Irreversibility Asymmetry Corridor: Forcing the Arrow and the Classical Equality Condition

Irreversibility isn’t assumed here—it’s forced. Once the Uniqueness Corridor locks the entropy slot to KL (up to scale), the next pressure is the arrow: why “production” can only go one way. This paper shows that any stochastic coarse-graining must reduce distinguishability (so one-step production is always nonnegative), and it pins down exactly when the loss vanishes: only when the map is sufficient for the pair, meaning the likelihood ratio is preserved on the fibers. The result is a clean, additive irreversibility ledger across segmented transitions, with the quantum recovery-map framing explicitly deferred to the quantum extension.