Improve lower bound for the Fourier Entropy-Influence constant to 6.521845710923046575 (n=18 certified construction)

README.md

@@ -107,7 +107,7 @@ Bounds for which the level of available verification is currently at minimal lev
 | [68](https://teorth.github.io/optimizationproblems/constants/68a.html) | Korenblum's constant | 0.3554 | 0.6778994 |
 | [69](https://teorth.github.io/optimizationproblems/constants/69a.html) | Sendov radius constant | 1 | 2 |
 | [70](https://teorth.github.io/optimizationproblems/constants/70a.html) | Reverse Brunn-Minkowski constant | 1 | $<\infty$ |
-| [71](https://teorth.github.io/optimizationproblems/constants/71a.html) | Fourier Entropy-Influence constant | 6.278 | $\infty$ |
+| [71](https://teorth.github.io/optimizationproblems/constants/71a.html) | Fourier Entropy-Influence constant | 6.521845710923046575 | $\infty$ |
 | [72](https://teorth.github.io/optimizationproblems/constants/72a.html) | Polya-Vinogradov best constant (squarefree asymptotic) | 0 | $\frac{1}{4\pi}\approx 0.07958$ |
 | [73](https://teorth.github.io/optimizationproblems/constants/73a.html) | Flatness constant in dimension 3 | $2+\sqrt{2}$ | $<3.972$ |
 | [74](https://teorth.github.io/optimizationproblems/constants/74a.html) | 10-point multi-point Seshadri constant on $\mathbb{P}^2$ | $\frac{117}{370}$ | $\frac{1}{\sqrt{10}}$ |

constants/71a.md

@@ -37,23 +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 17 variables (exact integer
+An explicit balanced, logic-monotone function on 18 variables (exact integer
 Fourier spectrum and truth table certified exactly), via the O'Donnell--Tan
 amplification rule $C \ge H/(I-1)$, gives
 
 $$
-C_{71}\ >\ 6.514326913930565372,
+C_{71}\ >\ 6.521845710923046575,
 $$
 
 and the same certificate shows the bound holds even restricted to monotone
 functions.
 
-<a href="#MI2026b">[MI2026b]</a>
+<a href="#Num2026">[Num2026]</a>
 
 Hence the best established range is
 
 $$
-6.514326913930565372\ <\ C_{71}\ \le\ \infty.
+6.521845710923046575\ <\ C_{71}\ \le\ \infty.
 $$
 
 ## Known upper bounds
@@ -71,6 +71,7 @@ $$
 | $>6.4547837$ | [[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> |
+| $>6.521845710923046575$ | [[Num2026](#Num2026)] | Explicit balanced **logic-monotone** function on 18 variables via the [[OT2013](#OT2013)] amplification rule $C \ge H/(I-1)$; exact influence $261/128$; obtained from the [[MI2026b](#MI2026b)] function by equalising the auxiliary-variable action (the single 4-cell auxiliary is split 2+2 with the new 18th variable), raising $H$ by exactly twice the moved spectral weight at identical influence — certified gain exactly $1/133$; exact-rational spectrum + interval arithmetic; replayable single-file certificate. The function is monotone, so the same bound holds even restricted to monotone functions. <a href="#Num2026-bound">[Num2026-bound]</a> |
 
 ## Additional comments and links
 
@@ -110,6 +111,10 @@ $$
 	  **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."
 
+- <a id="Num2026"></a>**[Num2026]** Numaro ([numaro.tech](https://numaro.tech)). *A certified n=18 lower bound for the Fourier Entropy-Influence constant.* [Certificate archive](https://doi.org/10.5281/zenodo.21497769), submitted to this repository (2026).
+	- <a id="Num2026-bound"></a>**[Num2026-bound]**
+	  **loc:** certificate archive, README and `check_c71_n18.py` output.
+	  **quote:** "C_71 > 6.521845710923046575 — and, by the same logic-monotone certificate, even restricted to monotone functions (full floor-truncated value 6.5218457109230465756581439729485784683666); certified by the replayable script; the strict-improvement comparison is made against the previous record's certified upper endpoint, so the gain — exactly 1/133 — is itself certified."
 ## Contribution notes
 
 Prepared with assistance from ChatGPT 5.2 Pro.