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Claim. For each $n$ let $X_n\subset[-1,1]$ have $n$ distinct points, and let $r_n\ge0$ be integers with $r_n/n\to0$. Theorem 1 of the write-up Almost everywhere divergence of polynomial interpolation with sublinear excess degree (Zenodo record 10.5281/zenodo.22549777, version 7 of 2026-09-06 under the concept record 10.5281/zenodo.22312935, whose record lists its creator as anonymous) states that there is a continuous $f:[-1,1]\to\mathbb R$ such that every sequence of real polynomials $p_n$ of degree at most $n+r_n$ with $p_n=f$ on $X_n$ satisfies

$$\limsup_{n\to\infty}\lvert p_n(x)\rvert=\infty \quad\text{for almost every }x\in[-1,1],$$

the exceptional null set depending on the sequence. This answers Problem 1152 yes, in a stronger form: given $\epsilon(n)\to0$, put $r_n=\max\{0,\lceil\epsilon(n)n\rceil-1\}$, so that $\deg p_n<(1+\epsilon(n))n$ implies $\deg p_n\le n+r_n$, and unboundedness at $x$ excludes $p_n(x)\to f(x)$. The same $f$ serves every admissible sequence, as the question requires, and the quantifier order matches: the null set may depend on $(p_n)$. The write-up presents the theorem as the extension of the Erdős–Vértesi almost-everywhere divergence of Lagrange interpolation, for arbitrary arrays, to non-unique interpolation with $o(n)$ excess degree, in contrast with the theorem of Erdős, Kroó and Szabados [EKS89] in the site's commentary, that for a fixed $\epsilon>0$ suitable arrays give every continuous $f$ uniformly convergent interpolants of degree below $(1+\epsilon)n$. Its inputs are a construction of Olevskii and Ulanovskii in Bernstein spaces and the uniform Christoffel–Darboux kernel asymptotics of Kriecherbauer, Schubert, Schüler and Venker; a finite interpolation construction forces large values on a fixed fraction of a local interval uniformly over the admissible corrections, finitely many such data sets rule out common sets of bounded values, and the Baire category theorem gives one $f$.

Submission note. Posted to erdosproblems.com as a proof claim by Qiyuan Gu (account fireflysentinel) on 4 September 2026, giving "GPT 6 Astra, GPT 5.6 Sol and Claude Fable 5.1" as the AI used:

Let Xₙ be any set of n distinct points in [−1, 1], and let rₙ = o(n). We prove that there exists f ∈ C([−1, 1]; ℝ) such that every sequence of polynomials pₙ of degree at most n + rₙ interpolating f on Xₙ satisfies lim supₙ→∞ |pₙ(x)| = ∞ almost everywhere. This strengthens the divergence assertion in Erdős Problem #1152 and extends the Erdős–Vértesi phenomenon to o(n) excess degree. The proof combines logarithmic potential theory, localized Bernstein-space functions, weighted Christoffel-Darboux kernel asymptotics, a sign-change argument, and the Baire category theorem. Notes: The proof is drafted using GPT 6 Astra, running on top of GPT 5.6 Sol and Claude Fable 5.1. The author is solely responsible for all mathematical content.

Depends on. No page of this wiki: the inputs are cited from the literature.

Standing. A manuscript claim, claimed. The claimant is Qiyuan Gu, named on the site's proof-claims tab, where the claim was submitted on 2026-09-04 by another account on Gu's behalf, with the disclosure that the proof was drafted with GPT 6 Astra on top of GPT 5.6 Sol and Claude Fable 5.1 and that the author is solely responsible for the mathematics; the Zenodo record lists its creator as anonymous. The tab links the record's first version (22312936), which Zenodo reported as gone (HTTP 410) on 2026-10-07; the concept DOI resolves to version 7, linked above, which carries the paper and a Lean 4 archive that the paper calls a partial formalization. The archive covers the sign-change bound of Lemma 3, the scalar calculations of Lemma 4, the deduction from (6.3) through Remez's inequality, and the finite construction and Baire argument of Sections 7-8. It takes Remez's inequality and the remaining analytic estimates as hypotheses. No build or audit of the archive is recorded, so it is recorded as a link and contributes no formalized evidence. Not reviewed: the site's label is OPEN (page last edited 23 January 2026), the tab carries no comments as of 2026-10-07, its commentary does not mention the claim, and no outside review is known. Not refereed: no journal or arXiv version is known.