Exponential growth constant for diagonal Ramsey numbers

Upper bound, last-listed row

| $3.791993699438612 < 3.792$ | [Gri26] | Computer-assisted verification using Theorem 13 and Lemma 14 of [GNNW2024] |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $\sqrt{2} = 1.4142135623\dots$ | [Erd1947] | Introduces Erdős’ probabilistic method|tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• The row shown above: bound row $3.791993699438612 < 3.792$ line 14 citing [Gri26] — the claim we checked: that the cited reference gives the upper bound this row lists, 3.791993699438612 < 3.792, by a computer-assisted verification using Theorem 13 and Lemma 14 of [GNNW2024], as the row's comment says. What we read supports it: the proof note's Theorem 1 states that the limit superior of R(k,k)^(1/k) is at most 3.791993699438612 < 3.792, by a computer-assisted interval-arithmetic certificate, and names Theorem 13 and Lemma 14 of [GNNW2024] as its only outside input. source link (read in the repository at its latest commit (2 July 2026): the README, the four-page proof note (as page images, checked against its TeX source), the certificate file and the verifier's description of itself; the verifier was not run). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

1 bound row(s) here have been checked against material for their cited source (1 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.