PRIOR-WORK CORRECTION (referee audit 2026-08-03): the (6,4) pair WAS previously resolved — L. Hajdu, Á. Pintér, Combinatorial Diophantine equations, Publ. Math. Debrecen 56 (2000), 391–403, proved the only positive solution of the (4,6) equal-products equation is (7,2), i.e. 7·8·9·10 = 2·3·4·5·6·7 = 5040, equivalent to our (x,y)=(1,6). Our theorem is an independent verification, not the first resolution. It remains true that the pair is outside MacLeod–Barrodale (1970), outside the Saradha–Shorey ratio theorems, and outside Hajdu–Tijdeman 2022 Theorem 10.1 (hypothesis k ∤ 2ℓ fails since 4 | 12).