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Claim. For every fixed interval $I=[a,b]$ with $-1\le a<b\le1$ there are a constant $C_I\ge0$ and a threshold $n_I$ such that for every $n\ge n_I$ and every choice of $n$ distinct nodes in $[-1,1]$ the Lebesgue function $\lambda(x)=\sum_k|l_k(x)|$ satisfies

$$\sup_{x\in I}\lambda(x)\ge\frac2\pi\log n-C_I$$

(Theorem 1.10(i), equation (1.26), p. 9 of the third arXiv version). The constant and threshold depend on $I$ but not on the nodes. Since the $l_k$ are polynomials, $\lambda$ is continuous and the supremum over the compact interval is a maximum; for $n\ge\max\{n_I,2\}$ the choice $\varepsilon_n=(C_I+1)/\log n\to0$ gives the strict inequality $\max_{x\in[a,b]}\lambda(x)>(2/\pi-\varepsilon_n)\log n$, which is the question of Problem 1153 answered yes, with an additive $O(1)$ remainder in place of the $o(1)\log n$ asked for. The exact source statement and this elementary transfer are recorded on the transfer page of the source card Tao 2026; the transfer, and only the transfer, was independently reviewed on 2026-09-06. The proof localizes Bernstein's theory to functions holomorphic in a rectangle, bounded and real on the lower edge and with controlled growth on the other edges (Theorem 1.6), and combines residue representations with estimates at macroscopic, mesoscopic and microscopic scales; Tao's own proof has not been compiled or reviewed in this corpus. Part (ii) of the same theorem gives the integral bound $\int_I\lambda\ge(4|I|/\pi^2)\log n-o(\log n)$. Erdős and Turán posed the question [ErTu61]; on the whole interval Bernstein [Be31] asserted the sharp bound $(2/\pi-o(1))\log n$ (proving it in full only for trigonometric interpolation), Erdős and Turán proved $(2/\pi)\log n-O(\log\log n)$ [ErTu61, (3.13)], and Erdős [Er61c] improved the loss to $O(1)$ (his page Erdős 1961); Erdős and Szabados [ErSz78] obtained $\max_{[a,b]}\lambda\gg\log n$ on fixed subintervals without the sharp coefficient.

Acceptance. Reviewed: the site's curator, Thomas F. Bloom, labels the problem proved and records in its commentary that Tao resolved the question with the bound $(2/\pi)\log n-O(1)$ on every fixed interval (problem page last edited 2026-04-01, accessed 2026-10-07). Not refereed: the manuscript is a preprint, first submitted to arXiv on 2026-03-23, with the third version dated 2026-04-22 and no journal acceptance recorded as of the arXiv API response of 2026-09-06 recorded on the source card. No formalized evidence: Boris Alexeev's lean-proofs repository holds a Lean file, added on 2026-08-20 and linked above at a pinned commit, that declares itself a formalization of a solution to the problem. It names Tao as informal author and Codex and GPT-5.6 Sol as formal authors. Its theorem Erdos1153.erdos_1153 states the $\varepsilon$ form of the question, with a threshold uniform in the nodes, and not the additive $O(1)$ bound. This corpus has not built or audited it. The Lean development of Yang 2026 declares itself an alternative proof, not a formalization of this manuscript, and has its own pending page. Tao first posted a manuscript of the solution in the problem's discussion thread on 2026-02-27 (the first February link above); readers reported errors and one proof gap in it the same day, and Tao posted a revised copy that day (the second February link), announcing a complete rewrite. The arXiv paper of 2026-03-23, announced in the thread on 2026-03-24, is that rewrite and the source the curator credits; further small corrections reported on 2026-03-24 were to be addressed in a revision, and no comparison of the February reports with the third version is recorded. The author's disclosures of AI assistance, on p. 14 of the preprint, are recorded on the source card and confer no correctness credit.

Depends on. Nothing in this wiki; the result rests on the preprint linked above, and the transfer page is a library record, not a premise.