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Claim. The answer to Problem 90 is no. Theorem 1.1 of the 13-page manuscript Integral points on norm-one tori and the Erdős unit-distance exponent, which prints no author, affiliation or date, states that for some absolute constant $c_0>0$ the bound below holds for every $n$ in an infinite set $\mathcal N$ of integers, all at least an absolute $n_0$,

$$u(n)\ \ge\ n^{1+c_0\log\log\log n/\log\log n}\qquad(n\in\mathcal N),$$

where $u(n)$ is the largest number of unordered unit-distance pairs among $n$ planar points; in particular, for every $C>0$ there are infinitely many $n$ with $u(n)>n^{1+C/\log\log n}$, which is the negation of the bound the problem asks about. The gain tends to zero, so the result is weaker than the fixed-power claims on the other pages of this folder and stronger than the uniform-constant negation alone. The theorem is paged at Theorem 1.1 and the manuscript is carded at anon_2026_integral_points_norm_one_tori_unit_distance_exponent. The point sets project $\mathcal O_K^2$ to the plane through one real embedding of fields $K_m$, the quadratic twists by $\sqrt{\alpha}$, $\alpha=\sqrt D$, of the layers of an infinite unramified $2$-class field tower over $\mathbb Q(\sqrt D)$ with $D=3\cdot5\cdot7\cdot11\cdot13\cdot17\cdot19\cdot23$; the unit pairs are $\mathcal O_K$-points of the conic $u^2+v^2=1$, counted by van der Corput's theorem against Louboutin's residue estimate and Zimmert's regulator bound. The manuscript credits no person and no AI system, and the slug of this page records the absence of an author line. The file's embedded metadata gives a creation date of 26 May 2026, the date this page carries; no posting date is recorded, and the file was retrieved from a content-delivery address of Anthropic. The provenance record of the Lean comparator repository kim-em/erdos-unit-distance-comparator calls it a distinct paper with the same title as a one-page argument it credits to Levent Alpöge, and no relation between the two texts beyond the title is established here.

Depends on. No page of this wiki. The Golod--Shafarevich criterion, Gauss's genus theory, van der Corput's theorem and the class-number and regulator bounds it uses are outside inputs, recorded at statement level on the result page.

Acceptance. None documented. No publication, preprint record, author or review of the manuscript is known here; the site's page labels the problem disproved on the OpenAI model's construction and does not mention this manuscript. The corpus has not verified the proof, and the result page records the theorem at statement depth with a proof pointer. The claim is therefore claimed.