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Claim. Stefan Ringer, Normality of squarefree-weighted series, dated 27 September 2026, four pages, in the author's GitHub repository StefanRinger/erdos-259-research (committed 2026-09-28). Its Theorem 1 states that for every fixed integer $B\ge2$ the number

$$\alpha_B=\sum_{n\ge1}n\,\mu(n)^2B^{-n}$$

is normal to base $B$, with the discrepancy of the orbit $(\{B^n\alpha_B\})_{n\le M}$ bounded by a constant times $(\log\log M)^{-1}$; the base and the number vary together, and no absolute normality is asserted. At $B=2$, $\alpha_2$ is the sum of Problem 259, and a number normal to some base is irrational, so the theorem claims more than the question asks. The manuscript cites Chen and Ruzsa's proof of the irrationality, on their claim page, as already settling the question. Its footnote says that the AI systems GPT 6 Astra and Fable 5.1 assisted with the development and checking of the proofs; the author's thread comment of 2026-09-28, which posts the manuscript, repeats that attribution and says a Lean formalization will follow. The repository's lean folder is empty at the pinned commit.

Standing. Claimed. The manuscript is not refereed; no outside review of it and no acknowledgment by the site's curator is recorded, and the corpus records no check of its proof; it adds nothing to the problem's standing, which rests on Chen and Ruzsa's refereed proof.

Depends on. Nothing in this wiki.