The degree--sensitivity exponent

Upper bound, last-listed row

| $2$ | [P2021] | Improves the *constant factor* in the quadratic bound: $bs(f)\le \deg(f)^2/(\sqrt{10}-2)$, hence $s(f)\le \deg(f)^2/(\sqrt{10}-2)\approx 0.8604\,\deg(f)^2$ (still exponent $2$). |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $\log_3 6 \approx 1.63093$ | [HKP2011] | Kushilevitz function $h$ on $6$ bits has $s(h)=6$ and $\deg(h)=3$, and hence exponent $\log_3 6$. |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• The row shown above: bound row $2$ line 47 citing [P2021] — the claim we checked: that the cited arXiv paper proves bs(f) ≤ deg(f)^2 / (√10 − 2); the row's exponent 2 and its 0.8604 follow from that by arithmetic. What we read supports it. source link (read in the body: arXiv v2 (19 Jun 2021, the version the entry's unversioned link resolves to), Theorem 1 on p. 2, read from the page image. The theorem is printed as d²(f) ≥ (√10 − 2)bs(f), which is the row's bound rearranged; the proof was not checked). 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.