Discussion and dependency boundary

The operator $X_J$ is the exact difference between two specified statistical models. A channel transmits that difference as $\Lambda (X_J)$, and an implementability class selects which linear functionals can test it. This separation prevents several otherwise tempting identifications.

The perfect-copy budget is a syntactic lower bound, not a complete accessibility criterion. Fidelity measures residual branch distinguishability. Scalar visibility does not retain the relative phases needed to decide operator cancellation. Agreement on one question can conceal a large discrepancy on the same subsystem.

The Möbius hierarchy makes the location of higher-order behavior precise. The coherent state is order one whenever more than one record branch is supported. Perfect-record subsystem interfaces likewise have order one or infinity. Higher finite orders arise through more restrictive channels, including binary measurement channels. For the FR example, the value $1/6$ is the two-record weight of Wigner's question at the symmetric point, not a state-level classification and not a new physical no-go theorem.

The distinction between a single product conjunction and a product measurement with classical processing is equally important. An exponentially small conjunction probability bias does not imply an exponential obstacle to a local parity witness. Additional experimental restrictions must therefore be stated as an actual effect or protocol class, not inferred from the word “unentangled.”

to supplied landmark terminology. The comparison record accompanying the earlier drafts refers to Landmark I, VII-E, and Em01-A. None is a formal premise here. The typed record equation described for Landmark I concerns uniqueness of a destructive primitive in its specified strategy class; it is not the copying-and-discarding identity of Proposition prop:deeper, and is not used as a physical Frauchiger–Renner no-go. The three recording interfaces distinguished in the supplied VII-E description are kept separate in (eq:coherentcopy)–(eq:nondestructive). The supplied Em01-A witness-to-graph non-implication concerns a different distributional construction, not the finite-dimensional cancellation of Section sec:cancellation.

Likewise, the down-set in Corollary cor:union is a family of subsystems for fixed $\rho ,J$. It is not a family of authorized characteristic extensions, a declared gravitational path, or an admission condition in another manuscript. No theorem transports the results of this paper to those objects. The supplied landmark summaries are comparison material, not a verification of their full source manuscripts.