Operational versus gravitational islands

In gravitational island calculations, one supplies a gravitational state, admissible regions and surfaces, and a generalized entropy involving bulk entropy and a geometric term EngelhardtWall,IslandReview,Penington. None of those objects is supplied by declaring a finite register to be a vault.

Here an “island assignment” means only that a specified logical factor, initially outside the receiver's access, has certified representatives obtainable from the receiver's later output. It is not an equation asserting

not physical access to $B$, and not a minimization over surfaces.