diff --git a/constants/3a.md b/constants/3a.md index 7c84b23..e307d7a 100644 --- a/constants/3a.md +++ b/constants/3a.md @@ -1,4 +1,4 @@ -# The Gyamarti-Hennecart-Ruzsa sum-difference constant +# The Gyarmati-Hennecart-Ruzsa sum-difference constant ## Description of constant @@ -18,18 +18,21 @@ $$ |A-B| \gg |A+B|^{C_{3a}}.$$ | Bound | Reference | Comments | | ----- | --------- | -------- | | $1$ | Trivial | | -| $1.14465$ | [GHR2007] | -| $1.1479$ | [GGSWT2025] | AlphaEvolve -| $1.173050$ |[G2025] | -| $1.173077$ |[Z2025]| +| $1.14465$ | [GHR2007] | | +| $1.1479$ | [GGSWT2025] | AlphaEvolve | +| $1.173050$ |[G2025] | | +| $1.173077$ |[Z2025]| | | $1.1740744$ | [G2026] | Base-$21$ digit construction with exact counting certificate. | | $1.1835129324$ | [MI2026] | Base-$33$ digit construction with exact counting certificate. | +| $1.19102809$ | [K2026] | Base-$34065$ masked-digit limit construction with $M=\langle1518,1524,1587,2024,2032,2116\rangle\cap[0,17032]$ and a directed-rounding certificate. | ## Additional comments and links -- Thanks to a lemma from [GHR2007], any finite set $U$ of non-negative integers containing zero yields a lower bound of the form -$C_{3a} \geq 1 + \log( \lvert U-U \rvert /\lvert U+U \rvert )/\log(2 \max(U)+1)$. However, the lower bounds obtained in this fashion cannot exceed $1.25$. +- A lemma from [GHR2007] states that a finite set $U$ of non-negative integers containing zero and satisfying $\lvert U-U\rvert<2\max(U)+1$ yields +$C_{3a} \geq 1 + \log( \lvert U-U \rvert /\lvert U+U \rvert )/\log(2 \max(U)+1)$. Lower bounds obtained in this fashion cannot exceed $1.25$. +- [K2026] generalizes the bounded-digit limit construction in [Z2025] by replacing bounded digits with digits restricted to a finite mask. +- The record mask in [K2026] is generated by the product grid $`\{3,4\}\times\{506,508,529\}`$; its column semigroup is the simple gluing $\langle506,508,529\rangle=23\langle22,23\rangle+508\mathbb N_0$. - [AlphaEvolve repository page for this problem](https://google-deepmind.github.io/alphaevolve_repository_of_problems/problems/44.html) ## References @@ -40,3 +43,4 @@ $C_{3a} \geq 1 + \log( \lvert U-U \rvert /\lvert U+U \rvert )/\log(2 \max(U)+1)$ - [MI2026] Mosaic Intelligence ([@111111](https://x.com/111111)). Exact-count certificate for problem 3a, [certificate archive](https://doi.org/10.5281/zenodo.20794135), [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/95) (2026). - [Z2025] Zheng, Fan. Sums and differences of sets: a further improvement over AlphaEvolve, 2025. [arXiv:2506.01896](https://arxiv.org/abs/2506.01896). - [G2026] Griego, Sebastian. Base-$21$ digit construction certificate for $C_{3a}$, [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/71) (2026). +- [K2026] Kleinwaks, Logan. A masked-digit lower bound for the Gyarmati–Hennecart–Ruzsa sum–difference constant, [proof and verification package](https://github.com/kleinwaks/masked-digit-sum-difference-bound), [submitted to this repository](https://github.com/teorth/optimizationproblems/pull/134) (2026).