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For fix some sequence of distinct numbers . Let .
Does there always exist a continuous function such that if is a sequence of polynomials, with degrees , such that for all , then for almost all ?
Source: erdosproblems.com/1152
A full solution has been claimed but not yet accepted. The statement is true.
OPEN, the site's label (page last edited 23 January 2026; the problem page and its proof-claims tab accessed 2026-10-06). The tab carries one full proof claim, by Qiyuan Gu, submitted 2026-09-04 with a Zenodo write-up drafted, as the tab discloses, using GPT 6 Astra, running on top of GPT 5.6 Sol and Claude Fable 5.1; it claims to answer the question yes in a stronger form: for any array and any excess degree some continuous makes every sequence of interpolants of degree at most satisfy at almost every . The claim is recorded, unadopted, on its claim page (Gu, 2026); the derived standing departs from the site's label because this pending full claim makes the problem claimed as proved, and it stays pending since no outside review or refereed publication of it is known. For a fixed the opposite holds for suitable arrays: Erdős, Kroó and Szabados [EKS89] give arrays for which every continuous has interpolants of degree below converging uniformly, as the site's commentary records.