Operational and geometric meanings

Einstein–Rosen bridges, Morris–Thorne wormholes, and the ER $=$ EPR proposal concern geometric or gravitational structures EinsteinRosen,MorrisThorne,MaldacenaSusskind. Gravitational traversability constructions also specify interactions, matter stress, and backreaction GaoJafferisWall,MaldacenaStanfordYang. Those structures are not specified by an isometry $L\to R\otimes B$.

Here “mouth” is an overlay label for an output factor. “Throat” is an overlay label for the complete complementary channel and its input dependence. The complement is a channel, not a third tensor factor, a tunnel, or a proper-length quantity. “Operational traversability” means successful quantum return through the declared receiver. It is directional and does not claim a causal curve from one spatial mouth to another.