Complete destructive-clock channel

This is the I-B/En09-A pattern, proved on the present finite interface IB,En09. The conditional state on a positive-probability branch is its subnormalized block divided by its trace. No normalized state is assigned to a zero-probability branch. Conditional reference steering is compatible with the unchanged unconditional marginal.

If distinct calibrated labels $t_k$ must equal the time of one fixed readout event whenever their outcomes occur, at most one code has positive probability. Otherwise the table uses programme/history calibration. Reading it does not consume the geometric time axis.

The channel is not universally invertible: the clock states $(|{\tau }_0⟩\pm |{\tau }_1⟩)/\sqrt{2}$, with the same residual, have identical outputs. The record alone also cannot determine an arbitrary residual. Finally, no finite clock matrices satisfy $[T_C,H_C]=i{I}_C$, by taking traces.