Ancestry, influence, and physical cones

If a prescribed two-site block channel is the identity, the schedule can include both sites in $N_{u,t}(Y)$, although an observable on one site pulls back to that site alone. Scheduled reachability therefore does not imply actual influence. This is the upper-bound distinction emphasized in En05-A and VII-J CheungEn05A (Theorem thm:cone), CheungVIIJ (Theorem thm:release).

A physical directional-containment theorem would additionally require an independently certified map from the timed site network into the conical spacetime, compatible with every communication operation. It would need, for example, a proved inclusion of each embedded ancestor region in the appropriate geometric causal past. No such embedding is part of Theorem C5. VII-J's physical containment is conditional on that additional certification; it does not discharge the present interface CheungVIIJ.

scalar speed comparison is not directional containment. On a square lattice of spacing $a_0$, a cardinal hop or wait per tick of duration ${\tau }_0$ has asymptotic reachable velocities

The vector

has Euclidean norm $a_0/{\tau }_0$, but is outside that diamond. A scalar norm bound does not provide a missing directional inclusion.

commutation is not algebraic microcausality. The equality $\Phi \Psi =\Psi \Phi$ is a statement about operations. The relation

for spacelike regions is a statement about a separately defined observable net and its spacetime assignment. The former alone does not define or prove the latter. Indeed, identity channels commute on a qubit, although its observables $X,Z$ do not commute. En06-A accordingly requires a matching observable-limit hypothesis for its algebraic microcausality statement CheungEn06A (Theorem thm:algmicro).

Theorem C5 cannot be applied across an arbitrary state-dependent source law by calling that law a local channel. Nor does spectator-blind geometric control certify a local controller envelope. Feedback must include every read control in a separately specified local hybrid channel, as distinguished in VII-G CheungVIIG (Theorem thm:locality).