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Claim. Theorem 2.1 of Jia-Qi Yang, Erdős's Robust Polynomial Interpolation Problem: the Optimal Exponential Scale (manuscript of 2026-09-13, at the linked pinned commit): there is an absolute constant $A>0$ such that for every $C>0$ and $0\le\rho<1$ one can choose

$$\epsilon\ge\exp\Bigl(-A\Bigl(1+\frac C{1-\rho}\Bigr)\Bigr),\qquad n_0\le\exp\Bigl(A\Bigl(1+\frac C{1-\rho}\Bigr)\Bigr),$$

such that for every $n\ge n_0$ and every $x\in[-1,1]^n$, repeated nodes allowed, there are signs $y\in\{-1,1\}^n$ for which every complex polynomial $P$ with $\deg P\le(1+\epsilon)n$ and $\lVert P\rVert_{[-1,1]}\le C$ has $\lvert P(x_i)-y_i\rvert>\rho$ at more than $\epsilon n$ indices. At $\rho=0$ this is the assertion of Problem 1133 with sign data, with a non-strict degree bound in place of the strict one, so the claim is full. The manuscript adds that the exponential order is optimal: with $H=C/(1-\rho)$, interpolation at Chebyshev–Lobatto nodes rules out $\epsilon>e^{-\pi(H-3)/2}$ when $H>3$; and for the obstruction restricted to the full Chebyshev–Lobatto grids the optimal parameter $\epsilon_{\mathrm{Ch}}(C,\rho)$ satisfies $\log(1/\epsilon_{\mathrm{Ch}})=\frac\pi2H+O(\log(H+1))$, the sharp coefficient for arbitrary nodes being left open. The quantitative input is a finite interpolation estimate in Bernstein spaces of Olevskii and Ulanovskii (Proc. Steklov Inst. Math. 303 (2018), 178–192); the angular reduction $x=\cos\theta$ and the grouping of nodes into blocks follow the note posted by Chojecki, recorded on its own claim page, which the manuscript cites as an unsigned draft giving a qualitative proof without a rate. The grid result uses periodic sign data and averaging over periods, with a cardinal-interpolation construction for the matching upper bound; a further section treats random signs and angular perturbations of the nodes.

Submission note. Posted to erdosproblems.com as a proof claim by Jia-Qi Yang (account Yjq1368708545) on 13 September 2026, giving "GPT-6" as the AI used:

We prove the assertion in Erdős Problem 1133 and obtain stronger quantitative results. The obstruction holds for sign data with any prescribed pointwise tolerance $0\le\rho<1$. We determine the optimal exponential order of the obstruction parameter in $C/(1-\rho)$, where $C$ is the uniform norm bound. For the full Chebyshev–Lobatto grids, we further identify the sharp leading exponential coefficient $\pi/2$. The proof combines finite interpolation estimates in Bernstein spaces with angular rescaling and grouping. The sharp grid result uses periodic sign data and averaging to control exceptional samples, together with a cardinal interpolation construction giving the matching upper bound. Notes: GPT-6 was used for mathematical exploration and proof development. This submission concerns a quantitative refinement of the earlier draft and a sharp exponential coefficient for the full Chebyshev–Lobatto grids. Quantitative interpolation estimate used for the arbitrary-node result: A. Olevskii and A. Ulanovskii, “On irregular sampling and interpolation in Bernstein spaces,” Proceedings of the Steklov Institute of Mathematics 303 (2018), 178–192. https://doi.org/10.1134/S0081543818080151

Depends on. No page of this wiki: the inputs are cited from the literature (Olevskii–Ulanovskii; Beurling in Appendix B); the earlier note is credited for the method, not used as a premise.

Standing. A manuscript claim, claimed. The claimant submitted the claim to the site's proof-claims tab on 2026-09-13 as a full proof, disclosing that GPT-6 was used for exploration and proof development and that the submission is a quantitative refinement of the earlier note; the manuscript carries no author byline, and the repository's README calls it a preprint that has not been peer reviewed. Not reviewed: the site's label is OPEN (page last edited 31 December 2025; the tab, accessed 2026-10-06, carries no comments on the claim), and no outside review is known. Not refereed: no journal or arXiv version. Its proofs have not been reviewed.