Recovery, representation, and emergence are different targets

The finite measurement and implementation interfaces associated with Cheung's Enter calculus concern their stated operational class CheungI,CheungEnter. They do not select a field state, supply an unknown observable, or execute a native compilation.

For an elementary recovery distinction, let

The complete output preserves the input isometrically. The accessible $A$ output is constant. No decoder from $A$ alone can recover every input, because it receives the same state for all inputs. Thus complete preservation and recovery through declared access are different.

This is the comparison shape of the supplied Hawk04 records CheungHawk04A,CheungHawk04B. It is not a black-hole model. Selected Psy, Hawk, and En certificates retain their own preparation, residual, access, schedule, and approximation hypotheses. No corpus-wide theorem about those series is claimed.

Operator reconstruction, a supplied metric dictionary, derivation of Einstein dynamics, and holographic reconstruction are distinct projects. AdS/CFT error-correction and entanglement-wedge reconstruction have their own duality and algebraic hypotheses ADH,DHW. A resting conical collar or a finite decoder does not supply that dictionary.

Likewise, the IX partial-product and causal-interface records retain their own sharp-insertion domains and order boundaries. The relative IX-Free-2 selected-word construction through ${\hslash }^3$ is not erased by an earlier IX-Free stop, but does not supply IX-D's missing sharp time-ordered or normalized retarded maps CheungIX,CheungIXFreeTwo,CheungIXD.