Introduction and scope

Partitioned finite-range dynamics have an exact finite domain of dependence. Their geometry supplies the propagation bound; the semantics of a programming calculus supplies a separate interface between programs and complete instruments. These two statements should not be conflated.

This manuscript develops the comparison proposed for En05-A and revises the supplied manuscript 085VvAv3. The discrete cone, its relay attainment, and the distinction between semantic and syntactic admissibility are retained. The additional development is a precise alignment with channel-locality interfaces and a velocity-polytope obstruction to the simplest isotropic scaling proposal.

Cheung's En03-A gives one-layer adjoint support, schedule locality, local-record laws, and invariance under legal reorderings of fixed labelled channels CheungEn03. VII-J separates scheduled reachability, operational influence, and an independently declared physical causal relation, and gives a phase-explicit cycle-velocity description CheungVIIJ. Psy04-B emphasizes that scheduled ancestry need not equal influence CheungPsy04B. We prove the comparison statements needed here rather than importing those manuscripts as theorem premises.

The measurement accounting follows the distinctions in Landmark I, En04-A, and Hawk04-B: destructive readout returns a classical record; discarding that record gives a partial trace; and recovery from a complete output is not recovery from a selected residual CheungI,CheungEn04,CheungHawk04B. The syntax-specific results of Landmark I are optional semantic input once the carrier is a qubit interface. They are not needed to prove the geometric cone.

.

1. We formulate snapshots as unnormalized hybrid states and prove their equivalence with reduced-channel factorization and adjoint support containment.

2. We prove exact schedule locality and its metric envelope, with complete classical controls and untouched references included.

3. We retain the sharp relay witness $c_{\mathrm{lat}}=r$, while making finite-program soundness and tail-routing simulation precise.

4. We distinguish readout laws, residual response, classical-record reconstruction, and entanglement-assisted transport.

5. We state and prove the timed velocity-polytope comparison and the fixed-periodic-model isotropy obstruction.

6. We correct the boost-closure and continuum interfaces. In particular, we do not retain a physical retiming-stability conclusion from an axiom that is incompatible with ordinary bidirectional relays.

boundary. The metric, schedule, register interfaces, and update rules are declared inputs. The results do not derive a metric from entanglement, Einstein dynamics, a Page curve, an island, a horizon, or a holographic identification. Results about reversible quantum cellular automata are related but have additional hypotheses; no classification theorem for arbitrary instruments is asserted SchumacherWerner,Arrighi. The present exact support bound is structurally different from the exponentially suppressed propagation outside an effective cone in Hamiltonian Lieb–Robinson estimates LiebRobinson.