Stage 5: gravitational and recovery readings remain separations

The mathematical data here are a finite set, its uniform law, a stochastic matrix, and a Boolean truth table. They specify neither a metric nor a gravitational interaction.

The parameter $t$ in $P_t=T_{e^{-t}}$ is a classical Markov-semigroup parameter. Calling it time does not identify it with a spacetime coordinate or an evaporation process. The number operator $\mathsf{N}$ acts on functions on the cube; no physical Lindblad generator is specified. This does not deny that a classical Markov process can be embedded in a larger matrix evolution. Such an embedding is additional data, as the preceding quantum-extension example illustrates.

A Page curve requires a specified time-indexed radiation state and access partition. An island or horizon requires geometric and dynamical structure. A gravity-generated-entanglement test requires a preparation, mediator model, output state, and comparison class. None occurs in the contraction experiment.

Cheung's Oai265-A separates static entropy records from recovery and radiation histories, and the supplied XIV-I/J passages separate defined internal kernels from an unconstructed full characteristic composition CheungOai265A,CheungXIVI,CheungXIVJ. Those are relevant cautions about transferring premises, not analytic inputs to our finite cube calculation.

Enter, where invoked in the comparison manuscripts, remains destructive readout. A classical record does not become a reference-preserving unknown-state decoder because it contains a particularly informative bit CheungI,CheungVIIIB,CheungEn07A.

No Page curve, island, horizon, Hawking-radiation derivation, gravity-generated entanglement, exclusion of classical gravity, or spacetime-emergence theorem is established.