From 8b87d52bdec08f7b4d3ef6cf2cd55f3e9c30366a Mon Sep 17 00:00:00 2001
From: Mosaic Intelligence <463464q435q43@users.noreply.github.com>
Date: Wed, 1 Jul 2026 22:24:36 +0200
Subject: [PATCH] Improve C_71 lower bound to 6.514326913930565372

---
 constants/71a.md | 17 ++++++++++++-----
 1 file changed, 12 insertions(+), 5 deletions(-)

diff --git a/constants/71a.md b/constants/71a.md
index cbcf53b..20a00a1 100644
--- a/constants/71a.md
+++ b/constants/71a.md
@@ -37,22 +37,23 @@ $$
 The conjecture is equivalent to $C_{71}<\infty$, and this remains open.
 <a href="#ODWZ2011-open-problem">[ODWZ2011-open-problem]</a>
 
-An explicit balanced, logic-monotone function on 14 variables (truth table
-certified exactly), amplified by self-composition (O'Donnell--Tan), gives
+An explicit balanced, logic-monotone function on 17 variables (exact integer
+Fourier spectrum and truth table certified exactly), via the O'Donnell--Tan
+amplification rule $C \ge H/(I-1)$, gives
 
 $$
-C_{71}\ >\ 6.4901128435233943,
+C_{71}\ >\ 6.514326913930565372,
 $$
 
 and the same certificate shows the bound holds even restricted to monotone
 functions.
 
-<a href="#MI2026">[MI2026]</a>
+<a href="#MI2026b">[MI2026b]</a>
 
 Hence the best established range is
 
 $$
-6.4901128435233943\ <\ C_{71}\ \le\ \infty.
+6.514326913930565372\ <\ C_{71}\ \le\ \infty.
 $$
 
 ## Known upper bounds
@@ -69,6 +70,7 @@ $$
 | $6.278$ | [[OT2013](#OT2013)] | Explicit example with ratio at least $6.278$. <a href="#OT2013-lb-6-278">[OT2013-lb-6-278]</a> |
 | $>6.4547837$ | [[Hod2017](#Hod2017)] | Theorem 4.4 gives $C\ge \beta(1/2)>6.4547837$, even when restricted to monotone functions. <a href="#Hod2017-thm4.4">[Hod2017-thm4.4]</a> |
 | $>6.4901128435233943$ | [[MI2026](#MI2026)] | finite balanced **logic-monotone** function on 14 variables (explicit truth table), via O'Donnell–Tan amplification $C \ge H/(I-1)$; certified by exact-rational spectrum + interval arithmetic. The seed is monotone and composition preserves monotonicity, so the same bound holds even restricted to monotone functions. <a href="#MI2026-bound">[MI2026-bound]</a> |
+| $>6.514326913930565372$ | [[MI2026b](#MI2026b)] | Explicit balanced **logic-monotone** function on 17 variables via the [[OT2013](#OT2013)] amplification rule $C \ge H/(I-1)$; exact influence $261/128$; certified by exact-rational spectrum + interval arithmetic; replayable certificate, see PR. The function is monotone, so the same bound holds even restricted to monotone functions. <a href="#MI2026b-bound">[MI2026b-bound]</a> |
 
 ## Additional comments and links
 
@@ -103,6 +105,11 @@ $$
 	  **loc:** certificate archive and this pull request
 	  **quote:** "C_71 > 6.4901128435233943 — and, by the same logic-monotone certificate, even restricted to monotone functions (full floor-truncated value 6.49011284352339435967722960726821776674269968263998854502375); certified by the replayable script below."
 
+- <a id="MI2026b"></a>**[MI2026b]** Mosaic Intelligence ([@111111](https://x.com/111111)). *A certified n=17 lower bound for the Fourier Entropy-Influence constant.* [Certificate archive](https://doi.org/10.5281/zenodo.21113935), submitted to this repository (2026).
+	- <a id="MI2026b-bound"></a>**[MI2026b-bound]**
+	  **loc:** certificate archive and this pull request
+	  **quote:** "C_71 > 6.514326913930565372 — and, by the same logic-monotone certificate, even restricted to monotone functions (full floor-truncated value 6.51432691393056537265062517595609726535914349523745739524537); certified by the replayable script below."
+
 ## Contribution notes
 
 Prepared with assistance from ChatGPT 5.2 Pro.