Quasistatic mass evolution and its limitations

The ledger is not an exact evaporating metric. A small value of (eq:adiabaticindicator) is a diagnostic, not a proved channel-error bound. Every use of a sequence of fixed-background channels below requires an independently stated approximation allowance. The evolution stops at a declared $M_{\mathrm{cut}}$ well above the regime where the adopted semiclassical treatment is uncontrolled.