Proposition: Common-final-tick obstruction

The limit class defined literally in TRANSPORT, whose designated readouts all occur at one final tick, is not closed under boosts. This fails already for two independent deterministic readouts.

Proof. Every realizing family in that class has one acquisition time $a_n=t_n^{+}\Delta t_n$ for every designated readout. If two readout events converge, their limiting time coordinates must therefore agree.

Two singleton deterministic readouts at $r_1=(0,0)$ and $r_2=(0,L{e}_1)$, $L>0$, are realizable, with law ${\delta }_{(0,0)}$. A boost of nonzero velocity $v$ in direction $e_1$ gives time coordinates $0$ and $-\gamma vL/c^2$, which differ. The transformed object has no realizing family satisfying the common-final-tick definition.