The Gyarmati-Hennecart-Ruzsa sum-difference constant

Upper bound, last-listed row

| $4/3 = 1.333\dots$ | [GHR2007] | |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $1.19102809$ ($1.19519192$*) | [K2026b] | Lean-formalized proof of $1.19519192$* via controlled-carry masked-digit limit construction with $M=\langle1971,2016,2100,2628,2688,2800\rangle\cap[0,26972]$ in base $27022$ and Lean-formalized explicit finite construction of $1.19102809$ with $M=\langle1518,1524,1587,2024,2032,2116\rangle\cap[0,17032]$ in base $34065$ using $10^{13}$ digits. Also includes formalization of necessary results from [GHR2007]. |value changed 2026-08-23

Checked against material for its cited source

• Another row, not one shown above: bound row $1.1584$ line 27 citing [GGSWT2025] — the claim we checked: that [GGSWT2025] reports the lower bound 1.1584, credited in the row to AlphaEvolve and obtained from a related set U2 of 54265 integers found by running the same experiment longer, and reports 1.1584 rather than 1.1479 as the final figure in Section 6.25. What we read supports it: Section 6.25 says AlphaEvolve first found a set U1 of 2003 integers giving 1.1479, and by running the experiment longer a related set U2 of 54265 integers giving 1.1584. That is AlphaEvolve's final figure there; the section's last paragraph reports later bounds by others, 1.173050 and 1.173077. source link (read in the arXiv HTML of version 3 (22 Dec 2025), Section 6.25, with the decisive paragraph checked against version 1; the entry names no version). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
• Another row, not one shown above: bound row $1.173077$* line 29 citing [Z2025] — the claim we checked: that the cited reference gives the lower bound 1.173077, reached only in the limit of a constructed sequence of U sets and not certified by a finite-depth computation. The row's quoted sentence is checked word for word against the source. What we read supports it: the paper's Theorem 1 states the bound 1.173077, its construction lets the set's parameters go to infinity, and it evaluates no finite set. The row's quotation is the abstract's sentence without its first three words, "In this work,", and with "We" capitalised; every other word matches. This verdict does not cover the correctness of the paper's mathematics, and the numerical optimisation its reported value comes from. source link (read in the body, all 11 pages of arXiv v1 (2 Jun 2025) as page images; arXiv's history lists v1 only, so it is the cited edition). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

2 bound row(s) here have been checked against material for their cited source (2 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.