Abstract

We construct a controlled finite representation of selected radiation modes in a specified stationary Schwarzschild free-field model. A finite orthonormal packet family has a normal, zero-mean, gauge-invariant Gaussian state determined by its full packet covariance. We retain complex off-diagonal correlations, derive its thermal normal-mode representation and occupation generating function, and construct a deterministic flagged total-occupation cutoff. For this state, the cutoff trace-distance error is exactly the discarded probability.

We prove covariance-to-state continuity, reference-compatible cutoff bounds for general inputs, bandwidth-dependent energy estimates, and occupation-dependent scattering-channel bounds that retain complex amplitudes. A common ancillary interface supplies a precise condition under which a state approximation controls an encoded channel. Separately, a declared Clifford message channel is calibrated by the selected state's nonvacuum probability. Its unrestricted and atomic-delivery memory-limited recovery errors are evaluated exactly. This benchmark transfers one field statistic; its decoder does not access the selected field state's full correlations.

The implementation appendix specifies phase-sensitive covariance regressions, complete decoder extensions, basis dictionaries, event-wise resource ledgers, radial boundary bounds, and failure-preserving SDP residual checks. It is not reported as executed. The analytical results concern selected stationary radiation states and explicitly declared finite channels, not collapse, backreaction, complete evaporation, or a microscopic Hawking information-release mechanism.