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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 |
|---|---|---|
| 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)` 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) |
papers/face_monochromatic_pairs/experiments/test_conj_5_26_n_21_22.py
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@@ -0,0 +1,199 @@
"""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:heawood-empirical}{{5.24}{20}}
\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:implication-4ct}{{5.28}{22}}
\bibcite{Heawood1898}{1}
\bibcite{AH77a}{2}
\bibcite{AHK77}{3}
@@ -85,5 +84,6 @@
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{0pt}
\newlabel{tocindent3}{0pt}
\newlabel{rem:implication-4ct}{{5.28}{23}}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{23}{}\protected@file@percent }
\gdef \@abspage@last{23}
papers/face_monochromatic_pairs/paper.fdb_latexmk
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["pdflatex"] 1779709018 "paper.tex" "paper.pdf" "paper" 1779709020
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"paper.tex" 1779726385 80516 3cdeee92fefe09fa5794bef1ddc2caf8 ""
(generated)
"paper.aux"
"paper.log"
papers/face_monochromatic_pairs/paper.log
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This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 25 MAY 2026 12:27
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
d $\OML/cmm/m/it/10 F$ \OT1/cmr/m/n/10 as $\OML/cmm/m/it/10 A \OT1/cmr/m/n/10 =
(\OML/cmm/m/it/10 A[]; A[]; A[]; A[]; A[]\OT1/cmr/m/n/10 )$.
@@ -205,22 +202,22 @@ d $\OML/cmm/m/it/10 F$ \OT1/cmr/m/n/10 as $\OML/cmm/m/it/10 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
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 $\OMS/cmsy
/m/n/10 j\OML/cmm/m/it/10 V\OT1/cmr/m/n/10 ([]) \OMS/cmsy/m/n/10 n
[]
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\OT1/cmtt/m/n/10 experiments/check[]S[]adjacency.py\OT1/cmr/m/n/10 , \OT1/cmtt/
m/n/10 experiments/check[]S[]face[]structure.py\OT1/cmr/m/n/10 )
[]
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\OML/cmm/m/it/10 K[]; K[]$ \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 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
mr/m/n/10 ).
[]
[19]
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\OT1/cmr/m/n/10 (Every length ap-pear-ing is $\OMS/cmsy/m/n/10 6^^Q \OT1/cmr/m/
n/10 0([]3)$, 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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\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]
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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-
[]
[22] [23] (./paper.aux)
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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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@@ -409,7 +443,7 @@ fonts/type1/public/amsfonts/cm/cmti8.pfb></usr/local/texlive/2022/texmf-dist/fo
nts/type1/public/amsfonts/cm/cmtt10.pfb></usr/local/texlive/2022/texmf-dist/fon
ts/type1/public/amsfonts/cm/cmtt9.pfb></usr/local/texlive/2022/texmf-dist/fonts
/type1/public/amsfonts/symbols/msam10.pfb>
Output written on paper.pdf (23 pages, 1328195 bytes).
Output written on paper.pdf (23 pages, 1329304 bytes).
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papers/face_monochromatic_pairs/paper.pdf
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papers/face_monochromatic_pairs/paper.tex
+15 -12
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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
theorem to derive a proper $3$-edge-colouring of $G'$, contradicting
minimality. We verify the strengthened conjecture computationally on all
chord-apex+Kempe colourings of reduced duals with $|V(G)| \leq 20$
($142{,}812$ colourings, all pass); the unstrengthened form
chord-apex+Kempe colourings of reduced duals with $|V(G)| \leq 22$
($2{,}321{,}496$ colourings, all pass); the unstrengthened form
(clauses 1--3) is verified up to $|V(G)| \leq 21$ ($535{,}182$
colourings, all pass).
\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
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
chord-apex+Kempe colourings of reduced duals up to $|V(G)| \leq 20$
($142{,}812$ colourings), and the unstrengthened (clauses 1--3) form
chord-apex+Kempe colourings of reduced duals up to $|V(G)| \leq 22$
($2{,}321{,}496$ colourings), and the unstrengthened (clauses 1--3) form
up to $|V(G)| \leq 21$ ($535{,}182$ colourings).
\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
Conjecture-\ref{conj:face-monochromatic-pair-on-merged-kempe-cycle}-witness
$(F, e_1, e_2)$ 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}
\small
\renewcommand{\arraystretch}{1.15}
\begin{tabular}{r|r|r|r|l}
$n$ & \#tri & \#col.\ tested & \#sat. & status \\
\hline
$14$ & $1$ & $216$ & $216$ & all pass \\
$16$ & $3$ & $864$ & $864$ & all pass \\
$17$ & $4$ & $4{,}650$ & $4{,}650$ & all pass \\
$18$ & $12$ & $8{,}070$ & $8{,}070$ & all pass \\
$19$ & $23$ & $21{,}138$ & $21{,}138$ & all pass \\
$20$ & $73$ & $107{,}874$ & $107{,}874$ & all pass \\
$14$ & $1$ & $216$ & $216$ & all pass \\
$16$ & $3$ & $864$ & $864$ & all pass \\
$17$ & $4$ & $4{,}650$ & $4{,}650$ & all pass \\
$18$ & $12$ & $8{,}070$ & $8{,}070$ & all pass \\
$19$ & $23$ & $21{,}138$ & $21{,}138$ & 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
total ($n \le 20$) & $116$ & $142{,}812$ & $142{,}812$ & \\
total ($n \le 22$) & $959$ & $2{,}321{,}496$ & $2{,}321{,}496$ & \\
\end{tabular}
\end{center}
\noindent A subtlety: only about half of the
papers/face_monochromatic_pairs/test_conj_5_26_n_21_22_results.jsonl
+846
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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": []}
{"n_G": 21, "tri_idx": 26, "n_col_with_witness": 2436, "n_pass": 2436, "n_fail": 0, "tri_elapsed_s": 8.2, "wall_elapsed_s": 205.44, "failures": []}
{"n_G": 21, "tri_idx": 27, "n_col_with_witness": 2412, "n_pass": 2412, "n_fail": 0, "tri_elapsed_s": 7.93, "wall_elapsed_s": 213.37, "failures": []}
{"n_G": 21, "tri_idx": 28, "n_col_with_witness": 2784, "n_pass": 2784, "n_fail": 0, "tri_elapsed_s": 8.85, "wall_elapsed_s": 222.23, "failures": []}
{"n_G": 21, "tri_idx": 29, "n_col_with_witness": 2538, "n_pass": 2538, "n_fail": 0, "tri_elapsed_s": 7.94, "wall_elapsed_s": 230.17, "failures": []}
{"n_G": 21, "tri_idx": 30, "n_col_with_witness": 2292, "n_pass": 2292, "n_fail": 0, "tri_elapsed_s": 6.43, "wall_elapsed_s": 236.6, "failures": []}
{"n_G": 21, "tri_idx": 31, "n_col_with_witness": 2112, "n_pass": 2112, "n_fail": 0, "tri_elapsed_s": 6.32, "wall_elapsed_s": 242.92, "failures": []}
{"n_G": 21, "tri_idx": 32, "n_col_with_witness": 2100, "n_pass": 2100, "n_fail": 0, "tri_elapsed_s": 6.87, "wall_elapsed_s": 249.79, "failures": []}
{"n_G": 21, "tri_idx": 33, "n_col_with_witness": 3366, "n_pass": 3366, "n_fail": 0, "tri_elapsed_s": 10.15, "wall_elapsed_s": 259.93, "failures": []}
{"n_G": 21, "tri_idx": 34, "n_col_with_witness": 3672, "n_pass": 3672, "n_fail": 0, "tri_elapsed_s": 11.94, "wall_elapsed_s": 271.88, "failures": []}
{"n_G": 21, "tri_idx": 35, "n_col_with_witness": 1872, "n_pass": 1872, "n_fail": 0, "tri_elapsed_s": 5.88, "wall_elapsed_s": 277.76, "failures": []}
{"n_G": 21, "tri_idx": 36, "n_col_with_witness": 1278, "n_pass": 1278, "n_fail": 0, "tri_elapsed_s": 4.87, "wall_elapsed_s": 282.63, "failures": []}
{"n_G": 21, "tri_idx": 37, "n_col_with_witness": 1176, "n_pass": 1176, "n_fail": 0, "tri_elapsed_s": 4.1, "wall_elapsed_s": 286.73, "failures": []}
{"n_G": 21, "tri_idx": 38, "n_col_with_witness": 2910, "n_pass": 2910, "n_fail": 0, "tri_elapsed_s": 8.59, "wall_elapsed_s": 295.32, "failures": []}
{"n_G": 21, "tri_idx": 39, "n_col_with_witness": 1824, "n_pass": 1824, "n_fail": 0, "tri_elapsed_s": 6.34, "wall_elapsed_s": 301.66, "failures": []}
{"n_G": 21, "tri_idx": 40, "n_col_with_witness": 2340, "n_pass": 2340, "n_fail": 0, "tri_elapsed_s": 6.75, "wall_elapsed_s": 308.41, "failures": []}
{"n_G": 21, "tri_idx": 41, "n_col_with_witness": 2268, "n_pass": 2268, "n_fail": 0, "tri_elapsed_s": 8.02, "wall_elapsed_s": 316.43, "failures": []}
{"n_G": 21, "tri_idx": 42, "n_col_with_witness": 1938, "n_pass": 1938, "n_fail": 0, "tri_elapsed_s": 6.37, "wall_elapsed_s": 322.79, "failures": []}
{"n_G": 21, "tri_idx": 43, "n_col_with_witness": 1896, "n_pass": 1896, "n_fail": 0, "tri_elapsed_s": 6.34, "wall_elapsed_s": 329.13, "failures": []}
{"n_G": 21, "tri_idx": 44, "n_col_with_witness": 1590, "n_pass": 1590, "n_fail": 0, "tri_elapsed_s": 6.1, "wall_elapsed_s": 335.23, "failures": []}
{"n_G": 21, "tri_idx": 45, "n_col_with_witness": 1890, "n_pass": 1890, "n_fail": 0, "tri_elapsed_s": 6.09, "wall_elapsed_s": 341.32, "failures": []}
{"n_G": 21, "tri_idx": 46, "n_col_with_witness": 2034, "n_pass": 2034, "n_fail": 0, "tri_elapsed_s": 6.37, "wall_elapsed_s": 347.69, "failures": []}
{"n_G": 21, "tri_idx": 47, "n_col_with_witness": 1512, "n_pass": 1512, "n_fail": 0, "tri_elapsed_s": 5.53, "wall_elapsed_s": 353.22, "failures": []}
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{"n_G": 21, "tri_idx": 49, "n_col_with_witness": 1536, "n_pass": 1536, "n_fail": 0, "tri_elapsed_s": 5.18, "wall_elapsed_s": 365.76, "failures": []}
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{"n_G": 21, "tri_idx": 55, "n_col_with_witness": 1518, "n_pass": 1518, "n_fail": 0, "tri_elapsed_s": 5.01, "wall_elapsed_s": 403.25, "failures": []}
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{"n_G": 21, "tri_idx": 63, "n_col_with_witness": 2688, "n_pass": 2688, "n_fail": 0, "tri_elapsed_s": 7.7, "wall_elapsed_s": 456.69, "failures": []}
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{"n_G": 21, "tri_idx": 65, "n_col_with_witness": 1626, "n_pass": 1626, "n_fail": 0, "tri_elapsed_s": 10.14, "wall_elapsed_s": 472.79, "failures": []}
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{"n_G": 21, "tri_idx": 70, "n_col_with_witness": 1542, "n_pass": 1542, "n_fail": 0, "tri_elapsed_s": 5.82, "wall_elapsed_s": 507.34, "failures": []}
{"n_G": 21, "tri_idx": 71, "n_col_with_witness": 1740, "n_pass": 1740, "n_fail": 0, "tri_elapsed_s": 6.47, "wall_elapsed_s": 513.82, "failures": []}
{"n_G": 21, "tri_idx": 72, "n_col_with_witness": 1416, "n_pass": 1416, "n_fail": 0, "tri_elapsed_s": 3.79, "wall_elapsed_s": 517.61, "failures": []}
{"n_G": 21, "tri_idx": 73, "n_col_with_witness": 1458, "n_pass": 1458, "n_fail": 0, "tri_elapsed_s": 5.07, "wall_elapsed_s": 522.69, "failures": []}
{"n_G": 21, "tri_idx": 74, "n_col_with_witness": 1248, "n_pass": 1248, "n_fail": 0, "tri_elapsed_s": 4.64, "wall_elapsed_s": 527.33, "failures": []}
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{"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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