The isotropic constant of a log-concave probability measure

Upper bound, last-listed row

| $C_{20b}<\infty$ (dimension-free) | [KL2024] | Final dimension-free bound (slicing/hyperplane theorem) |tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $C_{20b}\ge 1/\sqrt{12}\approx 0.288675$ | Classical | Achieved by the cube $[-\tfrac12,\tfrac12]^n$ (volume $1$) |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $L_{n}^{\mathrm{body}} \le C\,(\log n)^{2.082\ldots}$ line 79 citing [K2023] — the claim we checked: that K2023 states the bound L_n ≤ C·(log n)^2.082..., and whether it credits Lehec, as the row's comment does. What we read states the bound and credits it to Lehec, by personal communication. This verdict does not cover Lehec's own argument, which is unpublished. source link (read in the body: arXiv v2, which the journal (Ars Inveniendi Analytica) publishes as its version of record, p. 2, read from the page image. The paper reports this bound as Lehec's result, received by personal communication, and does not prove it; the row's comment credits Lehec the same way). 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.