Abstract

We study complete quantum–classical instruments executed on a locally finite metric substrate under partitioned updates of diameter at most $r$. We give a self-contained comparison between snapshot factorization, Heisenberg support containment, and reference-preserving channel no-signalling. The schedule past is an upper bound on operational influence, not an assertion that every scheduled ancestor affects a readout. An explicit relay attains the metric bound, giving $c_{\mathrm{lat}}=r$ on the stated lattice substrates. Arbitrary block instruments and calculus-generated instruments are distinguished; finite-program soundness requires a compositional interface, and simulation requires routing from every starting tick.

Destructive Enter readout, coherent recording, operational discard, and complete residual response are kept separate. Transmissive exceptional blocks violate the original-metric cone, whereas inert exceptional blocks admit a local refinement. Long-range completely positive channels remain affine and cannot universally clone unknown states. Entanglement-assisted state transfer is stated with its communication and timing resources.

The comparison with periodic dependency graphs supplies a sharp isotropy obstruction: a fixed finite periodic transport model has a velocity polytope, and the cardinal model has an ${\ell }^1$ velocity ball rather than a Euclidean ball. We also identify a limitation of the earlier boost-closure formulation: together with unrestricted composition and well-founded executability, it excludes ordinary bidirectional one-tick relays as well as super-cone devices.

Finally, continuum domain of dependence, operational no-signalling, algebraic microcausality, and frame-invariant maximal speed are proved only under explicit geometric, operational, observable-algebra, and frame-covariance hypotheses. The operational hypotheses include matched realizations of local modifications; the algebraic hypotheses concern observables, not merely commuting superoperators. Existence of a family satisfying the full package remains open. No physical metric, Einstein dynamics, or invariant physical speed is derived.