Proof and interpretation checklist

The following checks are retained to prevent scope expansion during later revision.

1. Half-diamond normalization. Every channel error contains the factor $1/2$. The constant-channel benchmark is $1-d^{-2}$, not one.

2. All logical coherences. The code loading and evolution are linear isometries. No classical code ensemble replaces a quantum input.

3. Reference retention. Channel estimates are uniform on arbitrary code-reference states. A selected preparation is not used as a substitute.

4. Complete residual. Source, uncollected reservoir, carrier output, and any preparation environment are retained at the relevant interface.

5. No undeclared early radiation. The reservoir starts in vacuum, independently of the code. No early-radiation purification is supplied to the decoder.

6. Infinite dynamics. The benchmark uses a self-adjoint second-quantized operator. The interacting successor uses quasi-local dynamics, not an unjustified infinite matrix sum.

7. Finite versus asymptotic access. Finite collection is evaluated at a declared time. The endpoint uses a declared outgoing scattering representation.

8. Endpoint derived, not designed afterward. The outgoing map is obtained from the same Hamiltonian by wave-operator completeness.

9. Bound-state test. Purely absolutely continuous spectrum is proved for the benchmark. Infinite bath size alone is not accepted as a substitute.

10. No irreversible claim at fixed finite regulator. The recurrence theorem remains part of the release.

11. Energy accounting. Source, bath, and interaction energies are distinguished. An energy ledger is not renamed gravitational dynamics.

12. No model splicing. The quadratic recovery theorem is not transferred to interacting SYK or to another paper's gravitational geometry.

13. No unverified catalogue premises. The external numbered mathematics families are documentary comparisons only.

14. No execution overclaim. An implementation specification, reported manifest, or symbolic formula is not described as an executed or independently validated calculation.