A physical clock only after declaring durations

This is a certificate for one schedule, not an unrestricted runtime lower bound. A deadline earlier than this programme's completion does not prove every decoder impossible. The memory-error obstruction does prove impossibility for one-slot observers at targets below $1/2$, independent of deadline.

Neither $t_{\mathrm{IT}}$, $t_{\mathrm{op}}$, nor these physical times is identified with a Page time.