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Claim. For a triangular array of nodes $a_i^n\in[-1,1]$, $1\le i\le n$, let $\lambda_n(x)=\sum_{i\le n}\lvert p_i^n(x)\rvert$ be the Lebesgue function of the $n$th row and $\mathcal{L}^nf$ the Lagrange interpolant of $f$ on that row. The claim answers both questions of Problem 671 yes: there is a node system with $\limsup_n\lambda_n(x)=\infty$ at every $x\in[-1,1]$ such that for every continuous $f:[-1,1]\to\mathbb{R}$ some $x\in[-1,1]$ has $\mathcal{L}^nf(x)\to f(x)$. Such a system answers the second question directly and the first as well, since every point then has an unbounded Lebesgue function and a convergence point exists for every $f$. The tab entry's summary says only that the system named as GPT Pro resolves both questions in the affirmative and that the Lean formalization was performed by the system named as GPT-5.5 in Codex; the construction is described on this page only as far as the later re-derivation on [[problems/analysis/E0671/claims/2026_07_24_quietmethod|QuietMethod's claim page]] attributes it to this claim: a coalescing-node construction in stages. The claimant is Liam Price, who filed the claim; the result is declared as the work of the AI systems named.

Submission note. Posted to erdosproblems.com as a proof claim by Liam Price (account Leeham) on 15 July 2026, giving "GPT Pro and GPT 5.5" as the AI used:

GPT Pro resolves both questions in the affirmative. The Lean formalisation was performed by GPT-5.5 in Codex.

Posted to the site's forum by Liam Price on 22 June 2026:

GPT Pro resolves both questions in the affirmative. You can find the argument here as well as the Lean formalisation by Codex here.

Standing. Price first posted the write-up and the working Lean link on the problem's discussion thread on 22 June 2026 and filed the claim on the proof-claims tab on 15 July 2026 as a full proof. The thread post of 22 June says that the system named as GPT Pro resolves both questions in the affirmative and links the write-up and the Lean formalization by the system named as Codex. The tab entry's thirteen comments concern the formalization link only: the live-editor address carries the whole Lean source, 60,947 characters, while the site truncates an external link at 2048 characters, so the tab's copy of the address is truncated and opens a blank page. The full address is in the thread post of 22 June 2026 and in the claimant's comment of 15 July 2026 on the claim thread, both linked above; the site's curator asked that future Lean code be hosted in a repository. No comment addresses the mathematics, the site's label is OPEN with the page last edited 23 January 2026, before the claim, and its commentary does not mention the claim. No refereed publication and no outside review was found. This corpus has not built the Lean source, and no acceptance evidence exists, so the claim stays claimed. The later claim of QuietMethod declares itself an independent verification and quantitative refinement of this one.

Depends on. Nothing beyond the cited write-up.