From 74b57d629e527493d749cb53410f4a7a71c27979 Mon Sep 17 00:00:00 2001 From: Taksh Date: Thu, 13 Aug 2026 06:53:14 +0530 Subject: [PATCH] Sync C_47 lower bound in README with the constant page The table lists the Melas value (11+sqrt(61))/12 ~ 1.5675208, which the 47a page records as the weaker of its two lower bounds: it comes from c_2 >= c_1 monotonicity. The same table's other row, Aldaz 2000 Proposition 1.4 specialized to n = 2, gives 3/4 - sqrt(2)/4 + sqrt(6)/2 ~ 1.6211915, which is strictly larger and so is the better known lower bound. The page's bound tables are chronological and may list bounds inferior to earlier ones, so the last row is not always the best; here the README had followed the last row. --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 2cd4f9b..526be3f 100644 --- a/README.md +++ b/README.md @@ -81,7 +81,7 @@ Bounds for which the level of available verification is currently at minimal lev | [44](https://teorth.github.io/optimizationproblems/constants/44a.html) | Maximal number of relevant variables in degree-$d$ Boolean functions | 1.5 | 4.394 | | [45](https://teorth.github.io/optimizationproblems/constants/45a.html) | Density of odd integers that are the sum of a prime and a power of two | 0.107648 | 0.490180063290061 | | [46](https://teorth.github.io/optimizationproblems/constants/46a.html) | Fourier restriction constant for the 2-sphere | 3 | $\frac{22}{7}\approx 3.142857$ | -| [47](https://teorth.github.io/optimizationproblems/constants/47a.html) | Centered Hardy-Littlewood maximal constant in dimension $2$ | $\frac{11+\sqrt{61}}{12}\approx 1.5675208$ | 4 | +| [47](https://teorth.github.io/optimizationproblems/constants/47a.html) | Centered Hardy-Littlewood maximal constant in dimension $2$ | $\frac{3}{4}-\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{2}\approx 1.6211915$ | 4 | | [48](https://teorth.github.io/optimizationproblems/constants/48a.html) | One-dimensional convex sub-Gaussian comparison constant | $\approx 5.33386$ | $\approx 5.33386$ | | [49](https://teorth.github.io/optimizationproblems/constants/49a.html) | Erdős–Szemerédi $3$-sunflower-free capacity | >1.551 ($\geq 1.554*$) | $\frac{3}{2^{2/3}} \approx 1.88988$ | | [50](https://teorth.github.io/optimizationproblems/constants/50a.html) | Approximation ratio for quantum Max Cut | 0.614 | $<1$ (0.5 for product states) |