The complexity threshold of random 3-SAT

Upper bound, last-listed row

| 4.490 | [DKMP2009] ||tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| 3.52| [HS2003], [KKL2003]||tracked since 2026-07-24 — no movement seen yet

Checked or tried against material for its cited source

• Another row, not one shown above: bound row 4.643 line 33 citing [DB1997] — the cited source could not be read at all (tried 2026-09-24). the source we could not read (NOT read — ScienceDirect returned a bot challenge, the article is not open access, and no index carries its abstract). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
• Another row, not one shown above: bound row 4.602 line 34 citing [KKKS1998] — the claim we checked: that the cited 1998 paper proves the upper bound 4.602 on the random 3-SAT threshold, with the exact figure the paper prints recorded beside this verdict. What we read supports it. source link (read in the cited journal edition (the Wiley-typeset article, printed pp. 253–269, served by Carleton University's repository): the abstract on p. 253, the introduction on p. 255 and Theorem 3 on p. 266, read from page images. The paper prints its bound as 4.601+, "a value between 4.601 and 4.60108", and never as 4.602; the row's 4.602 is that bound rounded up). 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. Also attempted, and the source could NOT be read: the bound row 4.643 citing [DB1997] line 33. That row is not counted as read. A row not listed here has NOT been checked.