Abstract

We distinguish scheduled reachability, intervention-based quantum influence, and an independently supplied physical causal relation. For finite quantum networks, including their classical controllers, we prove that the complete timed dependency graph bounds the Heisenberg support of every jointly observed output. Absence of a scheduled path implies absence of signalling, including with an untouched entangled reference. A causal embedding of the dependency edges then gives an exact physical containment theorem for the encoded–computed–decoded channel.

The directional route is developed separately. A finite, phase-expanded periodic graph has a cycle-velocity polytope and an explicit finite-time remainder. Support-function comparison certifies convex velocity inclusion, but an asymptotic inclusion alone does not certify short-time communication. A spatially varying example gives an exact earliest-arrival law. For approximate simulation we prove the signalling bound with consistent diamond-norm constants and separate simulation accuracy from causal safety. A finite-volume Hamiltonian argument gives a reference-stable influence-tail certificate; a product-formula estimate supplies a corresponding simulation error.

For VII-F's three-to-six particle-link event, the ambient spinless cone remains fixed. Its uniformly spacelike, ordered slices give a conservative causal gate speed $1/(1+2\sqrt{2}/3)$ in the slicing parameter. We certify physical inclusion across the event using persistent spatially marked registers, rather than abstract cell labels. An explicitly buffered, nontrivial two-qubit transport target is implemented exactly by causal routes and local gates, together with the separately localized event-code permutation. The target preserves arbitrary reference entanglement and has a unit signalling witness along an allowed causal route.

No spacetime metric, field equation, Lorentz invariance, or gravitational backreaction is derived. The finite causal carrier model is not a quantum-field discretization. The separate characteristic quantum-product programme is not advanced.