# 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)
