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Claim. The note A Note on the Erdős–Szemerédi LCM-Window Problem for Exponents Greater Than 1/4 (repaired version dated 30 April 2026), posted that day by the forum user old-bielefelder in the discussion thread of Problem 873, proves in its Theorem 1 that for every $\varepsilon>1/4$ there is an integer $k=k(\varepsilon)$ with $F(A,X,k)\ll_{\varepsilon,k}X^{\varepsilon}$ uniformly over increasing sequences $A$, so that $F(A,X,k)<X^{\varepsilon}$ for all large $X$. The proof combines Letendre's Proposition 1, a uniform bound for the number of divisors of $n$ in a short interval near $n^{\theta}$ (library card letendre_2025_divisors_integer_short_interval), with two packing lemmas: the $k$ terms of a window with least common multiple below $X$ are divisors of that multiple lying in a short interval. The post says that ChatGPT 5.5 Thinking produced the note and repaired it after the poster's questions.

The second note, An Elementary 1/4 + ε Proof and a Localization of the 1/4 Barrier in the Erdős–Szemerédi LCM-Window Problem (rechecked version dated 18 August 2026), posted on 18 August 2026 with the statement that ChatGPT 5.6 Sol produced it, proves the same range without Letendre's result. Its Theorem 1 gives, for every integer $k\ge2$ and uniformly in $A$,

$$F(A,X,k)\ll_k X^{\Delta_k}\log(2X),\qquad \Delta_k=\begin{cases} \frac14+\frac1{4k},&k\text{ odd},\\[2pt] \frac14+\frac1{4(k-1)},&k\text{ even}, \end{cases}$$

so $\Delta_k$ decreases to $1/4$. Both notes say that their arguments do not reach the exponent $1/4$.

Covers. The question for every $\varepsilon>1/4$, with $X$ large. Not covered: $\varepsilon\le1/4$.

Standing. Claimed: neither note has an arXiv or journal record. Earlier on 30 April 2026, before the first note was posted, Terence Tao asked in the thread whether Letendre's paper bears on the problem at all. A reply reports an automated check of the first note that found no issues; it is a thread comment, not a review. The site's label is OPEN.

Depends on. No page of this wiki.