Problem, scope, and contributions

Hawk01-A distinguished delayed-query retrieval from source spectra, observer access, and an assumed information-transfer mechanism CheungHawkA. Here the logical task is stronger:

Under what declared dynamical, conservation, endpoint, and access assumptions does radiation preserve every state of a specified quantum code, together with every external reference correlation?

Distinguishing selected preparations is not substituted for this arbitrary-input requirement.

We establish three connected results. First, residual leakage and arbitrary-input recoverability are related by the established channel information–disturbance framework, with all normalization factors displayed KSW2006,BenyOreshkov2010. Second, a consistent conserving sequence realizes complete code preservation using identifiable joint radiation correlations. Third, an explicit entropy-history separation shows why scalar radiation entropies, detached from their dynamical and reconstruction setting, do not determine that channel property.

The exact recovery interfaces in Hawk01-A and Em05-B, the key-transfer separation in Em03-E, and the readout/recovery/resource distinctions in En02-B–E provide useful source precedents CheungHawkA,CheungEm05B,CheungEm03E,CheungEn02B, CheungEn02C,CheungEn02D,CheungEn02E. Their models are not identified with the model below, and their conclusions are not transferred as black-hole theorems.

versus assumed. The isometries, conservation identities, channels, decoders, entropy formulas, and recovery optima below are mathematical results within the specified finite model. The degenerate radiation sectors, their couplings, transfer schedule, and endpoint map are model assumptions. They are not derived from the Schwarzschild geometry or the Hawking spectrum.

unpriced assistance. The construction starts from one logical input and fixed pure ancillary preparations. It does not require pre-collected radiation or a supplied correlated early key. It generates its early resource in the first emission and includes its purifier in subsequent residual and endpoint accounting.

implicit terminal extrapolation. The pre-endpoint construction is stopped above a declared $M_{\mathrm{cut}}$. A separate endpoint rule is then imposed. Setting that rule to complete evaporation is an additional assumption, not an extrapolation of fixed-background quantum field theory.