Rename the shared helper module to a number-resistant name. Update
all 26 dependent scripts via sed.
Add experiments/test_n_21_to_24.py — extends the empirical check
beyond |V(G)| ≤ 20 to n_G ∈ [21, 24]. Checks per chord-apex+Kempe
colouring:
(1) h_φ constant on V(K_b)? (counterexample to Corollary 5.4)
(2) h_φ constant on V(K_b) ∪ V(K_c)? (counterexample to Conj 5.1)
(3) Deciding face exists?
Writes results incrementally to test_n_21_to_24_results.jsonl (one
JSON line per triangulation, plus n-level and grand summaries).
Emits PROGRESS lines every 10 minutes (default) to stdout for live
monitoring.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
experiments/check_S8_hit8_pG.py finds that all 30 |S|=8 bad
colourings with hit = 8 have p_G = 11 EXACTLY. Not p_G ∈ {9, 10, 11}
as I'd expected, but always 11.
This means: when |S| = 8 and 8 G'-pentagons are hit, the parent
triangulation v has NO degree-5 neighbours (= all 5 neighbours have
degree ≥ 6), and hence the reduced dual has 12 - 1 - 0 = 11
G'-pentagons. Three G'-pentagons are uncovered, not merely one.
Updated Remark (gprime-pigeonhole-stop) in paper to reflect this
stronger regularity: the size of S = V \ (V(K_b) ∪ V(K_c)) is
structurally tied to the count of pentagonal F_k adjacent to F_v in
chord-apex+Kempe colourings. A non-empirical proof of this is open.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis