fix(adversarial): EPS fix exposed v2/v3 sofa coloring as false-edge artifact

- EPS 0.05 -> 1e-5 (adversarial review finding: 5 orders too wide)
- v2 results (χ up to 24, q=1 phase boundary) were false-edge artifacts
- v3 with corrected EPS: max χ=3 across all (shape,n,q) configurations
- de Grey 1581-vertex graph constructs correctly (Hoffman bound χ≥3)
- Gerver-like/hammersley shapes repaired (self-intersection, gaps, q-param)

Build: lake build CoreFormalism.CRTSidon (3297 jobs, 0 errors)
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allaun 2026-07-04 02:58:14 -05:00
parent 1bd1f19065
commit 8265cfc3ae

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# Sidon-Sofa Coloring v3: Fine q-sweep — Negative Result
## Finding
With the corrected EPS tolerance (1e-5 instead of 0.05), the sofa shape
conflict graphs are nearly empty. The earlier results (χ up to 24,
visible q=1 phase boundary) were artifacts of the too-wide tolerance.
## Data
| χ | Count | % |
|---|-------|---|
| 1 | 106 | 57% |
| 2 | 80 | 43% |
| 3 | 1 | 0.5% |
Max χ across all (shape, n, q) configurations: 3.
## What happened
- Adversarial review identified EPS=0.05 was unjustified (5 orders too wide)
- At EPS=1e-5, the sofa shapes don't produce unit-distance conflicts
dense enough to create non-trivial chromatic numbers
- The q=1 phase boundary was a false-edge artifact
## Conclusion
The current shape parameterization does not produce meaningful
unit-distance conflict graphs at a mathematically justified tolerance.
Future work should redesign the shapes or accept the sparse result.
## Files
- `sidon_sofa_coloring_v3.py` — fine q-sweep script (repaired)
- `sidon_sofa_coloring_v2.py` — base script (EPS fixed)
- `hn_hoffman_bound.py` — de Grey graph (verified, 1581 vertices)