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Kenta Kitamura, publishing on GitHub under the login KitaKen1, published on 6 September 2026 a Lean 4 repository whose commit of that day is titled a Lean proof claim for Problem 1040(ii) and whose README calls it an independent Lean 4 formalization and proof claim for the second question. The repository defines the transfinite diameter of a set $F$ as the infimum over $n$ of its finite Fekete diameters, the largest geometric mean of the pairwise distances of $n+2$ points of $F$, and its main theorem erdos1040_secondQuestion states that every closed infinite $F\subseteq\mathbb C$ whose transfinite diameter in this sense is at least $1$ has $\mu(F)=0$: the areas of $\{z:|p(z)|<1\}$ over monic $p$ with all roots in $F$ have infimum $0$. The README reports the theorem proved without sorry under Lean v4.33.1 with the axioms propext, Classical.choice and Quot.sound only, and carries an AI-generated mathematical explanation of the argument. It also says that the identification of this infimum with the classical limit of the finite Fekete diameters, and with the logarithmic capacity, is absent from the repository. The README says that the proof development, formalization, documentation and verification workflow were prepared with assistance from ChatGPT and OpenAI Codex using GPT-6 (Astra), under human direction. The statements above are those of the README at the linked revision; the development is not built or checked here.

Submission note. Posted to the site's forum by Kenta Kitamura on 6 September 2026:

I was surprised to find that three Lean proofs of the second question in Erdős Problem 1040 appeared on 6 September 2026:

1: Kenta Kitamura (KitaKen1) on GitHub: https://github.com/KitaKen1/erdos-1040-capacity-one-lean 2: shlummi on the Erdős Problems forum: proof claim 3: Declan Gessel (declangessel) on Formal Conjectures and the Erdős Problems forum: Formal Conjectures PR #5300 / Erdős Problems forum proof claim

All three reports used AI: KitaKen1 used ChatGPT and OpenAI Codex with GPT-6 (Astra); shlummi reported using OpenAI Codex, DeepSeek, and Claude/Opus; and Declan Gessel reported using GPT-6 Astra in Codex.

Covers. The second question, for the repository's definition of the transfinite diameter as the infimum of the finite Fekete diameters: every closed infinite $F$ with that infimum at least $1$ has $\mu(F)=0$. The bridge from that definition to the classical limit and to the logarithmic capacity is not formalized, as the README says. The claim says nothing about the first question, whose negative answer is recorded on Aletheia's page.

Standing. The development was announced in a thread comment of 6 September 2026, posted under the name KentaKitamura, which lists it beside the Lean-backed claims of shlummi and of Gessel as the three Lean proofs of the second question that appeared that day and names the AI systems of each. It was not filed on the site's proof-claims tab and has no manuscript beyond its README; the site labels the problem OPEN, no reviewer is named, nothing is refereed, and the corpus has built and audited nothing, so the claim lists no evidence and stays claimed. The three other claims of the second question are Tzachristas's page, shlummi's page and Gessel's page.

The claim rests on no other page.