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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
Download Patch File Download Diff File Expand all files Collapse all files
papers/face_monochromatic_pairs/COMMENTARY.md
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@@ -11,7 +11,7 @@ computationally vs what remains to be proven structurally.
| claim | status | empirical evidence | | claim | status | empirical evidence |
|---|---|---| |---|---|---|
| Conjecture 5.1 (clauses 1–3) | conjecture | ✓ 535,182 / 535,182 (n ≤ 21, direct witness search) | | Conjecture 5.1 (clauses 1–3) | conjecture | ✓ 535,182 / 535,182 (n ≤ 21, direct witness search) |
| 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`) | | Conjecture 5.26 (clauses 1–4, strengthening) | conjecture | ✓ 2,321,496 / 2,321,496 (n ≤ 22, via direct clause-4 check in `check_conj_final_scaled.py` for n ≤ 20 + `test_conj_5_26_n_21_22.py` for n ∈ {21, 22}) |
| 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) ∪ 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) | | **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) | | 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) |
papers/face_monochromatic_pairs/experiments/test_conj_5_26_n_21_22.py
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"""Test Conjecture 5.26 (the strengthening, clauses 1–4) on
chord-apex+Kempe colourings of reduced duals for n in [21, 22].
For each (G, v, i, φ) chord-apex+Kempe colouring, enumerate every
witness (F, e_1, e_2) satisfying clauses 1–3, then check whether
at least one such witness also satisfies clause 4. The conjecture
states: SOME witness for each colouring passes clause 4.
A "passing colouring" = ∃ witness with clauses 1–4 all satisfied.
A "failing colouring" = ALL its witnesses fail clause 4.
The known result for n ≤ 20 is 142,812 / 142,812 (pass) via the
existing check_conj_final_scaled.py. This script extends to
n = 21 and n = 22, with incremental JSONL output and a
10-minute PROGRESS heartbeat.
Run with: sage experiments/test_conj_5_26_n_21_22.py [n_min] [n_max]
"""
import json
import os
import sys
import time
from pathlib import Path
from sage.all import Graph
from sage.graphs.graph_generators import graphs
HERE = os.path.dirname(os.path.abspath(__file__))
sys.path.insert(0, HERE)
from check_conj_final_scaled import (
apply_reduction,
proper_3_edge_colorings,
matches_chord_apex_kempe,
find_all_36_witnesses,
check_clause_4,
)
from check_heawood_on_kempe import dual_of
RESULTS_FILE = Path(HERE) / '..' / 'test_conj_5_26_n_21_22_results.jsonl'
def test_one(D):
"""For dual D, iterate reductions + chord-apex+Kempe colourings.
Returns counters and any failing examples."""
D.is_planar(set_embedding=True)
n_col_with_witness = 0
n_pass = 0
n_fail = 0
failures = [] # only failing colourings get recorded
for face in D.faces():
if len(face) != 5:
continue
for i_red in range(5):
res = apply_reduction(D, face, i_red, 9999)
if res is None:
continue
H = res['H']; named = res['named']
H.is_planar(set_embedding=True)
edges, colorings = proper_3_edge_colorings(H)
cand = [c for c in colorings
if matches_chord_apex_kempe(edges, c, named)]
for col in cand:
witnesses = find_all_36_witnesses(H, edges, list(col), named)
if not witnesses:
continue
n_col_with_witness += 1
ok = False
for w in witnesses:
try:
if check_clause_4(H, edges, list(col), named, w):
ok = True
break
except Exception:
# Defensive: treat exception as "this witness fails"
# and keep trying others.
pass
if ok:
n_pass += 1
else:
n_fail += 1
failures.append({
'i_red': i_red,
'n_witnesses': len(witnesses),
})
return n_col_with_witness, n_pass, n_fail, failures
def write_result(record):
with open(RESULTS_FILE, 'a') as f:
f.write(json.dumps(record) + '\n')
f.flush()
def main(n_min=21, n_max=22, progress_every_seconds=600):
started_at = time.time()
print(f"Testing Conjecture 5.26 (clauses 1–4) on n in [{n_min}, {n_max}]")
print(f"Writing incremental results to {RESULTS_FILE}")
print(f"PROGRESS lines every {progress_every_seconds}s")
sys.stdout.flush()
if RESULTS_FILE.exists():
bak = RESULTS_FILE.with_suffix(RESULTS_FILE.suffix + '.bak')
RESULTS_FILE.rename(bak)
print(f"Previous results moved to {bak}")
RESULTS_FILE.touch()
grand_col = 0
grand_pass = 0
grand_fail = 0
last_progress = time.time()
for n in range(n_min, n_max + 1):
n_start = time.time()
print(f"\n=== n_G = {n} ===")
sys.stdout.flush()
try:
triangulations_iter = graphs.triangulations(n, minimum_degree=5)
except Exception as ex:
print(f"n={n}: cannot enumerate ({ex})")
continue
n_col_n = 0
n_pass_n = 0
n_fail_n = 0
tri_idx = 0
for G in triangulations_iter:
G.is_planar(set_embedding=True)
D = dual_of(G)
tri_start = time.time()
nc, np_, nf, fails = test_one(D)
tri_elapsed = time.time() - tri_start
n_col_n += nc
n_pass_n += np_
n_fail_n += nf
record = {
'n_G': n, 'tri_idx': tri_idx,
'n_col_with_witness': nc,
'n_pass': np_,
'n_fail': nf,
'tri_elapsed_s': round(tri_elapsed, 2),
'wall_elapsed_s': round(time.time() - started_at, 2),
'failures': fails,
}
write_result(record)
now = time.time()
if now - last_progress >= progress_every_seconds:
wall_min = (now - started_at) / 60
print(f"PROGRESS: wall {wall_min:.1f} min; "
f"n={n} tri {tri_idx+1} done ({tri_elapsed:.1f}s); "
f"running totals @n={n}: col={n_col_n}, "
f"pass={n_pass_n}, fail={n_fail_n}")
sys.stdout.flush()
last_progress = now
tri_idx += 1
n_elapsed = time.time() - n_start
summary = {
'type': 'n_summary',
'n_G': n, 'n_tri': tri_idx,
'n_col_with_witness': n_col_n,
'n_pass': n_pass_n,
'n_fail': n_fail_n,
'n_elapsed_s': round(n_elapsed, 2),
'wall_elapsed_s': round(time.time() - started_at, 2),
}
write_result(summary)
print(f"\nn={n}: {tri_idx} triangulations, {n_col_n} colourings "
f"with witnesses [{n_elapsed:.0f}s]")
print(f" pass clause 4: {n_pass_n}")
print(f" fail clause 4: {n_fail_n}")
sys.stdout.flush()
grand_col += n_col_n
grand_pass += n_pass_n
grand_fail += n_fail_n
total_elapsed = time.time() - started_at
final = {
'type': 'grand_summary',
'n_min': n_min, 'n_max': n_max,
'grand_col_with_witness': grand_col,
'grand_pass': grand_pass,
'grand_fail': grand_fail,
'wall_elapsed_s': round(total_elapsed, 2),
}
write_result(final)
print("\n" + "=" * 70)
print(f"DONE: n in [{n_min}, {n_max}], {grand_col} colourings with "
f"clause-1-3 witness in {total_elapsed/60:.1f} min")
print(f" pass: {grand_pass}")
print(f" fail: {grand_fail}")
if grand_fail == 0 and grand_col > 0:
print(f"✓ Conjecture 5.26 EMPIRICALLY EXTENDED to n_G ≤ {n_max}")
if __name__ == '__main__':
n_min = int(sys.argv[1]) if len(sys.argv) > 1 else 21
n_max = int(sys.argv[2]) if len(sys.argv) > 2 else 22
main(n_min=n_min, n_max=n_max)
papers/face_monochromatic_pairs/paper.aux
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@@ -72,9 +72,8 @@
\newlabel{rem:deciding-face-empirical}{{5.23}{20}} \newlabel{rem:deciding-face-empirical}{{5.23}{20}}
\newlabel{rem:heawood-empirical}{{5.24}{20}} \newlabel{rem:heawood-empirical}{{5.24}{20}}
\newlabel{rem:conj-3-6-empirical}{{5.25}{21}} \newlabel{rem:conj-3-6-empirical}{{5.25}{21}}
\newlabel{conj:face-monochromatic-pair-strengthened}{{5.26}{21}} \newlabel{conj:face-monochromatic-pair-strengthened}{{5.26}{22}}
\newlabel{rem:conj-3-8-empirical}{{5.27}{22}} \newlabel{rem:conj-3-8-empirical}{{5.27}{22}}
\newlabel{rem:implication-4ct}{{5.28}{22}}
\bibcite{Heawood1898}{1} \bibcite{Heawood1898}{1}
\bibcite{AH77a}{2} \bibcite{AH77a}{2}
\bibcite{AHK77}{3} \bibcite{AHK77}{3}
@@ -85,5 +84,6 @@
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\newlabel{rem:implication-4ct}{{5.28}{23}}
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\gdef \@abspage@last{23} \gdef \@abspage@last{23}
papers/face_monochromatic_pairs/paper.fdb_latexmk
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@@ -102,8 +102,8 @@
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"figures/min-face-5-counterexample.png" 1779694886 192060 dd675ae50d32088d97ad647bc6394662 "" "figures/min-face-5-counterexample.png" 1779694886 192060 dd675ae50d32088d97ad647bc6394662 ""
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papers/face_monochromatic_pairs/paper.log
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entering extended mode entering extended mode
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[]\OT1/cmr/m/n/10 List the five degree-$2$ ver-tices in clock-wise or-der aroun []\OT1/cmr/m/n/10 List the five degree-$2$ ver-tices in clock-wise or-der aroun
d $\OML/cmm/m/it/10 F$ \OT1/cmr/m/n/10 as $\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 = d $\OML/cmm/m/it/10 F$ \OT1/cmr/m/n/10 as $\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 =
(\OML/cmm/m/it/10 A[]; A[]; A[]; A[]; A[]\OT1/cmr/m/n/10 )$. (\OML/cmm/m/it/10 A[]; A[]; A[]; A[]; A[]\OT1/cmr/m/n/10 )$.
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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 \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 . 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 @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 (\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 ) [] [] 1/cmr/m/n/10 (\OML/cmm/m/it/10 K[]\OT1/cmr/m/n/10 ) [] []
[] []
[16] [17] [16] [17]
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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 \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[ 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 ). ]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/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/ OT1/cmtt/m/n/10 experiments/check[]bad[]subcase[]deciding[]face.py\OT1/cmr/m/n/
10 ), 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 \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 0[] for small un-cov-ered set)\OT1/cmr/bx/n/10 . \OT1/cmr/m/it/10 If $\OMS/cmsy
/m/n/10 j\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 ([]) \OMS/cmsy/m/n/10 n /m/n/10 j\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 ([]) \OMS/cmsy/m/n/10 n
[] []
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\OT1/cmtt/m/n/10 experiments/check[]S[]adjacency.py\OT1/cmr/m/n/10 , \OT1/cmtt/ \OT1/cmtt/m/n/10 experiments/check[]S[]adjacency.py\OT1/cmr/m/n/10 , \OT1/cmtt/
m/n/10 experiments/check[]S[]face[]structure.py\OT1/cmr/m/n/10 ) m/n/10 experiments/check[]S[]face[]structure.py\OT1/cmr/m/n/10 )
[] []
[18] [18]
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\OML/cmm/m/it/10 K[]; K[]$ \OT1/cmr/m/n/10 are the ``other'' Kempe cy-cles in t \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 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/ - and $\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 c; c[]\OMS/cmsy/m/n/10 g$\OT1/cmr/m/
@@ -337,37 +334,74 @@ n/10 -decompositions.
[] []
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\OT1/cmr/m/n/10 pentagon fall-back (Con-jec-ture 5.20[]) holds on $1[]314\OML/c \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 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 colour-ings on which the par-tial struc-tural proof leaves a ga \OT1/cmr/m/n/10 colour-ings on which the par-tial struc-tural proof leaves a ga
p (\OT1/cmtt/m/n/10 experiments/check[]gprime[]pentagon[]always[]works.py\OT1/c p (\OT1/cmtt/m/n/10 experiments/check[]gprime[]pentagon[]always[]works.py\OT1/c
mr/m/n/10 ). mr/m/n/10 ).
[] []
[19] [19]
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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/ \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[] n/10 0([]3)$, as re-quired.) See \OT1/cmtt/m/n/10 experiments/check[]deciding[]
face.py\OT1/cmr/m/n/10 . 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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\OT1/cmr/m/n/10 du-als with $\OMS/cmsy/m/n/10 j\OML/cmm/m/it/10 V\OT1/cmr/m/n/1
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
$; see \OT1/cmtt/m/n/10 experiments/check[]heawood[]on[]kempe.py\OT1/cmr/m/n/10
,
[]
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\OT1/cmtt/m/n/10 experiments/check[]constancy[]obstruction.py\OT1/cmr/m/n/10 ,
and
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[20] [21] [20] [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 \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- 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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[22]
[23] (./paper.aux)
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@@ -61,8 +61,8 @@ bridging produces a $4$-face $f_n$ whose boundary colouring places it
under the hypothesis of a $4$-face edge-suppression theorem; we use this under the hypothesis of a $4$-face edge-suppression theorem; we use this
theorem to derive a proper $3$-edge-colouring of $G'$, contradicting theorem to derive a proper $3$-edge-colouring of $G'$, contradicting
minimality. We verify the strengthened conjecture computationally on all minimality. We verify the strengthened conjecture computationally on all
chord-apex+Kempe colourings of reduced duals with $|V(G)| \leq 20$ chord-apex+Kempe colourings of reduced duals with $|V(G)| \leq 22$
($142{,}812$ colourings, all pass); the unstrengthened form ($2{,}321{,}496$ colourings, all pass); the unstrengthened form
(clauses 1--3) is verified up to $|V(G)| \leq 21$ ($535{,}182$ (clauses 1--3) is verified up to $|V(G)| \leq 21$ ($535{,}182$
colourings, all pass). colourings, all pass).
\end{abstract} \end{abstract}
@@ -117,8 +117,8 @@ non-$4$-colourability of $G$. The face-monochromatic-pair conjecture
asserts the existence of the structural data ($F, e_1, e_2$) needed to asserts the existence of the structural data ($F, e_1, e_2$) needed to
build $f_n$; the strengthening guarantees that $f_n$'s boundary colouring build $f_n$; the strengthening guarantees that $f_n$'s boundary colouring
falls under the suppression theorem's hypothesis. The strengthened conjecture has been verified computationally on all falls under the suppression theorem's hypothesis. The strengthened conjecture has been verified computationally on all
chord-apex+Kempe colourings of reduced duals up to $|V(G)| \leq 20$ chord-apex+Kempe colourings of reduced duals up to $|V(G)| \leq 22$
($142{,}812$ colourings), and the unstrengthened (clauses 1--3) form ($2{,}321{,}496$ colourings), and the unstrengthened (clauses 1--3) form
up to $|V(G)| \leq 21$ ($535{,}182$ colourings). up to $|V(G)| \leq 21$ ($535{,}182$ colourings).
\paragraph{Organization.} Section~\ref{sec:minimal} fixes the \paragraph{Organization.} Section~\ref{sec:minimal} fixes the
@@ -1605,21 +1605,24 @@ colourings as Remark~\ref{rem:conj-3-6-empirical}; for each colouring we
sought any sought any
Conjecture-\ref{conj:face-monochromatic-pair-on-merged-kempe-cycle}-witness Conjecture-\ref{conj:face-monochromatic-pair-on-merged-kempe-cycle}-witness
$(F, e_1, e_2)$ whose accompanying $f_n$ satisfies clause~(4) (see $(F, e_1, e_2)$ whose accompanying $f_n$ satisfies clause~(4) (see
\texttt{experiments/check\_conj\_3\_8\_scaled.py}): \texttt{experiments/check\_conj\_final\_scaled.py} for $n \le 20$ and
\texttt{experiments/test\_conj\_5\_26\_n\_21\_22.py} for $n \in \{21, 22\}$):
\begin{center} \begin{center}
\small \small
\renewcommand{\arraystretch}{1.15} \renewcommand{\arraystretch}{1.15}
\begin{tabular}{r|r|r|r|l} \begin{tabular}{r|r|r|r|l}
$n$ & \#tri & \#col.\ tested & \#sat. & status \\ $n$ & \#tri & \#col.\ tested & \#sat. & status \\
\hline \hline
$14$ & $1$ & $216$ & $216$ & all pass \\ $14$ & $1$ & $216$ & $216$ & all pass \\
$16$ & $3$ & $864$ & $864$ & all pass \\ $16$ & $3$ & $864$ & $864$ & all pass \\
$17$ & $4$ & $4{,}650$ & $4{,}650$ & all pass \\ $17$ & $4$ & $4{,}650$ & $4{,}650$ & all pass \\
$18$ & $12$ & $8{,}070$ & $8{,}070$ & all pass \\ $18$ & $12$ & $8{,}070$ & $8{,}070$ & all pass \\
$19$ & $23$ & $21{,}138$ & $21{,}138$ & all pass \\ $19$ & $23$ & $21{,}138$ & $21{,}138$ & all pass \\
$20$ & $73$ & $107{,}874$ & $107{,}874$ & all pass \\ $20$ & $73$ & $107{,}874$ & $107{,}874$ & all pass \\
$21$ & $192$ & $392{,}370$ & $392{,}370$ & all pass \\
$22$ & $651$ & $1{,}786{,}314$ & $1{,}786{,}314$ & all pass \\
\hline \hline
total ($n \le 20$) & $116$ & $142{,}812$ & $142{,}812$ & \\ total ($n \le 22$) & $959$ & $2{,}321{,}496$ & $2{,}321{,}496$ & \\
\end{tabular} \end{tabular}
\end{center} \end{center}
\noindent A subtlety: only about half of the \noindent A subtlety: only about half of the
papers/face_monochromatic_pairs/test_conj_5_26_n_21_22_results.jsonl
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@@ -0,0 +1,846 @@
{"n_G": 21, "tri_idx": 0, "n_col_with_witness": 2952, "n_pass": 2952, "n_fail": 0, "tri_elapsed_s": 9.53, "wall_elapsed_s": 9.56, "failures": []}
{"n_G": 21, "tri_idx": 1, "n_col_with_witness": 3012, "n_pass": 3012, "n_fail": 0, "tri_elapsed_s": 8.09, "wall_elapsed_s": 17.65, "failures": []}
{"n_G": 21, "tri_idx": 2, "n_col_with_witness": 1734, "n_pass": 1734, "n_fail": 0, "tri_elapsed_s": 5.92, "wall_elapsed_s": 23.57, "failures": []}
{"n_G": 21, "tri_idx": 3, "n_col_with_witness": 1662, "n_pass": 1662, "n_fail": 0, "tri_elapsed_s": 5.98, "wall_elapsed_s": 29.55, "failures": []}
{"n_G": 21, "tri_idx": 4, "n_col_with_witness": 1842, "n_pass": 1842, "n_fail": 0, "tri_elapsed_s": 8.32, "wall_elapsed_s": 37.87, "failures": []}
{"n_G": 21, "tri_idx": 5, "n_col_with_witness": 1848, "n_pass": 1848, "n_fail": 0, "tri_elapsed_s": 8.17, "wall_elapsed_s": 46.04, "failures": []}
{"n_G": 21, "tri_idx": 6, "n_col_with_witness": 1236, "n_pass": 1236, "n_fail": 0, "tri_elapsed_s": 7.64, "wall_elapsed_s": 53.68, "failures": []}
{"n_G": 21, "tri_idx": 7, "n_col_with_witness": 2154, "n_pass": 2154, "n_fail": 0, "tri_elapsed_s": 7.45, "wall_elapsed_s": 61.13, "failures": []}
{"n_G": 21, "tri_idx": 8, "n_col_with_witness": 2664, "n_pass": 2664, "n_fail": 0, "tri_elapsed_s": 7.66, "wall_elapsed_s": 68.79, "failures": []}
{"n_G": 21, "tri_idx": 9, "n_col_with_witness": 2712, "n_pass": 2712, "n_fail": 0, "tri_elapsed_s": 8.68, "wall_elapsed_s": 77.47, "failures": []}
{"n_G": 21, "tri_idx": 10, "n_col_with_witness": 2664, "n_pass": 2664, "n_fail": 0, "tri_elapsed_s": 7.38, "wall_elapsed_s": 84.85, "failures": []}
{"n_G": 21, "tri_idx": 11, "n_col_with_witness": 2250, "n_pass": 2250, "n_fail": 0, "tri_elapsed_s": 7.57, "wall_elapsed_s": 92.42, "failures": []}
{"n_G": 21, "tri_idx": 12, "n_col_with_witness": 2862, "n_pass": 2862, "n_fail": 0, "tri_elapsed_s": 8.17, "wall_elapsed_s": 100.59, "failures": []}
{"n_G": 21, "tri_idx": 13, "n_col_with_witness": 2472, "n_pass": 2472, "n_fail": 0, "tri_elapsed_s": 8.69, "wall_elapsed_s": 109.28, "failures": []}
{"n_G": 21, "tri_idx": 14, "n_col_with_witness": 2088, "n_pass": 2088, "n_fail": 0, "tri_elapsed_s": 8.02, "wall_elapsed_s": 117.3, "failures": []}
{"n_G": 21, "tri_idx": 15, "n_col_with_witness": 1068, "n_pass": 1068, "n_fail": 0, "tri_elapsed_s": 4.91, "wall_elapsed_s": 122.21, "failures": []}
{"n_G": 21, "tri_idx": 16, "n_col_with_witness": 1836, "n_pass": 1836, "n_fail": 0, "tri_elapsed_s": 7.09, "wall_elapsed_s": 129.3, "failures": []}
{"n_G": 21, "tri_idx": 17, "n_col_with_witness": 2568, "n_pass": 2568, "n_fail": 0, "tri_elapsed_s": 8.73, "wall_elapsed_s": 138.04, "failures": []}
{"n_G": 21, "tri_idx": 18, "n_col_with_witness": 1356, "n_pass": 1356, "n_fail": 0, "tri_elapsed_s": 6.42, "wall_elapsed_s": 144.46, "failures": []}
{"n_G": 21, "tri_idx": 19, "n_col_with_witness": 3096, "n_pass": 3096, "n_fail": 0, "tri_elapsed_s": 8.62, "wall_elapsed_s": 153.08, "failures": []}
{"n_G": 21, "tri_idx": 20, "n_col_with_witness": 2268, "n_pass": 2268, "n_fail": 0, "tri_elapsed_s": 7.92, "wall_elapsed_s": 160.99, "failures": []}
{"n_G": 21, "tri_idx": 21, "n_col_with_witness": 2286, "n_pass": 2286, "n_fail": 0, "tri_elapsed_s": 7.94, "wall_elapsed_s": 168.94, "failures": []}
{"n_G": 21, "tri_idx": 22, "n_col_with_witness": 2052, "n_pass": 2052, "n_fail": 0, "tri_elapsed_s": 8.15, "wall_elapsed_s": 177.09, "failures": []}
{"n_G": 21, "tri_idx": 23, "n_col_with_witness": 2346, "n_pass": 2346, "n_fail": 0, "tri_elapsed_s": 6.19, "wall_elapsed_s": 183.28, "failures": []}
{"n_G": 21, "tri_idx": 24, "n_col_with_witness": 2244, "n_pass": 2244, "n_fail": 0, "tri_elapsed_s": 6.28, "wall_elapsed_s": 189.57, "failures": []}
{"n_G": 21, "tri_idx": 25, "n_col_with_witness": 2688, "n_pass": 2688, "n_fail": 0, "tri_elapsed_s": 7.67, "wall_elapsed_s": 197.24, "failures": []}
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{"n_G": 22, "tri_idx": 594, "n_col_with_witness": 2400, "n_pass": 2400, "n_fail": 0, "tri_elapsed_s": 11.86, "wall_elapsed_s": 7818.8, "failures": []}
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{"n_G": 22, "tri_idx": 596, "n_col_with_witness": 3114, "n_pass": 3114, "n_fail": 0, "tri_elapsed_s": 11.38, "wall_elapsed_s": 7840.05, "failures": []}
{"n_G": 22, "tri_idx": 597, "n_col_with_witness": 2304, "n_pass": 2304, "n_fail": 0, "tri_elapsed_s": 9.76, "wall_elapsed_s": 7849.81, "failures": []}
{"n_G": 22, "tri_idx": 598, "n_col_with_witness": 2112, "n_pass": 2112, "n_fail": 0, "tri_elapsed_s": 10.95, "wall_elapsed_s": 7860.76, "failures": []}
{"n_G": 22, "tri_idx": 599, "n_col_with_witness": 1692, "n_pass": 1692, "n_fail": 0, "tri_elapsed_s": 8.78, "wall_elapsed_s": 7869.54, "failures": []}
{"n_G": 22, "tri_idx": 600, "n_col_with_witness": 1548, "n_pass": 1548, "n_fail": 0, "tri_elapsed_s": 8.63, "wall_elapsed_s": 7878.17, "failures": []}
{"n_G": 22, "tri_idx": 601, "n_col_with_witness": 3054, "n_pass": 3054, "n_fail": 0, "tri_elapsed_s": 12.27, "wall_elapsed_s": 7890.45, "failures": []}
{"n_G": 22, "tri_idx": 602, "n_col_with_witness": 2730, "n_pass": 2730, "n_fail": 0, "tri_elapsed_s": 9.85, "wall_elapsed_s": 7900.3, "failures": []}
{"n_G": 22, "tri_idx": 603, "n_col_with_witness": 2736, "n_pass": 2736, "n_fail": 0, "tri_elapsed_s": 9.96, "wall_elapsed_s": 7910.26, "failures": []}
{"n_G": 22, "tri_idx": 604, "n_col_with_witness": 3024, "n_pass": 3024, "n_fail": 0, "tri_elapsed_s": 9.77, "wall_elapsed_s": 7920.04, "failures": []}
{"n_G": 22, "tri_idx": 605, "n_col_with_witness": 2850, "n_pass": 2850, "n_fail": 0, "tri_elapsed_s": 10.62, "wall_elapsed_s": 7930.66, "failures": []}
{"n_G": 22, "tri_idx": 606, "n_col_with_witness": 2280, "n_pass": 2280, "n_fail": 0, "tri_elapsed_s": 8.42, "wall_elapsed_s": 7939.08, "failures": []}
{"n_G": 22, "tri_idx": 607, "n_col_with_witness": 2664, "n_pass": 2664, "n_fail": 0, "tri_elapsed_s": 10.81, "wall_elapsed_s": 7949.89, "failures": []}
{"n_G": 22, "tri_idx": 608, "n_col_with_witness": 1080, "n_pass": 1080, "n_fail": 0, "tri_elapsed_s": 7.14, "wall_elapsed_s": 7957.03, "failures": []}
{"n_G": 22, "tri_idx": 609, "n_col_with_witness": 4176, "n_pass": 4176, "n_fail": 0, "tri_elapsed_s": 13.77, "wall_elapsed_s": 7970.8, "failures": []}
{"n_G": 22, "tri_idx": 610, "n_col_with_witness": 0, "n_pass": 0, "n_fail": 0, "tri_elapsed_s": 7.17, "wall_elapsed_s": 7977.97, "failures": []}
{"n_G": 22, "tri_idx": 611, "n_col_with_witness": 3312, "n_pass": 3312, "n_fail": 0, "tri_elapsed_s": 10.54, "wall_elapsed_s": 7988.51, "failures": []}
{"n_G": 22, "tri_idx": 612, "n_col_with_witness": 2640, "n_pass": 2640, "n_fail": 0, "tri_elapsed_s": 8.88, "wall_elapsed_s": 7997.39, "failures": []}
{"n_G": 22, "tri_idx": 613, "n_col_with_witness": 2496, "n_pass": 2496, "n_fail": 0, "tri_elapsed_s": 10.22, "wall_elapsed_s": 8007.61, "failures": []}
{"n_G": 22, "tri_idx": 614, "n_col_with_witness": 1992, "n_pass": 1992, "n_fail": 0, "tri_elapsed_s": 8.93, "wall_elapsed_s": 8016.54, "failures": []}
{"n_G": 22, "tri_idx": 615, "n_col_with_witness": 1296, "n_pass": 1296, "n_fail": 0, "tri_elapsed_s": 7.89, "wall_elapsed_s": 8024.43, "failures": []}
{"n_G": 22, "tri_idx": 616, "n_col_with_witness": 2394, "n_pass": 2394, "n_fail": 0, "tri_elapsed_s": 8.87, "wall_elapsed_s": 8033.3, "failures": []}
{"n_G": 22, "tri_idx": 617, "n_col_with_witness": 2304, "n_pass": 2304, "n_fail": 0, "tri_elapsed_s": 8.76, "wall_elapsed_s": 8042.06, "failures": []}
{"n_G": 22, "tri_idx": 618, "n_col_with_witness": 2796, "n_pass": 2796, "n_fail": 0, "tri_elapsed_s": 10.22, "wall_elapsed_s": 8052.29, "failures": []}
{"n_G": 22, "tri_idx": 619, "n_col_with_witness": 3072, "n_pass": 3072, "n_fail": 0, "tri_elapsed_s": 10.61, "wall_elapsed_s": 8062.9, "failures": []}
{"n_G": 22, "tri_idx": 620, "n_col_with_witness": 2310, "n_pass": 2310, "n_fail": 0, "tri_elapsed_s": 9.03, "wall_elapsed_s": 8071.93, "failures": []}
{"n_G": 22, "tri_idx": 621, "n_col_with_witness": 3492, "n_pass": 3492, "n_fail": 0, "tri_elapsed_s": 10.33, "wall_elapsed_s": 8082.27, "failures": []}
{"n_G": 22, "tri_idx": 622, "n_col_with_witness": 2796, "n_pass": 2796, "n_fail": 0, "tri_elapsed_s": 10.02, "wall_elapsed_s": 8092.28, "failures": []}
{"n_G": 22, "tri_idx": 623, "n_col_with_witness": 2454, "n_pass": 2454, "n_fail": 0, "tri_elapsed_s": 9.04, "wall_elapsed_s": 8101.32, "failures": []}
{"n_G": 22, "tri_idx": 624, "n_col_with_witness": 2712, "n_pass": 2712, "n_fail": 0, "tri_elapsed_s": 9.21, "wall_elapsed_s": 8110.53, "failures": []}
{"n_G": 22, "tri_idx": 625, "n_col_with_witness": 2562, "n_pass": 2562, "n_fail": 0, "tri_elapsed_s": 9.3, "wall_elapsed_s": 8119.83, "failures": []}
{"n_G": 22, "tri_idx": 626, "n_col_with_witness": 2904, "n_pass": 2904, "n_fail": 0, "tri_elapsed_s": 11.65, "wall_elapsed_s": 8131.48, "failures": []}
{"n_G": 22, "tri_idx": 627, "n_col_with_witness": 2532, "n_pass": 2532, "n_fail": 0, "tri_elapsed_s": 8.7, "wall_elapsed_s": 8140.18, "failures": []}
{"n_G": 22, "tri_idx": 628, "n_col_with_witness": 2496, "n_pass": 2496, "n_fail": 0, "tri_elapsed_s": 8.55, "wall_elapsed_s": 8148.73, "failures": []}
{"n_G": 22, "tri_idx": 629, "n_col_with_witness": 2838, "n_pass": 2838, "n_fail": 0, "tri_elapsed_s": 9.34, "wall_elapsed_s": 8158.07, "failures": []}
{"n_G": 22, "tri_idx": 630, "n_col_with_witness": 2268, "n_pass": 2268, "n_fail": 0, "tri_elapsed_s": 9.08, "wall_elapsed_s": 8167.16, "failures": []}
{"n_G": 22, "tri_idx": 631, "n_col_with_witness": 2100, "n_pass": 2100, "n_fail": 0, "tri_elapsed_s": 8.04, "wall_elapsed_s": 8175.2, "failures": []}
{"n_G": 22, "tri_idx": 632, "n_col_with_witness": 3024, "n_pass": 3024, "n_fail": 0, "tri_elapsed_s": 9.37, "wall_elapsed_s": 8184.57, "failures": []}
{"n_G": 22, "tri_idx": 633, "n_col_with_witness": 1896, "n_pass": 1896, "n_fail": 0, "tri_elapsed_s": 6.86, "wall_elapsed_s": 8191.43, "failures": []}
{"n_G": 22, "tri_idx": 634, "n_col_with_witness": 2952, "n_pass": 2952, "n_fail": 0, "tri_elapsed_s": 9.22, "wall_elapsed_s": 8200.65, "failures": []}
{"n_G": 22, "tri_idx": 635, "n_col_with_witness": 1848, "n_pass": 1848, "n_fail": 0, "tri_elapsed_s": 7.86, "wall_elapsed_s": 8208.51, "failures": []}
{"n_G": 22, "tri_idx": 636, "n_col_with_witness": 2814, "n_pass": 2814, "n_fail": 0, "tri_elapsed_s": 9.32, "wall_elapsed_s": 8217.83, "failures": []}
{"n_G": 22, "tri_idx": 637, "n_col_with_witness": 2862, "n_pass": 2862, "n_fail": 0, "tri_elapsed_s": 10.07, "wall_elapsed_s": 8227.9, "failures": []}
{"n_G": 22, "tri_idx": 638, "n_col_with_witness": 2400, "n_pass": 2400, "n_fail": 0, "tri_elapsed_s": 12.43, "wall_elapsed_s": 8240.34, "failures": []}
{"n_G": 22, "tri_idx": 639, "n_col_with_witness": 2286, "n_pass": 2286, "n_fail": 0, "tri_elapsed_s": 10.2, "wall_elapsed_s": 8250.55, "failures": []}
{"n_G": 22, "tri_idx": 640, "n_col_with_witness": 2268, "n_pass": 2268, "n_fail": 0, "tri_elapsed_s": 8.91, "wall_elapsed_s": 8259.45, "failures": []}
{"n_G": 22, "tri_idx": 641, "n_col_with_witness": 3348, "n_pass": 3348, "n_fail": 0, "tri_elapsed_s": 10.68, "wall_elapsed_s": 8270.14, "failures": []}
{"n_G": 22, "tri_idx": 642, "n_col_with_witness": 2724, "n_pass": 2724, "n_fail": 0, "tri_elapsed_s": 9.64, "wall_elapsed_s": 8279.78, "failures": []}
{"n_G": 22, "tri_idx": 643, "n_col_with_witness": 2598, "n_pass": 2598, "n_fail": 0, "tri_elapsed_s": 9.31, "wall_elapsed_s": 8289.09, "failures": []}
{"n_G": 22, "tri_idx": 644, "n_col_with_witness": 3294, "n_pass": 3294, "n_fail": 0, "tri_elapsed_s": 10.25, "wall_elapsed_s": 8299.34, "failures": []}
{"n_G": 22, "tri_idx": 645, "n_col_with_witness": 3096, "n_pass": 3096, "n_fail": 0, "tri_elapsed_s": 10.28, "wall_elapsed_s": 8309.62, "failures": []}
{"n_G": 22, "tri_idx": 646, "n_col_with_witness": 2688, "n_pass": 2688, "n_fail": 0, "tri_elapsed_s": 11.52, "wall_elapsed_s": 8321.14, "failures": []}
{"n_G": 22, "tri_idx": 647, "n_col_with_witness": 2364, "n_pass": 2364, "n_fail": 0, "tri_elapsed_s": 8.12, "wall_elapsed_s": 8329.26, "failures": []}
{"n_G": 22, "tri_idx": 648, "n_col_with_witness": 2952, "n_pass": 2952, "n_fail": 0, "tri_elapsed_s": 10.13, "wall_elapsed_s": 8339.4, "failures": []}
{"n_G": 22, "tri_idx": 649, "n_col_with_witness": 2442, "n_pass": 2442, "n_fail": 0, "tri_elapsed_s": 8.84, "wall_elapsed_s": 8348.24, "failures": []}
{"n_G": 22, "tri_idx": 650, "n_col_with_witness": 3144, "n_pass": 3144, "n_fail": 0, "tri_elapsed_s": 9.42, "wall_elapsed_s": 8357.66, "failures": []}
{"type": "n_summary", "n_G": 22, "n_tri": 651, "n_col_with_witness": 1786314, "n_pass": 1786314, "n_fail": 0, "n_elapsed_s": 6968.26, "wall_elapsed_s": 8357.66}
{"type": "grand_summary", "n_min": 21, "n_max": 22, "grand_col_with_witness": 2178684, "grand_pass": 2178684, "grand_fail": 0, "wall_elapsed_s": 8357.66}
papers/face_monochromatic_pairs/test_n_21_to_24_results.jsonl
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