= Solution
Yes in both directions. The <Page–Geilker experiment> tests whether a classical gravitational field is sourced by the expectation value of macroscopically superposed matter configurations. The <Colella–Overhauser–Werner experiment> uses the Earth's effectively classical field as an external potential and therefore does not distinguish an expectation-value semiclassical source law from a quantized gravitational field.
Conversely, the Colella–Overhauser–Werner experiment directly observes coherent <matter-wave interference> and a gravitationally generated relative phase in a neutron wavefunction. Page and Geilker did not maintain and recombine coherent branches of the macroscopic source, and their torsion-balance measurement was not an interference experiment. Thus their experiment did not test the neutron gravitational phase effect. The experiments probe opposite sides of the coupling: quantum matter responding coherently to gravity, and gravity responding to branch-dependent quantum matter.
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