diff --git a/README.md b/README.md index cfeef46..36e9dcf 100644 --- a/README.md +++ b/README.md @@ -41,7 +41,7 @@ Bounds for which the level of available verification is currently at minimal lev | [15a](https://teorth.github.io/optimizationproblems/constants/15a.html) | Matrix multiplication exponent | 2 | 2.371339 | | [15b](https://teorth.github.io/optimizationproblems/constants/15b.html) | Dual matrix multiplication exponent | >0.321334 | 1 | | [16](https://teorth.github.io/optimizationproblems/constants/16a.html) | Brezis–Gallouet–Wainger remainder constant on the 2D torus | $\frac{\beta + \pi}{\pi} \approx 1.82283$ | $\approx 2.15627$ | -| [17](https://teorth.github.io/optimizationproblems/constants/17a.html) | Exponential growth constant of diagonal Ramsey numbers | $\sqrt{2} \approx 1.4142$ | 3.7992027396 | +| [17](https://teorth.github.io/optimizationproblems/constants/17a.html) | Exponential growth constant of diagonal Ramsey numbers | $\sqrt{2} \approx 1.4142$ | 3.7919936995 | | [18](https://teorth.github.io/optimizationproblems/constants/18a.html) | Marton's conjecture constant (PFR) | 1 | 9 | | [19](https://teorth.github.io/optimizationproblems/constants/19a.html) | Berry–Esseen constant | 0.4097321837 | 0.4690 | | [20a](https://teorth.github.io/optimizationproblems/constants/20a.html) | Thin shell conjecture constant | 2 | $< \infty$ | diff --git a/constants/17a.md b/constants/17a.md index bb07208..58ef05c 100644 --- a/constants/17a.md +++ b/constants/17a.md @@ -11,6 +11,7 @@ $C\_{17}$ is the limit (if it exists) of $R(k)^{1/k}$ as $k \to \infty$, where t | $4$ | [ES1935] | | $4 - 2^{-7} = 4 - \frac{1}{128} = 3.9921875$ | [CGMS2023] | A simpler proof with $4 - 2^{-10}$ is also provided | | $4 e^{-0.14/e} = 3.7992027396\dots$ | [GNNW2024] | Optimizes parameters in the [CGMS2023] approach | +| $3.791993699438612 < 3.792$ | [Gri26] | Computer-assisted verification using Theorem 13 and Lemma 14 of [GNNW2024] | ## Known lower bounds @@ -36,10 +37,14 @@ For the purposes of this page, upper (resp. lower) bounds on $C_{17}$ should be - [Sah2023] Sah, A. *Diagonal Ramsey via effective quasirandomness.* Duke Math. J. 172 (2023), 545–567. - [CGMS2023] Campos, M.; Griffiths, S.; Morris, R.; Sahasrabudhe, J. *An exponential improvement for diagonal Ramsey.* [arXiv:2303.09521](https://arxiv.org/abs/2303.09521) - [GNNW2024] Gupta, P.; Ndiaye, N.; Norin, S.; Wei, L. *Optimizing the CGMS upper bound on Ramsey numbers.* [arXiv:2407.19026](https://arxiv.org/abs/2407.19026) +- [Gri26] Max Grinsztajn. +Code and certificate for a Ramsey upper bound below 3.792. +GitHub repository, 2026. +https://github.com/maaxgrin/ramsey-3792-bound - [BBCGHMST2024] Balister, P.; Bollobás, B.; Campos, M.; Griffiths, S.; Hurley, H.; Morris, R.; Sahasrabudhe, J.; Tiba, A. *A shorter proof of the exponential improvement for diagonal Ramsey.* [arXiv:2403.02803](https://arxiv.org/abs/2403.02803) - [CFS2015] Conlon, D.; Fox, J.; Sudakov, B. *Recent developments in graph Ramsey theory.* Surveys in Combinatorics 2015, London Math. Soc. Lecture Note Series 424, 49–118. - [GRS1990] Graham, R. L.; Rothschild, B. L.; Spencer, J. H. *Ramsey Theory.* 2nd ed., Wiley, 1990. ## Contribution notes -ChatGPT DeepResearch was used to prepare an initial version of this page. \ No newline at end of file +ChatGPT DeepResearch was used to prepare an initial version of this page.