Layer discipline and refusal of unsupported physics

The following objects stay separate:

1. the quantum channel or instrument and its specified observable;

2. the classical random optimization and its joint weight law;

3. the macroscopic norm and the regularity justified by the mapping.

The engineered constructions above demonstrate that a classical random metric can be installed in a quantum protocol. They do not show that every such protocol selects that metric.

Scheduled ancestry bounds support but need not equal operational influence. An identity block can have a two-site scheduling footprint while producing no cross-site influence. Physical causal containment requires an independently supplied embedding and timing contract. These are the distinctions documented in VII-J, En05-A, and XIX-C CheungVIIJ,CheungEn05A,CheungXIXC.

A record-only comparison also cannot replace a complete residual comparison. For example, a one-outcome identity channel and a one-outcome dephasing channel have the same deterministic record; on input $|+⟩⟨+|$ their residual outputs have trace distance $1/2$ CheungVIIIA. This is why the target lift is printed in Section sec:bridge1.

Channel equality does not determine a thermodynamic implementation: appending an unobserved energy-transfer process leaves a selected channel unchanged while changing reservoir heat or fuel usage. A heat or reusable-memory reset claim therefore needs Hamiltonians, reservoirs, initial correlations, and resource-return conditions CheungEn07B.