diff --git a/papers/face_monochromatic_pairs/COMMENTARY.md b/papers/face_monochromatic_pairs/COMMENTARY.md
index ad3287c..f97f04a 100644
--- a/papers/face_monochromatic_pairs/COMMENTARY.md
+++ b/papers/face_monochromatic_pairs/COMMENTARY.md
@@ -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) |
diff --git a/papers/face_monochromatic_pairs/paper.pdf b/papers/face_monochromatic_pairs/paper.pdf
index ddf002d..0fa153c 100644
Binary files a/papers/face_monochromatic_pairs/paper.pdf and b/papers/face_monochromatic_pairs/paper.pdf differ
diff --git a/papers/face_monochromatic_pairs/paper.tex b/papers/face_monochromatic_pairs/paper.tex
index 012052a..00e32b1 100644
--- a/papers/face_monochromatic_pairs/paper.tex
+++ b/papers/face_monochromatic_pairs/paper.tex
@@ -60,10 +60,11 @@ same-coloured edges $e_1, e_2 \in \partial F$ whose subdivision-and-%
 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 conjecture computationally on all
-chord-apex+Kempe colourings of reduced duals with $|V(G)| \leq 21$
-($535{,}182$ colourings, all pass: $142{,}812$ at $|V(G)| \leq 20$,
-plus $392{,}370$ new at $|V(G)| = 21$).
+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
+(clauses 1--3) is verified up to $|V(G)| \leq 21$ ($535{,}182$
+colourings, all pass).
 \end{abstract}
 
 \maketitle
@@ -115,9 +116,10 @@ $3$-edge-colouring of $G'$ can be recovered, contradicting the
 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. Both conjectures have
-been verified computationally on all chord-apex+Kempe colourings of
-reduced duals up to $|V(G)| \leq 21$ ($535{,}182$ colourings).
+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
+up to $|V(G)| \leq 21$ ($535{,}182$ colourings).
 
 \paragraph{Organization.} Section~\ref{sec:minimal} fixes the
 minimal-counterexample framework: $G$ is a triangulation,