GRAVITY AS A QUANTUM MEDIATOR AT THE MESOSCOPIC INTERFACE: Channel Structure, Entanglement Generation, and the Structural Failure of Semiclassical Gravity in BMV-Type Experiments

ABSTRACT Background The gravity–quantum interface lacks a minimal, operational theory for the weak-field, non-relativistic, mesoscopic regime. Semiclassical gravity (SCG), which sources the classical Einstein equations from the quantum expectation value of stress–energy, is the dominant approximation but was designed for cosmological and astrophysical contexts, not for two-body entanglement experiments in the laboratory. A structural silence exists: no framework specifies how gravity couples to quantum matter when entanglement between spatially delocalised mesoscopic masses is at stake. Gap The Named Binary distinguishing Semiclassical Gravity Interface (SCGI) from Quantum-Mediator Gravity Interface (QMGI) does not appear in the literature as a formal operational distinction with computable consequences. No framework simultaneously satisfies: standard quantum mechanics for matter, no-signalling, reduction to Newtonian gravity for classical configurations, and entanglement-generation capability. This four-constraint conjunction defines the structural gap. Approach We formalise the two-body BMV (Bose–Marletto–Vedral) configuration using Hilbert-space language and quantum channels, derive the effective entangling Hamiltonian, prove that C (t) = |sin (Δφ (t) /2) | where Δφ (t) is the entangling phase determined by geometry and interaction time, and derive the design inequality τₑnt ≪ τdec as the admissibility condition for entanglement detection. We establish the Strongest Formulation in the five-part programme template, specify a pre-registerable CCS with quantitative decision rule, confirm structural invariance across three independent physics domains, ground the framework in IGT theory, and provide a complete Weil Protocol practitioner review pack. Results Under the four-constraint conjunction (standard QM + no-signalling + Newtonian reduction + entanglement capability), gravity in the mesoscopic weak-field regime must be modelled as a quantum channel: SCGI fails because classical channels cannot increase entanglement between initially separable systems. The entangling phase scales as Δφ (t) ~ Gm²dt/ (ℏD²) ; detectable entanglement requires τₑnt/τdec < 1. Three independent distinguishing predictions follow that SCGI cannot make. Structural invariance is confirmed in quantum electrodynamics (photon-mediated entanglement), nuclear physics (exchange-mediated forces), and quantum optics (cavity-mediated entanglement). Implications Any tabletop detection of gravitationally induced entanglement between two mesoscopic masses in a BMV-type experiment would constitute a direct, model-independent, low-energy signature of the quantum nature of gravity. Any confirmed null result provides the strongest direct evidence for SCGI-type models and bounds the parameter space of quantum mediator theories. Weil Protocol practitioner review is required before policy adoption of experimental specifications; status INCOMPLETE. Human-stakes level: L2 · Weil Protocol: INCOMPLETE