The Forced Interior Black Hole Radiation from Ledger Accounting

Double-entry bookkeeping, taken as a finite substrate for physics, gives an exact account of black hole evaporation. A ledger of d accounts posts one unit per tick; the record of postings is the radiation. The ledger's arrow of time selects black holes over their reverses. The visible record's capacity to name what is still hidden overtakes the interior's capacity to hide it exactly at the midpoint of the evaporation, by pure counting, and the entropy of the visible record rises to its peak there and returns to zero: the Page curve, with no ensemble and no averaging. The main theorem is about information return: any exterior readout from which the infalling history can be recovered resolves the interior completely, so an evaporation that gives the record back cannot also keep an unresolved inside. Every step is machine-checked in Lean 4. The account consumes one physical law (a one-sided record-area law, which fixes the Bekenstein quarter), a six-line dictionary, and two units constants, an entropy scale c and a per-tick energy quantum E_0, which the ledger provably cannot select. It predicts no dimensionful number.