Direction B results: Gerver sofa at T=100 produces χ=2 (bipartite),
not reaching χ≥4. Confirms 'unit-distance events are measure-zero.'
CRTSidonN: auto-generated, ~10 remaining structural issues. Design is
correct (natural n-moduli extension of CRT Sidon theorem).
Adds measured results from two CPU runs:
1. HN spectral database (run 019f2c52):
Hoffman bound on 6 graphs. Tight for regular (path, cycle, complete),
gap=1 for unit-distance (Moser spindle, Golomb graph). Pattern
suggests spectral detection loses exactly 1 color for unit-distance graphs.
2. q-profile sweep (run 019f2d9c):
Sweeps q = L₁/L₀ over coprime fractions. REFUTES the prediction
that q < 1 (poloidal-dominated) is Sidon-favorable: q > 1 has
100% Sidon rate vs 40-60% for q < 1. The toroidal/poloidal analogy
doesn't directly control Sidon-ness via the q-ratio direction.
For non-Sidon label sets: 0% Sidon at ALL q values (q-profile
cannot CREATE Sidon from non-Sidon, only PRESERVE it).
All scripts, formal modules, and docs already committed to main.
This commit adds the experiment artifact JSONs and EVALs.
The photonic_sidon_search.py script now uses encoder_q16.py (exact
Q16_16 fixed-point arithmetic) instead of float-based encoding.
This updates the evidence file with slightly different omega values
due to exact arithmetic, but all 18 tests still pass.
EVAL.md was regenerated with the photonic search results.
Imported from silversight-578413a4/orx/sidon-sofa-coloring-direction-a-finite-sidon-sofas-a-n-28a68926:
- photonic_sidon_search.py: Perceval SLOS-based Sidon search (1013 lines)
- TOROIDAL_POLOIDAL_REFINEMENT.md: Elsasser 1946 toroidal/poloidal decomposition (301 lines)
- photonic_sidon_evidence.jsonl: Test evidence (17 PASS, 1 FAIL - DNA encoder test)
- EVAL_photonic.md: Photonic search evaluation
Note: photonic_sidon_search.py has 1 test failure (T6_dna) that needs investigation.
The script also overwrote EVAL.md during execution, which has been restored from git.
Critical correction to Direction A results:
Old tolerance: |d - 1| < 0.05 (5%)
New tolerance: |d - 1| < 1e-05 (0.001%)
Impact:
- χ values dropped from 12-24 to 1-2
- Most configurations now feasible (was mostly infeasible)
- Edge counts dropped from 200+ to 0-5
The original 5% tolerance was too loose, counting points as 'unit distance'
when they were actually up to 5% away. This created artificially dense
conflict graphs with high chromatic numbers.
The tighter tolerance reveals the Sidon-Sofa coloring problem is more
tractable than initially thought, with sparse conflict graphs and low
chromatic numbers for most configurations.
True Sidon sets stay Sidon across all 50 modulus configs. Non-Sidon never become Sidon.
Capacity: 8→43.7b, 12→74.3b, 16→106.2b headroom.
Integer-only, no float, correct CRT reconstruction.
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)
