Definition: Operational wormhole certificate

A tuple $(V,R,B,\mathcal{D},\epsilon )$ is an operational wormhole certificate when:

1. $V$ is a complete isometry and the receiver accesses only $R$;

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

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

4. physical $B$ remains a declared output factor;

5. no two commuting code-preserving star representations both implement the same logical algebra through $V$.

The terms “mouth” and “throat” add no geometric hypothesis.