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Improve lower bound for C_3b #92

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Improve lower bound for C_3b
463464q435q43 Jun 10, 2026
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Fill in PR number in C_3b reference
463464q435q43 Jun 10, 2026
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2 changes: 2 additions & 0 deletions constants/3b.md
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Expand Up @@ -25,6 +25,7 @@ $$ A \stackrel{G}{\pm} B := \{ a \pm b: a \in A, b \in B\}.$$
| $\frac{\log 27}{\log (27/4)} = 1.72598\dots$ | Ruzsa (unpublished) | |
| $1.77898$ | [L2015] | |
| $>1.77898$ | [GGSWT2025] | Improved [L2015] in the eighth decimal place (AlphaEvolve) |
| $1.77898884$ | [MI2026] | Entropy construction on a 13-point support. |


## Additional comments and links
Expand All @@ -40,5 +41,6 @@ $$ H(X-Y) \leq C_{3b} \max( H(X), H(Y), H(X+Y)).$$
- [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.
- [MI2026] Mosaic Intelligence ([@111111](https://x.com/111111)). 13-point entropy certificate for $C_{3b}$, [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/92) (2026).
- [KT1999] Katz, Nets Hawk; Tao, Terence. Bounds on arithmetic projections, and applications to the Kakeya conjecture. Math. Res. Lett. 6 (1999), no. 5-6, 625-630. DOI: 10.4310/MRL.1999.v6.n6.a3.
- [KT2002] Katz, N. H.; Tao, T. New bounds for Kakeya problems. J. Anal. Math. 87 (2002), 231–263. DOI: 10.1007/BF02792310.