Smallest $n$ for which the value of $BB(n)$ is undecidable

Upper bound, last-listed row

| 432 | [W2025] | With methods of [O2016] |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| 6 | [BB2025] | By computing $BB(5)$ |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row 4 line 23 citing [LS1965] — the claim we checked: that the cited 1965 paper determines the three-state busy beaver value, which is what the row's lower bound 4 rests on, as its comment says. What we read supports it: the paper determines both three-state busy beaver values, the most ones (6) and the most shifts (21), by computer enumeration plus a hand check of the 40 machines the program could not settle; the step from there to the row’s lower bound 4 is the mirror’s own reasoning, which the paper does not state and does not contradict. source link (read in the cited journal edition, Journal of the ACM 12(2), pp. 196–212, all seventeen pages from page images of the publisher’s PDF, fetched from an Internet Archive capture of the address the entry links because the publisher answered 403). 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.