The site's label is FALSIFIABLE, an open problem: a further solution would be a finite witness, one more $n$ with $n!+1$ a perfect square, while a proof that none exists has no such check. The site's problem page (last edited 1 April 2026) records no proof and lists no proof claim, but its discussion thread carries one: Ahmad Sabihi's manuscript claiming a short elementary proof, brought there on 19 October 2025 and recorded as rejected on its claim page (Sabihi, 2017) after Stijn Cambie exhibited an error in it. An arXiv manuscript of Salvador Cerdá (2015) claiming a solution was withdrawn by its author and is recorded on its claim page (Cerdá, 2015). Somnath Maiti's arXiv manuscript, whose version of 5 February 2026 states the conjecture as its Theorem 2.15, is a pending claim on its claim page (Maiti, 2026), and Naciri's refereed theorem settling the 7-free and prime-power cases is an accepted partial claim on its claim page (Naciri, 2025). The derived standing departs from the label: it is claimed, proved, because Maiti's pending full claim asserts a proof; no full claim is accepted.