Bohnenblust--Hille constant on the Boolean cube

Upper bound, last-listed row

| $\infty$ | Trivial | the best general estimate currently available is subexponential growth: $\mathrm{BH}^{\le d}_{\lbrace\pm1\rbrace}\le C^{\sqrt{d \ \log \, d}}$ for an absolute constant $C>1$ [DMP2019]. |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $2$ | [ADGP2025] | Degree $d$ address function achieves the bound $2^{\frac{d-1}{d}}$. At present, chasing incremental improvements of lower bounds seems less compelling than establishing any finite uniform upper bound. That said, exhibiting a construction that forces the constant to exceed $100$ would already be a genuinely interesting result. |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• The row shown above: bound row $\infty$ line 36 whose comment cites [DMP2019] — the claim we checked: the attribution in the row's comment, that DMP2019 proves the Bohnenblust–Hille constant for functions of degree at most d on the Boolean cube is at most C raised to the power √(d log d), for an absolute constant C. What we read supports it. This verdict does not cover the comment's words 'best general estimate currently available'. source link (read in the body of the arXiv preprint (v1, the only version), Theorem 1.1 on p. 3, and in the published Math. Ann. abstract, which states the same bound; the published body was not reached. Only the comment's attribution was checked. The row's bound cell, infinity credited to 'Trivial', was not). 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.