From cea3419cc71ba393c30c092f1e554da52e6a0ed3 Mon Sep 17 00:00:00 2001
From: Sebastian Griego <177274079+sebastian-griego@users.noreply.github.com>
Date: Tue, 12 May 2026 15:09:25 -0700
Subject: [PATCH] Improve C_3c lower bound

---
 constants/3c.md | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/constants/3c.md b/constants/3c.md
index c081f82..f2fdf84 100644
--- a/constants/3c.md
+++ b/constants/3c.md
@@ -29,6 +29,7 @@ $$ A \stackrel{G}{\pm} rB := \{ a \pm rb: a \in A, b \in B\}.$$
 | $1.61226$ | [L2015] | |
 | $1.668$ | [GGSWT2025] | |
 | $1.67471$ | [A2026] | |
+| $1.67473389$ | [SG2026] | Entropy construction on a 26-point support. |
 
 
 
@@ -38,13 +39,14 @@ $$ A \stackrel{G}{\pm} rB := \{ a \pm rb: a \in A, b \in B\}.$$
 ## Additional comments and links
 
 
-- Has many other formulations [GR2019], including an entropy formulation: $C_{3b}$ is the smallest constant such that for any pair of discrete random variables $X,Y$ one has
-$$ H(X-Y) \leq C_{3b} \max( H(X), H(Y), H(X+Y), H(X+2Y)).$$ This entropy formulation has been used to attain all known lower bounds.
+- Has many other formulations [GR2019], including an entropy formulation: $C_{3c}$ is the smallest constant such that for any pair of discrete random variables $X,Y$ one has
+$$ H(X-Y) \leq C_{3c} \max( H(X), H(Y), H(X+Y), H(X+2Y)).$$ This entropy formulation has been used to attain all known lower bounds.
 - Related to the arithmetic Kakeya conjecture [KT2002], [GR2019], which considers other sets of slopes than $0,1,2,\infty$.
 
 
 ## References
 - [A2026] Astor, T. Improved Arithmetic Kakeya-Type Counterexamples. TBA (2026)
+- [SG2026] Griego, Sebastian. 26-point entropy certificate for $C_{3c}$, submitted to this repository (2026).
 - [GGSWT2025] Georgiev, Bogdan; Gómez-Serrano, Javier; Tao, Terence; Wagner, Adam Zsolt. Mathematical exploration and discovery at scale. [arXiv:2511.02864](https://arxiv.org/abs/2511.02864)
 - [GR2019] Green, B.; Ruzsa, I. Z. On the arithmetic Kakeya conjecture of Katz and Tao. Periodica Mathematica Hungarica, Volume 78, Issue 1, pp 135–151 (2019). DOI: 10.1007/s10958-018-2003-3.
 - [L2015] Lemm, Marius. New counterexamples for sums-differences. Proceedings of the American Mathematical Society, Vol. 143, No. 9 (SEPTEMBER 2015), pp. 3863-3868 (6 pages). DOI: 10.1090/proc/12731.