Maximal number of relevant variables in degree-$d$ Boolean functions

Upper bound, last-listed row

| $4.394$ | [Wel2022] | Best published bound found (Theorem 1.1). |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $3/2$ | [CHS2020] | Construction with $R_d \ge 3\cdot 2^{d-1}-2$, hence $\sup_d R_d/2^d \ge 3/2$. (Also observed by Shinkar and Tal.) |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $26$ line 28 citing [CHS2020] — the claim we checked: that CHS2020 states or proves an upper bound of 26 on C_44 = sup_d R_d / 2^d; and, separately, the row's comment 'First explicit universal constant bound'. What we read could not settle it. source link (reached in the arXiv preprint (v3). Its Section 3, p. 4, proves C* ≤ 26 as a step toward its main bound C* ≤ 6.614. The Combinatorica edition the entry cites was reached only at its abstract, which carries 6.614 and not 26). 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.