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Claim. A note posted by the account sallerk on 31 August 2026, linked from a comment on the site's thread the same day, states as its Proposition that "Every planar set of n ≤ 15 points with no three collinear determines at least ⌊n/2⌋ distinct distances", which is the first question of Problem 1082 for every $n\le15$. Let $g(k)$ be the largest planar set with at most $k$ distinct distances, and $h(k)$ the largest such set with no three points on a line. A counterexample with $k$ distances needs $n\ge2k+2$ points, so the question for these $n$ is $h(k)\le2k+1$. Since $h(k)\le g(k)$, the published values $g(1),\dots,g(6)=3,5,7,9,12,13$ (Erdős and Fishburn, Discrete Math. 160 (1996); Shinohara, Discrete Math. 308 (2008); Wei, Electron. J. Combin. 19(4) (2012), #P38) settle every $k\le6$ except $k=5$. For $k=5$, Shinohara's uniqueness of the twelve-point five-distance set, a triangular-lattice set that contains collinear triples, together with $g(4)=9$, gives $h(5)\le11$. The note discloses that its searches, computations and drafting were done with AI assistance and names no system.

Covers. The first question for every $n\le15$. Nothing for $n\ge16$: the smallest possible counterexample has sixteen points and seven distances, which stays open because $g(7)$ is unknown. Nothing on the second question.

Depends on. No page of this wiki; the note rests on the published values of $g(k)$ it cites.

Acceptance. None documented. The note is linked from a thread comment and is neither refereed nor reviewed; the site's label for the problem is FALSIFIABLE. The claim is claimed.