Conclusion

A recovery claim is operational only after its information target, accessible interface, complete decoder, reference convention, and validation assumptions have been fixed. We supplied those interfaces and proved them locally on a connected finite encoding.

The resulting statements are stronger than exact named-observable readout and narrower than unrestricted gravitational reconstruction. They certify a specified implemented channel, distinguish failure of a certificate from a genuine obstruction, and permit separately proved resource and all-decoder bounds. The subsystem and algebra targets remain valid on correlated inputs. The confidence bounds retain the input-dimension factor, include calibration explicitly, and never silently discard unsuccessful branches.

The minimum outcome is therefore achieved: a finite logical subsystem and hybrid algebra, constructive access-restricted programmes, and simultaneous reference-preserving certificates for their complete channels. Larger networks, tighter mixed-target estimators, and apparatus-specific audits may be added without changing the logical separation between code theory, implementation, certification, and gravitational interpretation.