Abstract

We distinguish complete unitary preservation, subsystem quantum recovery, destructive observation, and operational discard in a reference-preserving channel formulation. A finite acyclic typed fragment represents allocation, specified unitary transformations, destructive computational readout, and classical forgetting. Quantum recovery returns a quantum register; terminal readout returns a classical record and is a different task.

For a complete isometry $V:C\to R\otimes B$, we give an explicit global recovery channel and prove that exact recovery from $R$ is equivalent to constancy of the complete complementary channel to $B$. A process retaining only classical outcomes cannot reconstruct an arbitrary $d$-dimensional quantum code with half-diamond error below $1-d^{-1}$. Unobserved readout of $B$, followed by discarding its outcomes, is exactly partial trace over $B$ and leaves the radiation channel unchanged. Its coherent dilation retains the information omitted from the classical interface.

Independently, a finite-band quartic source–scalar-reservoir Hamiltonian is constructed and approximated by finite-dimensional proxies with explicit complete-channel allowances. Separate qubit dictionaries preserve the accessible–inaccessible partition. For a commuting four-Majorana control, the exact errors and complete residual leakage are

Thus the complete output is reversible although neither output alone need recover the diary.

Access-preserving endpoint continuity and fixed-proxy recurrence are proved separately from syntactic termination. The gravitational implication remains conditional on a same-model unitary dilation, outgoing access construction, and constant endpoint residual. No positive noncommuting recovery window, physical field-to-memory receiver, quantum-gravity unitarity theorem, or gravitational evaporation endpoint is established.