Proposition: Antitelephone under a separate device interface

Suppose a physical device class has scalable lossless bit signals of speed $u>c$ in each admitting inertial frame, is Lorentz covariant including translated reflected return devices, and permits timelike waiting and the resulting wired compositions. It cannot also satisfy well-founded causal executability.

Proof. Send from $(0,0)$ to $(L/u,L)$. Choose $v<c$ with

Such $v$ exists because $c/u+u/c>2$. A reflected return signal of speed $u$ in the $v$-boosted frame meets the original spatial-origin worldline at

This follows by solving its line of slope $-u$ against the origin worldline $x^{\prime }=-v{t}^{\prime }$. Wait from $(t_2,0)$ to $(0,0)$, closing the dependency chain. Executability excludes the directed cycle.