experiments/test_n_21_to_24.py (run in flight) completed n=21:
- 192 triangulations of min degree 5.
- 392,370 chord-apex+Kempe colourings tested.
- 0 constancy violations on V(K_b), V(K_c), or V(K_b) ∪ V(K_c).
- 0 missing deciding faces.
Combined with the previous n≤20 results (= 142,812 colourings), the
total empirical verification of the deciding-face conjecture (hence
of Conjecture 5.1) is now 535,182 / 535,182 on chord-apex+Kempe
colourings up to |V(G)| ≤ 21.
Paper changes:
- Abstract + intro: updated to reflect 535,182 / 535,182 at n ≤ 21.
- Section 5.1 intro to the Heawood reduction: updated 0/142,812 →
0/535,182.
- Remark (Empirical near-proof, rem:heawood-empirical): extended
the table with the n=21 row (392,370 colourings, all
non-constant). Total row updated to n ≤ 21 / 535,182.
- Added paragraph noting that test_n_21_to_24.py is extending the
check to n ∈ {21, 22, 23, 24}; runs for n=22, 23, 24 are in
flight at time of writing.
COMMENTARY.md updates:
- Summary table updated: 142,812 → 535,182 (n ≤ 21).
- Added row for the deciding-face conjecture (= 535,182 verified).
Note: the detailed structural-coverage analysis (e.g., the 1,314
"bad" colourings + the 30 |S|=8 hit=8 sub-case) was performed on
n ≤ 20 only and is NOT yet recomputed for n=21. Those specific
numbers in the paper still refer to the n ≤ 20 dataset and are
correctly tagged as such.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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