Restriction exponent for the 2-sphere (Stein's $L^\infty$ extension problem)

Upper bound, last-listed row

| $\frac{22}{7}\approx 3.142857$ | [WW2024] | |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $3$ | Stationary phase / explicit computation | Take $f=1$. Conjectured to be sharp [Ste1979] |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $4-\frac{2}{15} \approx 3.86667$ line 18 citing [Bo1991] — the claim we checked: that Bourgain's cited 1991 paper in Geometric and Functional Analysis states the upper bound this row attributes to it, 4 − 2/15 ≈ 3.86667. What we read does NOT support it: for this problem in three dimensions the paper's condition works out to p > 31/8 = 3.875 (Proposition 6.47 on p. 182, with p(3) = 7/3; p. 185 takes p₀ = 31/8 from it), and we did not find 4 − 2/15 in the pages read; its note added in proof, on p. 186, refers the reader to Bourgain's paper On the restriction and multiplier problem in R³ for "some refinements of the techniques and results of the present paper". This verdict does not cover whether the bound itself holds, and the correctness of any proof. source link (read in the published article, Geometric and Functional Analysis 1(2), 1991, pp. 147–187, from the Göttingen Digitisation Centre's page images: the introduction (pp. 147–149), p. 170, all of Section 6 on restriction to spheres (pp. 175–182) and Section 7 to the end (pp. 183–187); pp. 150–169 and 171–174 were not read). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
• Another row, not one shown above: bound row $3+\frac{3}{14}\approx 3.21429$ line 25 citing [WW2022] — the claim we checked: that the cited arXiv paper proves the restriction estimate for p > 3 + 3/14, and whether it is stated for the sphere or the paraboloid. What we read states that range for the paraboloid, not the sphere. This verdict does not cover the step from paraboloid to sphere that the mirrored page's own remark covers. source link (read in the body: arXiv v2 (14 Oct 2022, the version the entry's unversioned link resolves to), Theorem 1.2 on p. 1, read from the page image. The theorem gives the range p > 3 + 3/14 for the paraboloid, with the L^p norm of f on the right; the paper's statement is not about the sphere, and the step to the sphere was not checked. The proof was not checked). 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.