Generator Corridor (Classical): From Segmented Maps to Continuous-Time Law Rate Matrices, Master Equations, and Detailed-Balance Slots

The missing “law layer” is forced: a generator that turns ledgers into rates. This paper is the next forced layer after the segmented irreversibility ledger. In the finite-state classical setting, it makes explicit the bookkeeping axioms needed to pass from step-indexed ledgers to a duration-indexed family of admissible maps (time-homogeneity, additive parameterization, and refinement-consistent identification). Under these hypotheses the semigroup law is forced; with strong continuity at 0, standard finite-dimensional semigroup theory yields an infinitesimal generator and the master equation. Probability preservation forces the generator to be an infinitesimal stochastic operator (rate matrix). The paper defines an instantaneous irreversibility rate as KL dissipation, proves nonnegativity, characterizes equality as vanishing edge currents on the bidirected edge set, and isolates detailed balance as the exact algebraic constraint (beyond stationarity) that eliminates all steady-state currents. A short bridge remark records the structural template for the later quantum corridor without importing quantum primitives.