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Claim. The answer to Problem 90 is no, with the exponent $1.0152$. Proposition 2 of Michael T. M. Emmerich, Optimizing explicit unit-distance lower-bound certificates, arXiv:2606.03419 (p. 17 of v5, 9 June 2026; already stated in v1 of 2 June 2026), states that, assuming Sawin's explicit criterion is applied exactly as in Sawin's paper, the report's Tailored Integer Evolution Strategy certificate supports $u(n)>n^{1.0152}$ for arbitrarily large $n$, where $u(n)$ is the largest number of unordered unit-distance pairs among $n$ planar points. The certificate keeps Sawin's prime set $T=\{3,5,\ldots,43\}$ and changes the prime set $S_{\mathbb Q}$, the multiplicities $k$ and the parameter $R=6672416/100000$, all recorded on the Proposition 2 page; its exponent gain is $\delta=0.0152616\ldots$. A fixed positive gain along an unbounded sequence of $n$ exceeds $C/\log\log n$ for every fixed $C$ once $n$ is large, so the bound the problem asks about fails. The report is carded at emmerich_2026_optimizing_explicit_unit_distance_lower_bound_certificates. Its abstract and Section 8 also report an Emmerich--Cordella certificate for an extended prime set, $\#T=67$, with $u(n)>n^{1.031}$, deposited on Zenodo on 6 June 2026, whose data the report does not print. The report's declaration says that OpenAI ChatGPT 5.5 was used as an auxiliary tool for programming, code review, debugging and cross-checking, and not to generate proofs or certificates.

Depends on. Sawin's claim page and Sawin's Proposition 10: the criterion is Sawin's Proposition 10 with the fields of Sawin's Lemmas 11 and 12.

Acceptance. None. No journal record is known. The report's Remark 2 treats its sharper decimals as candidates until they are checked with interval arithmetic and reviewed by an expert in the number-theoretic construction, and the corpus has not replayed the certificate. The claim is therefore claimed.