Proposition: An entangled finite state does not identify its generator

A specified finite bipartite density operator and its entanglement properties alone do not establish entanglement generation by a gravitational mediator or exclude a predeclared classical-gravity model.

Proof. The same density operator can be taken as an initial shared preparation, with no mediator in the specified experiment. It can also be obtained by preparing a purification at an ordinary quantum source and distributing its subsystems. Neither completion changes the density operator. Thus its static entanglement data do not specify the input preparation, allowed mediator dynamics, interventions, or classical comparison family. Exclusion of that family requires those additional declarations and a distinguishing prediction.