Stopping and completion are different claims

There are two admissible endings:

1. stop at $u_{\mathrm{cut}}$ with $M\ge M_{\mathrm{cut}}$ and retain the remaining hole and all auxiliaries in $B$;

2. specify an endpoint isometry and include its error in the complete comparison budget.

A mass formula extrapolated to zero is not an endpoint isometry. A Planck-scale mass bound is not a bound on the information capacity of inaccessible internal states.