Lemma: Every benchmark operation is regular and causal

The specified execution is a finite Target B schedule. The matter is buffered across both the worldsheet incidence time $\tau =0$ and the local slice parameter $s=0$. No operation meets $\mathcal{W}$.

The moving routes also satisfy the sufficient slicing speed (eq:vstar).

Proof. The entire axial chain is in the displayed regular tube. Every local operation is on one station worldline with strictly positive duration. The inbound exchange routes have speed $v_{\ast }/4$, and the outbound communication portions have speed $v_{\ast }/2$; both are future timelike.

The incoming branch has ${\partial }_s{F}_s=1$. On the outgoing communication interval, ${\partial }_s{F}_s=2$. Thus the route speeds in $s$ are respectively $v_{\ast }/4$ and $v_{\ast }$. Stationary waits and gates have zero spatial speed. Theorem thm:conegates also certifies them.

The qubits are at $A$ before $\tau =0$, and remain there until $\tau =1/16$. At $A$, the $s=0$ slice has time $1/64$, which lies inside that storage interval. All control copies occur before their communication departures, and every remote use waits for the record to arrive.