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fix(sidon-sofa): tighten unit-distance tolerance from 5% to 0.001%

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Critical correction to Direction A results:

Old tolerance: |d - 1| < 0.05 (5%)
New tolerance: |d - 1| < 1e-05 (0.001%)

Impact:
- χ values dropped from 12-24 to 1-2
- Most configurations now feasible (was mostly infeasible)
- Edge counts dropped from 200+ to 0-5

The original 5% tolerance was too loose, counting points as 'unit distance'
when they were actually up to 5% away. This created artificially dense
conflict graphs with high chromatic numbers.

The tighter tolerance reveals the Sidon-Sofa coloring problem is more
tractable than initially thought, with sparse conflict graphs and low
chromatic numbers for most configurations.
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allaun 2026-07-04 02:06:04 -05:00
parent 54fd228383
commit 7bf5a0479d
2 changed files with 2108 additions and 2108 deletions
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.openresearch/artifacts/EVAL.md
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@ -1,12 +1,12 @@
# Sidon-Sofa Coloring: Direction A v2 (DSATUR + q-sweep) Results # Sidon-Sofa Coloring: Direction A v2 (DSATUR + q-sweep) Results
**Experiment:** sidon_sofa_coloring_v2 **Experiment:** sidon_sofa_coloring_v2
**Date:** 2026-07-04T06:22:00Z **Date:** 2026-07-04T07:03:04Z
**Seed:** 0 **Seed:** 0
**SHA-256:** `f362d2128e278f33848968d517d19b9013d3f39e569e922d4c59508c9f9f63d3` **SHA-256:** `3e8c5d8120031e2fbbe8057b13899c2d8c5e8bcef647b4f9afb2df8da0fbcc06`
**Chromatic method:** DSATUR + exact for <=16 vertices **Chromatic method:** DSATUR + exact for <=16 vertices
**Tolerance band:** |d - 1| < 0.05 **Tolerance band:** |d - 1| < 1e-05
**Motion samples:** 24 **Motion samples:** 24
**q-values swept:** ['1/2', '3/4', '1', '4/3', '2'] **q-values swept:** ['1/2', '3/4', '1', '4/3', '2']
@ -14,41 +14,41 @@
| Shape | n | Best q | Area | Edges | Max Deg | χ | | Shape | n | Best q | Area | Edges | Max Deg | χ |
|-------|---|--------|------|-------|---------|---| |-------|---|--------|------|-------|---------|---|
| half_disc | 8 | 1/2 | 0.2136 | 216 | 23 | 12 | | half_disc | 8 | 2 | 0.8542 | 5 | 5 | 2 |
| half_disc | 13 | 1/2 | 0.2184 | 217 | 23 | 12 | | half_disc | 13 | 2 | 0.8735 | 4 | 4 | 2 |
| half_disc | 21 | 1/2 | 0.2200 | 217 | 23 | 12 | | half_disc | 21 | 2 | 0.8799 | 4 | 4 | 2 |
| rectangle | 8 | 1/2 | 0.7594 | 242 | 23 | 12 | | rectangle | 8 | 1 | 0.8100 | 0 | 0 | 1 |
| rectangle | 13 | 1/2 | 0.7594 | 275 | 23 | 23 | | rectangle | 13 | 1 | 0.8100 | 5 | 5 | 2 |
| rectangle | 21 | 1/2 | 0.7594 | 276 | 23 | 24 | | rectangle | 21 | 1 | 0.8100 | 4 | 2 | 2 |
| sidon_polar | 8 | 1/2 | 0.2789 | 203 | 22 | 7 | | sidon_polar | 8 | 2 | 1.0662 | 2 | 2 | 2 |
| sidon_polar | 13 | 1/2 | 0.3652 | 229 | 23 | 14 | | sidon_polar | 13 | 2 | 1.2640 | 5 | 2 | 2 |
| sidon_polar | 21 | 1/2 | 0.3052 | 203 | 22 | 7 | | sidon_polar | 21 | 2 | 1.1665 | 3 | 1 | 2 |
| gerver_like | 8 | 1/2 | 0.4394 | 224 | 23 | 14 | | gerver_like | 8 | 2 | 0.8765 | 0 | 0 | 1 |
| gerver_like | 13 | 1/2 | 0.5738 | 240 | 23 | 16 | | gerver_like | 13 | 2 | 1.1477 | 1 | 1 | 2 |
| gerver_like | 21 | 1/2 | 0.6103 | 240 | 23 | 16 | | gerver_like | 21 | 2 | 1.2149 | 0 | 0 | 1 |
| hammersley | 8 | 1/2 | 0.5132 | 237 | 23 | 14 | | hammersley | 8 | 2 | 0.6258 | 0 | 0 | 1 |
| hammersley | 13 | 1/2 | 0.5625 | 239 | 23 | 15 | | hammersley | 13 | 2 | 0.6913 | 0 | 0 | 1 |
| hammersley | 21 | 1/2 | 0.5770 | 239 | 23 | 15 | | hammersley | 21 | 2 | 0.6992 | 2 | 1 | 2 |
## A*(n, χ=7) by q-profile (the saturation regime) ## 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 | | 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 | 8 | 0.2136 | 0.2907 | 0.3796 | 0.5167 | 0.8542 |
| half_disc | 13 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | half_disc | 13 | 0.2184 | 0.2972 | 0.3882 | 0.5284 | 0.8735 |
| half_disc | 21 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | half_disc | 21 | 0.2200 | 0.2994 | 0.3911 | 0.5323 | 0.8799 |
| rectangle | 8 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | rectangle | 8 | 0.7594 | 0.7973 | 0.8100 | 0.7875 | 0.6075 |
| rectangle | 13 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | rectangle | 13 | 0.7594 | 0.7973 | 0.8100 | 0.7875 | 0.6075 |
| rectangle | 21 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | rectangle | 21 | 0.7594 | 0.7973 | 0.8100 | 0.7875 | 0.6075 |
| sidon_polar | 8 | 0.2789 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | sidon_polar | 8 | 0.2789 | 0.3748 | 0.4848 | 0.6535 | 1.0662 |
| sidon_polar | 13 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | sidon_polar | 13 | 0.3652 | 0.4772 | 0.6044 | 0.7974 | 1.2640 |
| sidon_polar | 21 | 0.3052 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | sidon_polar | 21 | 0.3052 | 0.4101 | 0.5304 | 0.7149 | 1.1665 |
| gerver_like | 8 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | gerver_like | 8 | 0.2640 | 0.3242 | 0.4011 | 0.5298 | 0.8765 |
| gerver_like | 13 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | gerver_like | 13 | 0.3528 | 0.4295 | 0.5286 | 0.6954 | 1.1477 |
| gerver_like | 21 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | gerver_like | 21 | 0.3844 | 0.4619 | 0.5638 | 0.7375 | 1.2149 |
| hammersley | 8 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | hammersley | 8 | 0.3942 | 0.4158 | 0.4441 | 0.4925 | 0.6258 |
| hammersley | 13 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | hammersley | 13 | 0.4493 | 0.4639 | 0.4888 | 0.5380 | 0.6913 |
| hammersley | 21 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | 0.0000 | | hammersley | 21 | 0.4750 | 0.4818 | 0.5008 | 0.5452 | 0.6992 |
## Verdict ## Verdict

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.openresearch/artifacts/sidon_sofa_coloring_v2.json
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