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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

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# 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 |
## Edges
| From | To | Type |
|------|----|------|
| primes_small_s5 | summary | feeds_summary |
| primes_small_s6 | summary | feeds_summary |
| primes_small_s7 | summary | feeds_summary |
| primes_small_s8 | summary | feeds_summary |
| 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 |
| primes_million_s6 | summary | feeds_summary |
| primes_million_s7 | summary | feeds_summary |
| primes_million_s8 | summary | feeds_summary |
| primes_million_s10 | summary | feeds_summary |
| primes_billion_s5 | summary | feeds_summary |
| primes_billion_s6 | summary | feeds_summary |
| primes_billion_s7 | summary | feeds_summary |
| primes_billion_s8 | summary | feeds_summary |
| primes_billion_s10 | summary | feeds_summary |
| primes_trillion_s5 | summary | feeds_summary |
| primes_trillion_s6 | summary | feeds_summary |
| primes_trillion_s7 | summary | feeds_summary |
| primes_trillion_s8 | summary | feeds_summary |
| primes_trillion_s10 | summary | feeds_summary |
| primes_quadrillion_s5 | summary | feeds_summary |
| primes_quadrillion_s6 | summary | feeds_summary |
| primes_quadrillion_s7 | summary | feeds_summary |
| primes_quadrillion_s8 | summary | feeds_summary |
| primes_quadrillion_s10 | summary | feeds_summary |
| primes_quintillion_s5 | summary | feeds_summary |
| primes_quintillion_s6 | summary | feeds_summary |
| primes_quintillion_s7 | summary | feeds_summary |
| primes_quintillion_s8 | summary | feeds_summary |
| primes_quintillion_s10 | summary | feeds_summary |
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