Does gravity-mediated entanglement prove the gravitational field is quantum?

The LOCC argument (local operations and classical communication cannot create entanglement) assumes the gravitational mediator acts as a classical channel. Determine under which explicit assumptions (locality, field-theoretic matter, linearity) observed entanglement at the rate $\phi = G m^2 t/(\hbar d)$ excludes classical gravity, and compute the entanglement producible by semiclassical or stochastic classical gravity coupled to quantum-field matter, which Aziz and Howl find enters at higher order in G and grows with mass toward the Planck mass (about $2 \times 10^{-5}$ g).

A theorem stating which classes of classical gravity models a given entanglement measurement excludes, with parameter regimes where classical contributions are provably negligible.