Definition: Operational wormhole certificate

A certificate for the whole logical diary is a tuple

such that:

1. $V:L\to R\otimes B$ is a complete isometry;

2. the receiver accesses $R$, not physical $B$;

3. $\mathcal{D}:\mathcal{B}(R)\to \mathcal{B}(L_{\mathrm{out}})$ is a specified, deterministic CPTP quantum-return map;

4. $${\Vert \mathcal{DN}-{\mathrm{id}}_L\Vert }_{\diamond }\le \epsilon ;$$

5. $B$ remains the declared physical residual;

6. no two commuting, code-preserving star representations both intertwine $V$ with the same algebra $\mathcal{B}(L)$.

We call the certificate nonclassical when $\epsilon <2b_d$, below the record-only lower bound. The mouth and throat terminology is an overlay on this contract.