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Claim. Theorem 1 of J. She, Nonexistence of consecutive powerful triplets around cubes with prime-square factors, Integers 25 (2025), Paper No. A103: there are no consecutive powerful numbers $x^3-1=p^2a^3$, $x^3$, $x^3+1=q^2b^3$ with $p,q$ prime and $a,b,x$ integers. Corollary 1 of the paper: for primes $p,q$ and integers $x,a$ with $a\neq0$, the equation $x^6-1=p^2q^2a^3$ has no solution. The proof is a case analysis on the common factors of $x\mp1$ and $x^2\pm x+1$, using the $3$-adic valuation, Thue equations and the integer points of the Mordell curve $y^2=x^3-432$ (card). The page is dated by the arXiv posting of 2025-07-07; the journal published the paper on 2025-11-25.

Covers. Triples centered at a cube whose outer members are both a prime squared times a cube, 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 2025-07-09, accepted 2025-10-22): the refereed evidence. The site labels the problem VERIFIABLE, an open label, so its commentary's mention of the paper is not reviewed evidence.