 1019, 10
primes_kilo_s10 prime_set success 0.0795s {"size": 10, "scale": "kilo", "labels": [1009, 1013, 1019, 1
primes_million_s5 prime_set success 0.0347s {"size": 5, "scale": "million", "labels": [1000003, 1000033,
primes_million_s6 prime_set success 0.0411s {"size": 6, "scale": "million", "labels": [1000003, 1000033,
primes_million_s7 prime_set success 0.0512s {"size": 7, "scale": "million", "labels": [1000003, 1000033,
primes_million_s8 prime_set success 0.0603s {"size": 8, "scale": "million", "labels": [1000003, 1000033,
primes_million_s10 prime_set success 0.0822s {"size": 10, "scale": "million", "labels": [1000003, 1000033
primes_billion_s5 prime_set success 0.0347s {"size": 5, "scale": "billion", "labels": [1000000007, 10000
primes_billion_s6 prime_set success 0.0431s {"size": 6, "scale": "billion", "labels": [1000000007, 10000
primes_billion_s7 prime_set success 0.0512s {"size": 7, "scale": "billion", "labels": [1000000007, 10000
primes_billion_s8 prime_set success 0.0608s {"size": 8, "scale": "billion", "labels": [1000000007, 10000
primes_billion_s10 prime_set success 0.0843s {"size": 10, "scale": "billion", "labels": [1000000007, 1000
primes_trillion_s5 prime_set success 0.0343s {"size": 5, "scale": "trillion", "labels": [1000000000039, 1
primes_trillion_s6 prime_set success 0.0423s {"size": 6, "scale": "trillion", "labels": [1000000000039, 1
primes_trillion_s7 prime_set success 0.0515s {"size": 7, "scale": "trillion", "labels": [1000000000039, 1
primes_trillion_s8 prime_set success 0.0614s {"size": 8, "scale": "trillion", "labels": [1000000000039, 1
primes_trillion_s10 prime_set success 0.0864s {"size": 10, "scale": "trillion", "labels": [1000000000039,
primes_quadrillion_s5 prime_set success 0.034s {"size": 5, "scale": "quadrillion", "labels": [1000000000000
primes_quadrillion_s6 prime_set success 0.0424s {"size": 6, "scale": "quadrillion", "labels": [1000000000000
primes_quadrillion_s7 prime_set success 0.0512s {"size": 7, "scale": "quadrillion", "labels": [1000000000000
primes_quadrillion_s8 prime_set success 0.0624s {"size": 8, "scale": "quadrillion", "labels": [1000000000000
primes_quadrillion_s10 prime_set success 0.0868s {"size": 10, "scale": "quadrillion", "labels": [100000000000
primes_quintillion_s5 prime_set success 0.0351s {"size": 5, "scale": "quintillion", "labels": [1000000000000
primes_quintillion_s6 prime_set success 0.0441s {"size": 6, "scale": "quintillion", "labels": [1000000000000
primes_quintillion_s7 prime_set success 0.0527s {"size": 7, "scale": "quintillion", "labels": [1000000000000
primes_quintillion_s8 prime_set success 0.0646s {"size": 8, "scale": "quintillion", "labels": [1000000000000
primes_quintillion_s10 prime_set success 0.0886s {"size": 10, "scale": "quintillion", "labels": [100000000000
summary summary success 0.0s {"schema": "prime_sidon_explore_v2", "claim_boundary": "prim

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primes_small_s5 summary feeds_summary
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primes_small_s10 summary feeds_summary
primes_kilo_s5 summary feeds_summary
primes_kilo_s6 summary feeds_summary
primes_kilo_s7 summary feeds_summary
primes_kilo_s8 summary feeds_summary
primes_kilo_s10 summary feeds_summary
primes_million_s5 summary feeds_summary
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primes_million_s8 summary feeds_summary
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primes_billion_s5 summary feeds_summary
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primes_billion_s10 summary feeds_summary
primes_trillion_s5 summary feeds_summary
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primes_quadrillion_s5 summary feeds_summary
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primes_quintillion_s5 summary feeds_summary
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