Question, contribution, and corrected logical structure

The motivating question is often phrased as “bulk reconstruction beyond the semiclassical limit.” That phrase contains at least three different mathematical tasks:

1. recovery of a declared quantum input or a named observable through a declared accessible channel;

2. determination of whether an exact quantum-error-correcting description remains valid;

3. justification of a classical geometric interpretation of the recovered data.

This manuscript answers specified versions of the first two tasks and formalizes the additional evidence required for the third. It does not construct a gravitational dictionary.

Exact quantum error correction, information–disturbance relations, observable correction, and quantum-system certification are established subjects KnillLaflamme,KSW,BenyKempfKribs,KlieschRoth. Holographic reconstruction results additionally use their own bulk–boundary and relative-entropy hypotheses JLMS,DongHarlowWall. Those hypotheses are not supplied merely by naming a channel “boundary” or a logical effect “bulk.”

Cheung's supplied manuscripts motivate the separation of complete data, accessible outputs, residual ownership, destructive readout, and physical correspondence CheungI,CheungHawk04A,CheungHawk04B, CheungEn07A,CheungEn07B,CheungEn07C,CheungXVIIA. The finite statements needed here are proved for the objects defined below. No unavailable model-specific result is an implicit premise.