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>
Empirical refinement of Lemma 5.3: h_phi is non-constant on V(K_b)
alone (not just on the union) and likewise on V(K_c) alone, in every
one of 142,812 chord-apex+Kempe colourings tested (n in [12, 20]).
This is strictly stronger than what we previously reported.
The proof of Lemma 5.3 already constructs the (F, e_1, e_2) witness
from any consecutive same-Heawood failure on either Kempe cycle
through merged -- never needing the other cycle. Pull that out into
a separate Corollary 5.4 ("Per-cycle form"), which makes the
empirical-to-conjecture path more direct.
Update Remark 5.5 to:
- Cite Corollary 5.4 instead of the contrapositive of Lemma 5.3.
- Replace "non-constant on V(K_b) U V(K_c)" with the per-cycle form.
- Extend the empirical table with separate columns for K_b and K_c
non-constancy.
Also commit experiments/check_constancy_obstruction.py, the script
that produced these refined empirical findings. It additionally
records that no single named vertex (v_n, A_i, ..., A_{i+4}) is
structurally majority or minority -- the minority rates cluster in
31-39%, ruling out a single-vertex-mismatch identity.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis