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face_mono: extend Conjecture 5.26 to n_G ≤ 22

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Adds experiments/test_conj_5_26_n_21_22.py, a clause-4 checker that
re-uses find_all_36_witnesses + check_clause_4 from
check_conj_final_scaled.py and runs them on n = 21, 22 with
incremental JSONL output and a 10-minute PROGRESS heartbeat.

Results (139 min wall, single thread):
  n=21: 192 tri, 392,370 colourings w/ clause-1–3 witness, all pass
  n=22: 651 tri, 1,786,314 colourings w/ clause-1–3 witness, all pass
  total at n ≤ 22: 2,321,496 / 2,321,496 (combined with the existing
  142,812 at n ≤ 20 from check_conj_final_scaled.py)

Paper edits:
- Abstract: "|V(G)| ≤ 20 (142,812)" → "|V(G)| ≤ 22 (2,321,496)" for
  the strengthening; clauses-1–3 count unchanged at 535,182 / n ≤ 21.
- Intro paragraph: matching update.
- Remark rem:conj-3-8-empirical table: added n=21 and n=22 rows; new
  total ($n \le 22$) = 959 triangulations, 2,321,496 colourings.
- Updated script reference in that remark to point at
  check_conj_final_scaled.py + test_conj_5_26_n_21_22.py.

COMMENTARY.md summary table: Conjecture 5.26 row bumped to
2,321,496 / 2,321,496 (n ≤ 22).

Also commits the test_*_results.jsonl artifacts (with per-tri
records + n-summaries + grand summary) for reproducibility.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-25 12:27:58 -04:00
parent d36c2513cc
commit 74030a5b8f
9 changed files with 2738 additions and 51 deletions
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\OT1/cmr/m/n/10 and the ex-haus-tive search that found it is in \OT1/cmtt/m/n/1
0 experiments/search[]min[]face5[]counterexample.py\OT1/cmr/m/n/10 .
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\OML/cmm/m/it/10 @F[] \OMS/cmsy/m/n/10 ^^R \OML/cmm/m/it/10 V\OT1/cmr/m/n/10
(\OML/cmm/m/it/10 K[]\OT1/cmr/m/n/10 ) \OMS/cmsy/m/n/10 [ \OML/cmm/m/it/10 V\OT
1/cmr/m/n/10 (\OML/cmm/m/it/10 K[]\OT1/cmr/m/n/10 ) [] []
[]
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\OT1/cmr/m/n/10 degree se-quence around $\OML/cmm/m/it/10 v$ \OT1/cmr/m/n/10 co
n-tains at least one degree-$5$ en-try (see \OT1/cmtt/m/n/10 experiments/check[
]v[]neighbour[]degrees.py\OT1/cmr/m/n/10 ).
[]
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\OT1/cmr/bx/n/10 the chord-apex con-struc-tion). \OT1/cmr/m/n/10 Con-cretely (\
OT1/cmtt/m/n/10 experiments/check[]bad[]subcase[]deciding[]face.py\OT1/cmr/m/n/
10 ),
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\OT1/cmr/bx/n/10 Lemma 5.21 \OT1/cmr/m/n/10 (Par-tial proof of Con-jec-ture 5.2
0[] for small un-cov-ered set)\OT1/cmr/bx/n/10 . \OT1/cmr/m/it/10 If $\OMS/cmsy
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\OT1/cmtt/m/n/10 experiments/check[]S[]adjacency.py\OT1/cmr/m/n/10 , \OT1/cmtt/
m/n/10 experiments/check[]S[]face[]structure.py\OT1/cmr/m/n/10 )
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\OML/cmm/m/it/10 K[]; K[]$ \OT1/cmr/m/n/10 are the ``other'' Kempe cy-cles in t
he $\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 c; c[]\OMS/cmsy/m/n/10 g$\OT1/cmr/m/n/10
- and $\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 c; c[]\OMS/cmsy/m/n/10 g$\OT1/cmr/m/
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\OT1/cmr/m/n/10 pentagon fall-back (Con-jec-ture 5.20[]) holds on $1[]314\OML/c
mm/m/it/10 =\OT1/cmr/m/n/10 1[]314 = 100%$ of chord-apex+Kempe
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\OT1/cmr/m/n/10 (Every length ap-pear-ing is $\OMS/cmsy/m/n/10 6^^Q \OT1/cmr/m/
n/10 0([]3)$, as re-quired.) See \OT1/cmtt/m/n/10 experiments/check[]deciding[]
face.py\OT1/cmr/m/n/10 .
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\OT1/cmr/m/n/10 this claim com-pu-ta-tion-ally on all chord-apex+Kempe colour-i
ngs of re-duced
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0 (\OML/cmm/m/it/10 G\OT1/cmr/m/n/10 )\OMS/cmsy/m/n/10 j ^^T \OT1/cmr/m/n/10 21
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\OT1/cmr/m/it/10 Remark \OT1/cmr/m/n/10 5.27\OT1/cmr/m/it/10 . \OT1/cmr/m/n/10
The strength-ened con-jec-ture was tested on the same chord-
[]
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\OT1/cmr/m/n/10 apex+Kempe colour-ings as Re-mark 5.25[]; for each colour-ing w
e sought
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\OT1/cmr/m/n/10 any Conjecture-5.1[]-witness $(\OML/cmm/m/it/10 F; e[]; e[]\OT1
/cmr/m/n/10 )$ whose ac-com-pa-ny-ing $\OML/cmm/m/it/10 f[]$ \OT1/cmr/m/n/10 sa
t-is-fies
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