Question, contribution, and evidence boundary

The construction follows the chain

The decisive distinction from Em03-C is that alternative radiation states are not supplied independently. The radiation channel is calculated from the Hamiltonians and preparations printed below.

Three levels of conclusion remain separate:

1. Finite dynamics: a message-dependent channel generated by a declared sequence of bounded interactions;

2. Semiclassical comparison: agreement or controlled disagreement with a named family of Em03-A–C occupation observables;

3. Black-hole identification: derivation of those interactions and degrees of freedom from a specified gravitational theory.

The first level is proved. A restricted comparison at the second level is proved. The third level is not claimed.

The information-transfer mechanism is the familiar Pauli randomization mechanism of a private quantum channel PrivateChannel. It is not presented as a new encryption scheme. The contribution is its explicit finite emission Hamiltonians, complete channel and complement calculations, exact recovery benchmarks, occupation calibration, and operational error accounting in one specified model.

General information–disturbance and approximate-correction theorems provide a broader setting KSW,BenyOreshkov. We do not import their constants into a different metric. The recovery and leakage constants needed here are proved directly. Hayden–Preskill models likewise retain unitarity, mixing, and radiation-access assumptions HaydenPreskill; none of those assumptions is derived by the present decoder.

. The supplied Em03-A, Em03-B, and Em03-C sources Em03A,Em03B,Em03C supply the stated semiclassical and operational comparison interfaces. No manuscript registry or companion retrieval account is a premise of the finite dynamics. In particular, no Em03-D source is assumed.

boundary. All results are analytical. Compilation, formal verification, numerical pulse execution, calibration, and experimental realization are not asserted. “Certified” means that an explicitly stated comparison follows from the printed mathematical hypotheses.

. All model Hilbert spaces are finite dimensional. We use

The diamond norm retains arbitrary external references. We write

Entropy is in bits. The binary entropy is

with $0{\log }_{2}0=0$. Channel and instrument conventions are standard Watrous; the particular formulas used below are proved in this manuscript.