3D critical Bochner–Riesz exponent

Upper bound, last-listed row

| $\frac{13}{4}=3.25$ | [[Wu2023](#Wu2023)], [[GOWWZ2025](#GOWWZ2025)] | Wu proved this range, and Guo–Oh–Wang–Wu–Zhang later recovered it by a different argument. [Wu2023-thm-3.25] [GOWWZ2025-r3-recover] |

exact pinned row

| $\frac{13}{4}=3.25$ | [[Wu2023](#Wu2023)], [[GOWWZ2025](#GOWWZ2025)] | Wu proved this range, and Guo–Oh–Wang–Wu–Zhang later recovered it by a different argument. <a href="#Wu2023-thm-3.25">[Wu2023-thm-3.25]</a> <a href="#GOWWZ2025-r3-recover">[GOWWZ2025-r3-recover]</a> |

tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $3$ | [[Wu2023](#Wu2023)] | Immediate from the definition of $C_{77}$; conjectured to be sharp. [Wu2023-conj-formula] |

exact pinned row

| $3$ | [[Wu2023](#Wu2023)] | Immediate from the definition of $C_{77}$; conjectured to be sharp. <a href="#Wu2023-conj-formula">[Wu2023-conj-formula]</a> |

tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• The row shown above: bound row $\frac{13}{4}=3.25$ line 36 citing [Wu2023] — the claim we checked: that [Wu2023] proves the result giving the upper bound 13/4 = 3.25 listed in this row. The later recovery attributed to [GOWWZ2025] is not checked here. What we read supports it: Theorem 1.2 states that the Bochner–Riesz conjecture holds in three dimensions when max{p, p/(p−1)} ≥ 3.25, and the paper proves it. source link (read in the arXiv preprint version 2 (6 Sep 2020): Theorems 1.2 and 1.3 on pp. 2–3 and the end of the proof on pp. 34–35, from page images; the journal edition the entry cites (Journal d'Analyse Mathématique 149, 2023) was reached only as its abstract, which states the same range). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
• Another row, not one shown above: bound row $\frac{10}{3}$ line 35 citing [Lee2006] — the claim we checked: that one of the row's Lee papers, Lee2004 or Lee2006, establishes the Bochner–Riesz range max{p, p′} ≥ 10/3 in R^3, and which one does. What we read supports the attribution to Lee2006. This verdict does not cover what Lee2004 itself states. source link (read in the body of Lee2006, the publisher's typeset JFA PDF (241 (2006) 56–98) from a Wayback capture of CORE's copy, pp. 59–60, read from page images. Lee2004, the row's first-listed reference, was NOT reached: its body is paywalled and no open copy was found). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

2 bound row(s) here have been checked against material for their cited source (2 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.