Abstract

We define and prove existence of operational wormhole certificates: complete finite encodings whose unknown logical input can be returned through one declared accessible interface, with a deterministic decoder and a worst-case reference-preserving error allowance. This terminology describes a recovery contract, not a spacetime wormhole.

The model has an unknown diary, an old-vault register maximally entangled with accessible early memory, and one input-independent scrambling unitary. A nested schedule hands over vault cells while retaining a positive-dimensional physical residual. We prove the exact complete-complement criterion, derive the finite Haar decoupling moment, and specify a deterministic decoder by a semidefinite program. One threshold supplies the same decoder core at every subsequent retained cut.

For every prescribed full-diamond tolerance $0<\epsilon <1$, an explicit finite parameter family has Haar measure at least $1/64$ on which three consecutive retained cuts admit the operational certificate. On the same devices and for one fixed pure diary input, late-radiation entropy rises and then falls within that window; the last cut retains one physical qubit. Append-only Enter records remain nondecreasing.

We correct two essential claims in the proposed analogy. Nested-access recovery error and complete residual leakage cannot peak at an intermediate Page cut: both are nonincreasing. Furthermore, measuring late radiation does not imply a record-only obstruction if an early quantum register survives; teleportation provides an exact counterexample. Terminal readout and forgetting equal partial trace on the returned interface, not physical annihilation or disappearance of the complete complement.

No metric, Einstein–Rosen bridge, Morris–Thorne throat, geometric ER $=$ EPR identification, or gravitational signal-crossing theorem is constructed.