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Claim. The note "A note on Erdős Problem #1201" (30 April 2026) states as its Theorem 1 that for every $\varepsilon>0$ the upper asymptotic density of the integers $n$ with $P^+(n(n+1)\cdots(n+h-1))\le n^{1-\varepsilon}$ tends to $0$ as $h\to\infty$; consequently, for every $\varepsilon,\eta>0$ there is a $k$ such that the set of $n$ with $P^+(n(n+1)\cdots(n+k))>n^{1-\varepsilon}$ has lower asymptotic density at least $1-\eta$, which answers the precise Statement of Problem 1201 yes. The argument applies Theorem 1 of Matomäki and Radziwiłł, compiled on the card matomaki_2016_multiplicative_functions_short_intervals, to the indicator of the $X^{\beta}$-smooth integers with $\beta=1-\varepsilon/2$: its long average over $[X,2X]$ is $\rho(1/\beta)+o(1)<1$ by the Dickman--de Bruijn count, every $n$ in the exceptional set makes the short average over $[n,n+h)$ equal to $1$, so the exceptional $n\in[X,2X]$ number at most a constant times $X(\log h)^{1/3}/(\delta^2h^{\delta/25})$ for a suitable fixed $\delta$, and a dyadic decomposition turns this into the bound on the upper density. The note calls its result an immediate but apparently unrecorded consequence of that theorem. The note's statements are recorded on its card chojecki_2026_note_erdos_problem_1201; no step of its proof has been checked independently.

Submission note. Posted to the site's forum by Przemysław Chojecki on 30 April 2026:

This can be deduced from Matomäki–Radziwiłł theorem on multiplicative functions with a fairly short argument. The note written by GPT-5.5 Pro is here. I haven't found this observation in literature.

Standing. Przemek Chojecki posted the note in the site's thread on 30 April 2026, presenting it as written by GPT-5.5 Pro; Chojecki is the claimant as its submitter, and GPT-5.5 Pro is the system Chojecki names. The thread's discussion turned on the formulation: Terence Tao wrote that the problem remained technically open because the existence of the natural density of the set was not established, only that its lower density is at least $1-\eta$; Will Sawin found it reasonable to read "density at least" (Sawin's words for the statement's bound) as lower density, and the site's curator, Thomas Bloom, agreed that this is generally how Erdős used the terms. The site's label is nevertheless unchanged (OPEN), the problem is not credited to the note, and no entry was filed on the proof-claims tab. A thread comment reports that a standard check found no issues, which is a screening report, not a review. The note itself carries no byline and, as of 2026-10-07, has no refereed publication, formalization or outside review. The claim stays claimed. The natural-density variant is recorded on the problem page and on Chojecki's conditional page.

Depends on. Nothing on the wiki; the outside inputs are the Matomäki--Radziwiłł theorem and the Dickman--de Bruijn count, named above.