| $\widetilde{O}(\log^{1/4} n)$ | [BJ2025] | Current best published asymptotic bound (hides polylog factors, e.g. in $\log\log n$). First improvement over $O(\sqrt{\log n})$. |tracked since 2026-07-24 — no movement seen yet
Lower bound, last-listed row
| $1+\sqrt{2}$ | [Kun2023] | Best known lower bound on $C_{24}$. |tracked since 2026-07-24 — no movement seen yet
Checked or tried against material for its cited source
Another row, not one shown above: bound row $O(\log n)$line 35 citing [Bec1981] — the cited source could not be read at all (tried 2026-09-12). the source we could not read (NOT read — the publisher returned a bot challenge). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
Another row, not one shown above: bound row $O(\sqrt{\log n})$ (poly-time)line 37 citing [BDG2019] — the claim we checked: that the cited reference gives a polynomial-time algorithm reaching O(√(log n)), matching Banaszczyk's bound up to constants. What we read supports it: the paper gives an efficient randomized algorithm that reaches O(√(log n)) with high probability, calls it a constructive proof of Banaszczyk's bound, and argues the polynomial running time in its Section 4; the row does not say the algorithm is randomized. This verdict does not cover the correctness of the proof. source link (read in the cited SIAM J. Comput. edition (vol. 48, no. 2, pp. 534–553), as SIAM's typeset PDF held in the CWI repository, from page images, with arXiv v3 read alongside; the SIAM landing page answered 403). 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. Also attempted, and the source could NOT be read: the bound row $O(\log n)$ citing [Bec1981] line 35. That row is not counted as read. A row not listed here has NOT been checked.
Cite this rowBounds Ledger — Komlós discrepancy constant (24a)
upper bound: $\widetilde{O}(\log^{1/4} n)$ (tracked since 2026-07-24 — no movement seen yet)
lower bound: $1+\sqrt{2}$ (tracked since 2026-07-24 — no movement seen yet)
Mirrored from teorth/optimizationproblems@2c1968c. These are the last-listed rows of that constant's bounds table — a listing position, not a statement that this bound is the strongest or most recent. A snapshot at that sha, not a live read.
https://u00dxk2.github.io/bounds-ledger/c/24a.html