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SilverSight/.openresearch/artifacts/EVAL.md
allaun 12f84c8973 feat: agent computation results — 16 QRNG runs, Hoffman bound, v3 sweep, CMYK fix 
Agent outputs from the 9-agent parallel run:

CMYKColoringCore.lean:
- Restored §3 section header (accidentally deleted during native_decide cleanup)
- Proof uses dec_trivial per AGENTS.md §5 (no native_decide, no sorries)
- All 8 sections (§1-§8) verified present

Computation scripts:
- hn_hoffman_bound.py: Hadwiger-Nelson Hoffman spectral bound
- sidon_sofa_coloring_v3.py: Fine q-value sweep + n=34 extension
- mcp_worker.py: MCP autoproof worker process

Artifacts (16 QRNG-seeded runs):
- sidon_sofa_coloring_v2_qrng_*.json (16 files, 106KB each)
- sidon_sofa_coloring_v2.json (base run)
- sidon_sofa_coloring_v2_cupfox.json (CupFox variant)
- hn_hoffman_bound.json (Hoffman bound results)
- EVAL_cupfox.md (evaluation document)
2026-07-04 02:02:50 -05:00

3 KiB
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Sidon-Sofa Coloring: Direction A v2 (DSATUR + q-sweep) Results

Experiment: sidon_sofa_coloring_v2 Date: 2026-07-04T06:22:00Z Seed: 0 SHA-256: f362d2128e278f33848968d517d19b9013d3f39e569e922d4c59508c9f9f63d3

Chromatic method: DSATUR + exact for <=16 vertices Tolerance band: |d - 1| < 0.05 Motion samples: 24 q-values swept: ['1/2', '3/4', '1', '4/3', '2']

Conflict Graph Statistics (best q per shape/n)

Shape n Best q Area Edges Max Deg χ
half_disc 8 1/2 0.2136 216 23 12
half_disc 13 1/2 0.2184 217 23 12
half_disc 21 1/2 0.2200 217 23 12
rectangle 8 1/2 0.7594 242 23 12
rectangle 13 1/2 0.7594 275 23 23
rectangle 21 1/2 0.7594 276 23 24
sidon_polar 8 1/2 0.2789 203 22 7
sidon_polar 13 1/2 0.3652 229 23 14
sidon_polar 21 1/2 0.3052 203 22 7
gerver_like 8 1/2 0.4394 224 23 14
gerver_like 13 1/2 0.5738 240 23 16
gerver_like 21 1/2 0.6103 240 23 16
hammersley 8 1/2 0.5132 237 23 14
hammersley 13 1/2 0.5625 239 23 15
hammersley 21 1/2 0.5770 239 23 15

A*(n, χ=7) by q-profile (the saturation regime)

Shape n q=1/2 q=3/4 q=1 q=4/3 q=2
half_disc 8 0.0000 0.0000 0.0000 0.0000 0.0000
half_disc 13 0.0000 0.0000 0.0000 0.0000 0.0000
half_disc 21 0.0000 0.0000 0.0000 0.0000 0.0000
rectangle 8 0.0000 0.0000 0.0000 0.0000 0.0000
rectangle 13 0.0000 0.0000 0.0000 0.0000 0.0000
rectangle 21 0.0000 0.0000 0.0000 0.0000 0.0000
sidon_polar 8 0.2789 0.0000 0.0000 0.0000 0.0000
sidon_polar 13 0.0000 0.0000 0.0000 0.0000 0.0000
sidon_polar 21 0.3052 0.0000 0.0000 0.0000 0.0000
gerver_like 8 0.0000 0.0000 0.0000 0.0000 0.0000
gerver_like 13 0.0000 0.0000 0.0000 0.0000 0.0000
gerver_like 21 0.0000 0.0000 0.0000 0.0000 0.0000
hammersley 8 0.0000 0.0000 0.0000 0.0000 0.0000
hammersley 13 0.0000 0.0000 0.0000 0.0000 0.0000
hammersley 21 0.0000 0.0000 0.0000 0.0000 0.0000

Verdict

v2 uses DSATUR (polynomial) chromatic number instead of brute-force, fixing the v1 timeout. q-profile sweep tests the toroidal/poloidal refinement prediction: q < 1 (poloidal-dominated, Gerver-like) should yield different conflict structure than q > 1 (toroidal-dominated, Hammersley-like). q = 1 (degenerate) is predicted to fail.

What to look for:

  • Does χ vary across q-values? (toroidal/poloidal effect)
  • Does q=1 produce degenerate (χ=1, no edges) conflict graphs?
  • Does q < 1 (Gerver-like) produce higher χ than q > 1?
  • Does larger n produce more edges and higher χ?