The nonimplication ledger

The intended refusal is better expressed as a nonimplication than as an assertion that the underlying objects can never coincide:

A decoder can implement a bulk–boundary map after the relevant identifications have been supplied and proved. It does not supply those identifications merely by being a decoder. The distinction is important even for holographic code models Pastawski2015.

There are three separate claims:

1. Operator reconstruction: the named boundary data determine the named bulk observable in the declared model.

2. Metric reconstruction: boundary data determine a bulk metric within a specified metric class.

3. Gravitational dynamics: microscopic assumptions imply specified gravitational field equations.

Only the first is established here. Results concerning entanglement-wedge reconstruction, entropy–area relations, or linearized gravitational equations require their own additional assumptions DHW2016,RT2006,Faulkner2014.