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Claim. There is an $\eta>0$ such that for all sufficiently large $X$ the interval $[X,X+X^{1/5-\eta}]$ contains a squarefree number. For the squarefree numbers of Problem 208 this says $s_{n+1}-s_n\ll s_n^{1/5-\eta}$, so $s_{n+1}-s_n\ll_\epsilon s_n^\epsilon$ for every $\epsilon>1/5-\eta$, improving the exponent $1/5$ of Filaseta and Trifonov. The abstract describes the method as a new way of counting lattice points near curves under extra restrictions, applied to the integers of a short interval divisible by a large square, with Green and Tao's quantitative equidistribution theorem for polynomial orbits on nilmanifolds as input. The source is M. Pandey, Squarefree numbers in short intervals, arXiv:2401.13981, first posted 2024-01-25, third version posted 2026-08-07; its library card is pandey_2024_squarefree_numbers_short_intervals.

Covers. The first question for every $\epsilon>1/5-\eta$, with the $\eta>0$ of the theorem, which the abstract does not quantify. Not covered: the first question for smaller $\epsilon$, and the second question.

Depends on. Nothing in this wiki; the claim rests on the cited preprint.

Standing. The preprint carries no journal reference or DOI of a published version in its arXiv record, so no refereed evidence exists. The site's curator credits the improved exponent in the problem's commentary, but the site labels the problem OPEN, so that credit is not acceptance. The claim stays claimed; the corpus records no check of the proof.