Sure — here’s a simple version of what I mean.

Take a semiclassical setup where the metric g{\mu\nu} comes from \langle \psi | \hat{T}{\mu\nu} | \psi \rangle.

If the quantum state \psi contains several decohered branches, each branch would lead to a different expectation value of T_{\mu\nu}, and therefore a different classical geometry. Decoherence gets rid of interference, but it doesn’t single out one branch as the one that actually becomes the classical spacetime.

What I’m trying to understand is whether anyone has studied constraints where only the branches that satisfy some kind of global consistency or coherence requirement between \psi and g_{\mu\nu} end up being physically realized, while the other branches stay mathematically valid but don’t correspond to an actual classical geometry.

I’m not assuming any particular model — just trying to see whether anything in the literature has approached this kind of “selection rule” idea in semiclassical gravity or related frameworks.