Recovery availability versus implementation

Theorems thm:constant and prop:approximate establish information-theoretic existence of decoders. They do not bound their circuit complexity, collection aperture, duration, coherent memory, or physical localization. Resource-constrained recovery is a separate task.

Hayden–Preskill recovery assumes a stated mixing model and access to appropriate early and late radiation HaydenPreskill. Island and replica-wormhole calculations determine entropy or reconstruction quantities under their gravitational and bath assumptions Penington,ReplicaWormholes. They are not imported as diamond-error theorems for the present scalar code interface.