Mass clocks and recurrence remain different questions

A supplied law

would give

This is obtained by integrating the supplied ordinary differential equation. Identifying its times with the cell schedule would be an additional declaration; it would not prove the decoupling hypothesis or construct a horizon CheungHawk04D,Hawk05C. No such mass clock is required in the present existence theorem.

A fixed finite autonomous Hamiltonian with a fixed access partition has arbitrarily late recurrences of its complete prepared channel. This follows by simultaneous recurrence of its finitely many eigenvalue phases. If its initial accessible channel is replacement, optimal recovery returns arbitrarily close to $a_d$, since recovery error is one-Lipschitz in channel diamond distance. That statement concerns the fixed autonomous model CheungHawk04A; it does not overturn a terminated SWAP schedule whose received outputs are isolated and stored.