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Claim. A note posted in the site's thread on 2026-03-09 by Nat Sothanaphan, who writes that GPT-5.2 Thinking produced it, extends van Doorn's results on the completeness of $(\lfloor t\alpha^n\rfloor)_{n\ge1}$ (van Doorn's claim page) in two ways, as the thread describes it: the infinite-area result that the sequence is complete whenever $1<\alpha\le1+1/(\lceil t\rceil+2\lceil\sqrt t\rceil)$ is sharpened, the denominator decreasing to $\lceil t\rceil+2\lceil\sqrt t\rceil-f(t)$ with $0\le f(t)<C$ for an absolute constant $C$ (van Doorn's reading of the note in van Doorn's reply of the same day); and the computer-certified rectangles of pairs $(\alpha,t)$ for which the sequence is complete are expanded, the note's Table 2 certifying for example all pairs with $\alpha\in[1.10,1.15]$ and $t\in[1,16]$. The poster states that no new main idea was obtained. The note was revised the same day, after van Doorn pointed out that its row $\alpha\in[1.55,1.60]$, $t\in[1,1.15]$ was already covered by Proposition 5 of van Doorn's paper, to mark that row as known. The preprint link is the Drive copy the thread links.

Submission note. Posted to the site's forum by Nat Sothanaphan on 9 March 2026:

GPT-5.2 Thinking has extended Woett's results a little bit in this note (edit: now this is the updated version). Specifically, the infinite-area result is sharpened and certified regions are expanded. However, no new main idea has been obtained. (This is probably my last work with GPT-5.2 Thinking.)

Covers. Pairs $(t,\alpha)$ of Problem 349 with $1<\alpha<\varphi$ in the sharpened infinite-area region and in the certified rectangles, for the corrected Statement, whose sums and index van Doorn's paper uses: completeness is proved on those pairs, so the claim's value is proved. It settles no pair outside them and does not bear on the conjectured completeness for all $t>0$ below the golden ratio.

Standing. Claimed: a note on a file-sharing service, not refereed, with no site mention and no review beyond van Doorn's thread reply, which called the sharpening marginal, noted that van Doorn's own code certifies larger regions in seconds, and thanked the poster, saying that van Doorn's computations seemed to have been independently verified. The system named is GPT-5.2 Thinking, as the poster names it.

Depends on. Van Doorn's claim page, whose Proposition 9 the note sharpens and whose certification method it extends.