didericis/math-research
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

face_monochromatic_pairs: fix Conjecture 5.26 (strengthening) coverage claim

Browse Source 
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 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-25 08:40:01 -04:00
parent 00229fa460
commit d36c2513cc
3 changed files with 10 additions and 8 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/face_monochromatic_pairs/COMMENTARY.md
+1 -1
View File
@@ -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) |