From d36c2513cc790474d3e5ed78020c1e8e97ec7797 Mon Sep 17 00:00:00 2001 From: didericis Date: Mon, 25 May 2026 08:40:01 -0400 Subject: [PATCH] face_monochromatic_pairs: fix Conjecture 5.26 (strengthening) coverage claim MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Previous commit (00229fa) incorrectly extended the empirical verification of Conjecture 5.26 (strengthening, clauses 1-4) to n=21. The running test (test_n_21_to_24.py) checks: - Non-constancy on V(K_b), V(K_c), V(K_b) ∪ V(K_c). - Deciding-face existence. These verify Conjecture 5.1 (clauses 1-3) via Corollary 5.4 and via the Heawood-face-sum route, respectively. They do NOT verify clause (4) of the strengthening (Conjecture 5.26), which requires constructing the subdivided graph and checking the new f_n's edge colouring. Conjecture 5.26 has been verified at n ≤ 20 (142,812 colourings) only, via `check_conj_final_scaled.py` (which explicitly constructs the clause-3 subdivision and checks clause-4). The n=21 results extend the weaker checks but NOT the strengthening. Paper fixes: - Abstract: clarified that strengthened conjecture is at n ≤ 20 (142,812), unstrengthened (clauses 1-3) at n ≤ 21 (535,182). - Intro paragraph after "we propose": same clarification. COMMENTARY.md fix: - Summary table: "Conjecture 5.26 (strengthening)" row reverted to "142,812 / 142,812 (n ≤ 20)". The other rows (about Heawood- based checks) remain at 535,182 / 535,182 (n ≤ 21). Co-Authored-By: Claude Opus 4.7 --- papers/face_monochromatic_pairs/COMMENTARY.md | 2 +- papers/face_monochromatic_pairs/paper.pdf | Bin 1329224 -> 1329164 bytes papers/face_monochromatic_pairs/paper.tex | 16 +++++++++------- 3 files changed, 10 insertions(+), 8 deletions(-) diff --git a/papers/face_monochromatic_pairs/COMMENTARY.md b/papers/face_monochromatic_pairs/COMMENTARY.md index ad3287c..f97f04a 100644 --- a/papers/face_monochromatic_pairs/COMMENTARY.md +++ b/papers/face_monochromatic_pairs/COMMENTARY.md @@ -11,7 +11,7 @@ computationally vs what remains to be proven structurally. | claim | status | empirical evidence | |---|---|---| | Conjecture 5.1 (clauses 1–3) | conjecture | ✓ 535,182 / 535,182 (n ≤ 21, direct witness search) | -| Conjecture 5.3 (clauses 1–4, strengthening) | conjecture | ✓ 535,182 / 535,182 (n ≤ 21) | +| Conjecture 5.26 (clauses 1–4, strengthening) | conjecture | ✓ 142,812 / 142,812 (n ≤ 20, via direct clause-4 check in `check_conj_final_scaled.py`) | | Non-constancy of `h_φ` on `V(K_b) ∪ V(K_c)` | sufficient to prove 5.1 via Lemma 5.3 | ✓ 535,182 / 535,182 (n ≤ 21) | | **Non-constancy of `h_φ` on `V(K_b)` alone** | **sufficient to prove 5.1 via Corollary 5.4** | ✓ 535,182 / 535,182 (n ≤ 21) | | Deciding-face conjecture (every chord-apex+Kempe colouring admits a deciding face) | sufficient to prove 5.1 via Heawood face-sum | ✓ 535,182 / 535,182 (n ≤ 21) | diff --git a/papers/face_monochromatic_pairs/paper.pdf b/papers/face_monochromatic_pairs/paper.pdf index ddf002dfc0135bdd0888455fd070ac34599e5934..0fa153caeb06c6f8b82a1eaba7db957ccfa668df 100644 GIT binary patch delta 119185 zcmV(_K-9m;kWq|~QII17Gc}hHtqCcA)mqDT+eQ-I`zyE$c*cOy54_^dIEs~ICXO?* zGP7{JfJj(`LjoKCw5;QN{M@SQ1_2pPoaJnUepGi?S5@D7P~TiXdU9#gRS^}bPFL4& zSIT6OPKs4(Y^36Bb-i7^4ldV9=fShJ(ZR*@@WsoYUS52EMZK3Vo~?^Cxc=dPVjbF| z2!5vCvmdTrQ5P$I`c}rTzkeE=U2pqNo?@Vv$ZaQU!GrGKL7DsS#0fev5IY! z8Cs9a#zxjZyXl9nTx%U{hG^k`NSj23S;a#9pLJdY6&COlHRtUGL&tAI({=3T{v!-*-Y1tyiz zk-~^O$~_u+Fofc8kDp#Y1^e 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