Physical scope

We use $\hslash =c=k_B=1$, with base-two entropy. Energy conservation refers to the displayed finite Hamiltonians. Equal-energy rails are orthogonal scalar modes, not particle polarizations. Rotational covariance, an autonomous clock, apparatus work, detector absorption, and a field-to-qubit transducer are not derived.

Reflections remain inaccessible and do not return to the core. No companion manuscript is a proof premise. The finite models do not establish semiclassical evaporation, a typical Page curve, or a gravitational island formula.