The missing gravitational interface

For comparison, holographic entropy prescriptions require geometric and field-theoretic input beyond a finite graph boundary. The Ryu–Takayanagi proposal involves bulk minimal-surface area in an AdS/CFT setting RyuTakayanagi. Quantum extremal surfaces extremize generalized entropy containing both geometric area and bulk entropy EngelhardtWall. Replica-wormhole calculations require a specified gravitational replica construction AlmheiriEtAl.

The present record supplies none of:

1. a spacetime and dimensionful metric;

2. a gravitational action, Newton constant, or entropy renormalization prescription;

3. an identified bulk or radiation algebra and its state;

4. an admissible surface class and homology conditions;

5. a generalized-entropy functional and an extremization theorem;

6. a replica path integral, saddle comparison, or analytic continuation;

7. a dynamical evaporation and radiation-access model.

A dimensionless count $|{\partial }_{\Lambda }A|$ cannot fill these slots by being called an area.

Likewise, the same finite graph can be embedded with arbitrary lattice spacing without changing its Hamiltonian matrices, spectral gap, or entropy record. A physical length or gravitational normalization is additional data.