The smallest ratio is controlled by one count at its minimum and the other at its maximum. Reversing those assignments gives the largest ratio. This statement follows from the adopted positive finite domain and requires no extrapolation to an infinite sequence of admitted counts.

Transformation factors require an additional check. A difference between count ratios can reach zero even when each ratio separately remains finite. The revised argument therefore applies the minimum count to the transformed observed measure, not merely to its local reference.

That separation repairs a common shortcut in bounded-measure reasoning. Finite inputs alone do not prove that every function of them stays away from zero. The October source combines explicit ratio bounds with the observed-measure restriction. Its conclusion remains conditional on the MQ admissibility premises and does not constitute a measured universal bound.