Submission and proof-obligation ledger

New emission data. The injection $J_0$, the remnant gate in $W_2$, and the three emission maps are explicit. Their dimensions and consistency are part of the model, not inherited black-hole dynamics.

Whole-channel correctness. The accessible channels are identified on all matrix units. Branch intertwiners preserve a common environment vector and therefore logical coherence with every reference.

Approximate lower bound. The one-slot bound applies directly to the conditional logical-reference states. No approximate off-code uniqueness is assumed.

Storage. Batch early radiation, supplier buffers, duplicate registers, recovered output, and quantum flags are counted in their respective ledgers. Undelivered radiation is not deleted by a change of notation.

Conjugate access. $U^{\ast }$ and its inverse $U^T$ are explicit granted operations. No generic conversion from an unknown $U$-oracle is claimed.

Amplification assumptions. Uniform angles follow from exact decoupling and the proved support identity $L^{†}L=m^{-2}S$. They are not presumed for arbitrary evolution.

Reflection compilation. Large all-zero phase operations have a declared implementation cost. If their implementation uses workspace, that workspace must be added. The one-message example needs only two-qubit phases and has an explicit ancilla-free realization.

Single-copy restrictions. A selective map is not renormalized into a deterministic channel. Destructive failures are not supplied with free retries.

Noise. Complete-channel gate errors, independent flagged erasure, and encoding uncertainty are separate models. A selected-state fidelity does not replace a diamond-error certificate.

Thresholds and clocks. The finite emission horizon, gate budget, access convention, delivery times, and gate durations are declared. None is a Page-time or evaporation-time identification.

Computational evidence. The source is supplied without an execution log. The proofs do not depend on sampled tests, numerical fitting, or an unavailable package.