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Claim. H. Kido, On isosceles sets in the 4-dimensional Euclidean space, Int. J. Combin. 2010, Article ID 803210, proves that the maximum cardinality of an isosceles set in $\mathbb{R}^4$, a set in which every three points determine an isosceles triangle, is $11$, and that there are exactly two 11-point isosceles sets in $\mathbb{R}^4$ up to isomorphism, as the abstract states. This answers the instance $d=4$ of Problem 503 with the value $11$, which Ionin's paper of 2009 also derives, with the same two extremal sets, on Ionin's claim page. Kido's earlier paper, Classification of isosceles eight-point sets in three-dimensional Euclidean space, European J. Combin. 27 (2006), 329–341, proved the uniqueness of the eight-point set in $\mathbb{R}^3$ and settles no instance by itself.

Covers. The instance $d=4$ of the problem, answered $11$, with the classification of the extremal sets. Nothing is claimed about other dimensions.

Acceptance. The paper is refereed: International Journal of Combinatorics, volume 2010, Article ID 803210, as its record gives it. The site labels the problem OPEN and does not cite the paper, so no reviewed evidence is listed. The page is dated to the publication year, the record giving no day.