An independently checkable small example

Choose

The units here are model energy units, not astrophysical mass or temperature assignments. Then

The endpoint radiation has eight completed-state rails of energy three and eight pending-state rails of energy four. The residual source becomes one vacuum state.

{Exact model outputs. Entropies and mutual informations are in bits. $H_{\mathrm{pure}}$ uses a pure code input; $H_{\Phi }$ uses the maximally entangled reference input. At $t=0$, $R$ is empty.}

The Bell-input optimal fidelities are, in order,

The conditional reference-information increments are zero for the key, one bit for attempt two, one-half bit for attempt three, and one-half bit for the endpoint.

The exact mean residual energies are

with the corresponding emitted energy giving total five in every branch, not merely on average.

Destructive number-record recovery gives

These values differ from the coherent-access column in Table tab:exactexample.

thermal comparison. To match the vacuum/one-particle restrictions of the two attempt marginals, solve $a_2(q)=w_j$. This gives

The omitted product-thermal probabilities are

Thus even this simple calibration exposes a large thermal discrepancy at the first attempt. These $q$ values are formal comparison parameters, not claims that a Schwarzschild greybody calculation produces them. For the four-rail key block, (eq:keythermalobstruction) gives minimal product-thermal distance