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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.
1.5 KiB
1.5 KiB
Hadwiger-Nelson Spectral Database
Date: 2026-07-04T08:50:51Z
SHA-256: 6af248bdf51d4a90b6e286e4decc33f60b153b4b162c677ecfbaf9f12b20641c
Includes de Grey: False
Spectral Bounds Comparison
| Graph | n | e | λ_max | λ_min | Hoffman | χ_Hoff | Welch-Wynn | χ_WW | Known χ | Gap |
|---|---|---|---|---|---|---|---|---|---|---|
| Moser spindle | 7 | 12 | 3.6458 | -2.0000 | 2.8229 | 3 | N/A | None | 4 | gap=1 |
| Golomb graph (8 vertices, 10 edges) | 8 | 10 | 2.6813 | -2.3234 | 2.1541 | 3 | N/A | None | 4 | gap=1 |
| Empty graph (10v baseline) | 10 | 0 | 0.0000 | 0.0000 | inf | None | N/A | None | 1 | ? |
| Path graph P10 (baseline) | 10 | 9 | 1.9190 | -1.9190 | 2.0000 | 2 | N/A | None | 2 | tight |
| Cycle C5 (baseline) | 5 | 5 | 2.0000 | -1.6180 | 2.2361 | 3 | N/A | None | 3 | tight |
| Complete K4 (baseline) | 4 | 6 | 3.0000 | -1.0000 | 4.0000 | 4 | N/A | None | 4 | tight |
Key Findings
- Hoffman bound (χ ≥ 1 - λ_max/λ_min): classic spectral bound
- Welch-Wynn bound (χ ≥ n/(n - λ_max)): another spectral bound
- Gap: difference between best spectral bound and known chromatic number
- 'tight' = spectral bound matches known χ
- 'gap=N' = spectral bound is N below known χ
The gap measures how much chromatic information is NOT captured by the spectrum. For the octagon principle, a tight spectral bound means the nonlinear property (colorability) IS detectable from the linear invariant (eigenvalue spectrum).