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Claim. Theorem 1 of T. H. Chan, A note on three consecutive powerful numbers, Integers 25 (2025), Paper No. A7: there are no three consecutive powerful numbers $x^3-1=p^3y^2$, $x^3$, $x^3+1=q^3z^2$ with $p,q$ prime and $x,y,z$ positive integers. Corollary 1 of the paper deduces that $64x^6-1=p^3q^3y^2$ has no solution in integers $x,y$ with $p,q$ prime. The proof combines factorization and $3$-adic valuation lemmas for $x^2\pm x+1$, a reduction of quartic equations to elliptic curves, and the Pell equation $x^2-3y^2=1$ with second-order recurrences (card). The journal published the paper on 2025-01-17, before its arXiv posting of 2025-03-27, so the page is dated by the journal.

Covers. Triples centered at a cube whose outer members are both a prime cubed times a square, a partial no to the question of Problem 364. Triples of other shapes, and those whose middle member is not a cube, are untouched.

Acceptance. Refereed in Integers (received 2024-10-17, accepted 2025-01-07): the refereed evidence. The site labels the problem VERIFIABLE, an open label, so its commentary's mention of the paper is not reviewed evidence.