Claimed, proved: no claim settling the problem is accepted. The site labels the problem OPEN (page last edited 2026-04-01). One pending full claim is on its proof-claims tab, recorded and not adopted: Gu 2026, a manuscript posted on Zenodo on 2026-09-08 (the record states publication date 2026-09-07) and registered on the site the same day, which asserts the answer yes with a nonnegative constant $c$ and credits GPT-6 Astra for the argument. It comes with a Lean development that derives the statement from four cited theorems taken as hypotheses; no review or acceptance of the claim is recorded. Two refereed partial results that the site's commentary credits are accepted: Erdős 1946 [Er46], the answer yes when $A$ is empty or when $f(n+1)-f(n)\to0$, and Mangerel 2021 [Ma22], the answer yes for completely additive $f$ with no outsized prime values whose decreases number $\ll X/(\log X)^{2+\delta}$.