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Claim. The answer to Problem 652 is yes. Surya Mathialagan, On bipartite distinct distances in the plane, Electron. J. Combin. 28 (2021), no. 4, Paper No. 4.33, 25 pages, posted as arXiv:1912.01883 on 4 December 2019, proves in its Theorem 14 (Section 3 of the published version) that for a set $P$ of $m$ points and a set $Q$ of $n$ points in the plane with $2\le m\le n^{1/3}$, some point of $P$ determines $\Omega(\sqrt{mn})$ distinct distances to the points of $Q$. The proof adapts Székely's crossing-number method: a graph joins the points of $Q$ along the distance circles centered at the points of $P$, and a bound on rich perpendicular bisectors controls the edge multiplicities. The theorem is stated and proved for its own purpose, the bipartite distinct distances problem of Elekes, where it gives the lower bound $D(m,n)=\Omega(\sqrt{mn})$ of the paper's Theorem 4 and shows Elekes's circle-grid construction tight in that range. The source card is mathialagan_2021_bipartite_distinct_distances_plane; the corpus's reconstruction there covers the paper's Theorem 3 and its lattice construction, not Theorem 14.

Why this answers the question. Order $n$ points so that $R(x_1)\le\cdots\le R(x_n)$ and fix $k$ with $2\le k\le n^{1/3}$. Apply the theorem with $P=\{x_1,\ldots,x_k\}$ and $Q$ the remaining $n-k$ points: some $x_i$ with $i\le k$ determines $\Omega(\sqrt{k(n-k)})$ distances to $Q$, so $R(x_k)\ge R(x_i)\gg\sqrt{kn}$ for every $n$-point set once $n$ is large. By the definition of $\alpha_k$ this forces $\alpha_k\gg k^{1/2}$, and $\alpha_k\to\infty$. The deduction is the one the site's curator records beside the theorem, and it uses nothing beyond the ordering. In the other direction the site records Elekes's result that $R(x_k)\ll_k n^{1/2}$ is attainable for every fixed $k$ and all large $n$, so each $\alpha_k$ is finite and the question was exactly whether these finite constants are bounded. A reader's comment on the site's thread (30 January 2026) observes that the paper's Section 2, which restates Elekes's construction, gives $\alpha_k=O(k^{1/2})$, which would make the order $k^{1/2}$ sharp; this page credits only the lower bound.

Acceptance. The paper is refereed: the Electronic Journal of Combinatorics accepted it on 1 November 2021 and published it on 19 November 2021. The site's curator, Thomas Bloom, labels the problem proved, cites the paper as [Ma21] and states the theorem with the deduction above (problem page last edited 18 January 2026), which is the reviewed evidence. The proof has the journal's refereeing and the curator's endorsement; no other review of it is recorded.

Later reports of the same deduction. The site's discussion thread of January 2026 records a web page by Mehmet Mars Seven presenting a deduction by ChatGPT 5.2-Pro of the answer from Theorem 14, relayed to the thread on 17 January 2026; on 18 January 2026 Terence Tao reported that Gemini Deepthink confirmed that deduction, and Tao, reading the paper, located the theorem as Theorem 3.6 of arXiv:1912.01883; Boris Alexeev noted that this is Theorem 14 of the published version. The deduction is the credited theorem's, so it has no page of its own. Feng and coauthors' preprint, which proves the answer yes by a different literature input with a weaker growth rate and cites Seven's page, has its own page, [[problems/distance_problems/E0652/claims/2026_01_29_feng|Feng and coauthors]].