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Yanping Luo, Ruiyi Yang and Keheng Zhu, Exterior power sums, arXiv:2607.22017v1 (24 July 2026), Theorem 1.1, claims the negative answer. For $z_1,\ldots,z_n\in\mathbb C$ write $p_k(z)=\sum_j z_j^k$ and $P_n(z)=\max_{2\le k\le n+1}|p_k(z)|$. The theorem states that for every $\lambda>0$ there is $N(\lambda)$ such that, whenever $n\ge N(\lambda)$ and every $|z_j|\ge 1$, one has $P_n(z)>e^{-\lambda n}$. Hence the infimum of $P_n$ over such configurations, with or without the normalization $z_1=1$, has $n$th root tending to $1$, and no constant $C>1$ with $P_n(z)<C^{-n}$ for every $n\ge 2$ can exist. The argument writes $F(t)=\prod_j(1-z_jt)$ as an exponential times a perturbation with small coefficients, shows that the approximation holds uniformly on a fixed open disk outside the closed unit disk, and observes that the normalized logarithmic derivatives $\frac1n F'/F$ are Cauchy transforms of probability measures supported in the closed unit disk (in the variables $\alpha_j=z_j^{-1}$); normality and the identity theorem force any constant limit of these transforms to be zero, which contradicts the nonzero constant the exponential approximation produces. The paper credits an earlier manuscript by Turturean with the weaker bound $\exp(-(0.0597\ldots+o(1))n)$ for the normalized infimum, which only limits an admissible constant to $C\le 1.0616$. The statements are those of the arXiv version; the proofs have not been checked.

Submission note. Posted to erdosproblems.com as a proof claim by RayYoung, Keheng Zhu, Yanping Luo (account RayYoung) on 15 July 2026, giving "GPT 5.6 Sol Pro" as the AI used:

We prove that the optimal maximum of the power sums has n th root tending to 1, so no fixed constant C>1 can satisfy Erdős’s requirement. Assuming exponential smallness leads to a contradiction: the generating polynomial would approximate an exponential outside the unit circle, forcing its normalized logarithmic derivative to approach a nonzero constant, which is impossible for a Cauchy transform of a probability measure supported in the unit disk. Notes: This result was obtained with the assistance of generative AI, particularly during the exploratory stage of the argument. We subsequently reorganized and rewrote the original AI-assisted proof to improve its readability, logical structure, attribution, and mathematical transparency.We warmly welcome comments, corrections, and further discussion from the community.

Standing. The result was filed on the site's proof-claims tab on 15 July 2026 by Ruiyi Yang (login RayYoung) for the three authors, with an Overleaf write-up; the tab names GPT 5.6 Sol Pro, and the claim's notes say that generative AI assisted the exploratory stage and that the authors then rewrote the proof. The arXiv preprint followed on 24 July 2026 and lists no journal reference. The site's label is unchanged (OPEN; page last edited 23 January 2026, before the claim) and its commentary does not name the authors, so no reviewer is named and the claim stays claimed. The formal-conjectures statement file for the problem marks it research solved with the answer no, citing this paper, and leaves its own proof unfilled; a statement file is not a formalization and is recorded here only in prose.

Lean repository. The tab links a Lean 4 repository (Lean v4.19.0, hosted under the login miracleqihe), whose README says that it machine-checks the polynomial and logarithmic-derivative identities, the Cauchy-transform bounds and the final contradiction step, but that the full theorem is not claimed as Lean-formalized: the series truncation and the analytic estimates of its Lemmas 3.1 and 3.2 are left to a written audit. A thread comment of 17 July 2026 made the same point, and the submitter replied that the repository reflects an earlier, incomplete stage of the work. The link is therefore recorded as code, not as a formalization, and the corpus has built nothing. A later proof of the same negative answer by a different method is recorded on [[problems/analysis/E0973/claims/2026_08_03_tan_wang_huang_chen|the page of Tan, Wang, Huang and Chen]], which credits this paper with the first answer.