A nontrivial finite history readout

For a concrete preparation, allocate the clock in $|{\tau }_0⟩$, rotate it to $D^{-1/2}{\sum }_k|{\tau }_k⟩$, and apply the controlled unitary ${\sum }_k{P}_k\otimes U_k$. All these operations can be declared at the sender's location before the reading.

Choose a static sender $x_0\in U$, set

and use history-label calibration. The labels refer to the declared points $\kappa (k)$, not to different actual locations of $e_{\mathrm{r}}$. The displayed preparation does not, by itself, prove that a physical matter trajectory visited all the conditional states at those earlier events. It constructs a calibrated finite history encoding.