Specified microscopic finite evolution

Start with the message in $K$, the ready output $D$ in $|0⟩$, and the independently prepared pair $|\beta {⟩}_{FB}$. Apply ${\mathrm{SWAP}}_{KD}$, then $U_{FD}$. The final state is exactly (eq:modelV).

These are specified finite unitary dynamics. If durations $t_1,t_2>0$ are desired, the swap is generated by

Writing $U={\sum }_{\alpha }{e}^{-i{\theta }_{\alpha }}{P}_{\alpha }$ with ${\theta }_{\alpha }\in (-\pi ,\pi ]$, the second pulse is generated by

Both generators are bounded. No spatial support, gravitational Hamiltonian, passive evaporation law, or black-hole mass balance is assigned to them.

A possible output schedule releases $F$ before the message-transfer pulse, releases $D$ after that pulse, and releases $B$ subsequently. The final unitary $U$ can be regarded as a declared processing operation on the collected $FD$ registers. This schedule is a finite interface schedule, not a spacetime embedding.