face_mono: extend Conjecture 5.26 to n_G ≤ 22

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>

papers/face_monochromatic_pairs/paper.tex

@@ -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