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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)