The cap set constant

Upper bound, last-listed row

| $2.756$ | [EG2016] | |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $2.2203$ | [ZWLPLZJZZZ2025] |X-evolvetracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $2.2202$ line 23 citing [RBNBKDREWFKF2023] — the claim we checked: that [RBNBKDREWFKF2023] gives the lower bound 2.2202 listed in this row, with the credit to Funsearch stated in the row. What we read supports it: the paper says FunSearch, which the authors pointed at symmetric admissible sets, found a partial admissible set in A(24,17) of size 237,984, which implies a lower bound of 2.2202 on the cap set capacity. source link (read in the published Nature article (vol. 625, pp. 468–475; online 14 Dec 2023) as the open-access full text at Europe PMC (PMC10794145), section Admissible sets; the Nature page itself was not requested). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
• Another row, not one shown above: bound row $2.2180$ line 22 citing [T2023] — the claim we checked: that the cited 2023 reference gives the lower bound 2.2180 (the row carries no comment column, so the value is the whole claim). What we read supports it: the paper's Theorem 1.2 gives, for large n, a cap set of size (2.218021…)^n, built from one explicit cap set in dimension 56232. The paper prints 2.218 or 2.218021…, never 2.2180; the row's four decimals are that value shortened. This verdict does not cover the construction itself, which we did not verify, and the correctness of the proof. source link (read in the body, all 18 pages of arXiv v2 (12 Dec 2023) as page images, with all 13 pages of v1 read alongside; v2 prints the journal's masthead, "Discrete Analysis, 2023:20, 18 pp."). 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.