Regularized Semiclassical Gravity with Window-Memory Falsification: A Unifying Framework for Quantum-Gravitational Interaction

We present a comprehensive theoretical framework addressing fundamental challenges in semiclassical quantum gravity through three interconnected mathematical innovations: (1) a novel geometric regularization technique for stress-energy tensor divergences in curved spacetime, (2) a window-memory consistency term enforcing causality constraints on gravitational backreaction, and (3) a falsification-based formalism identifying experimentally testable predictions. The framework yields finite, physically meaningful expectation values for quantum stress-energy operators, resolving long-standing issues in the semiclassical Einstein equations. We demonstrate that the regularized framework predicts observable deviations in superconducting quantum interference devices (SQUIDs) with estimated phase shifts of ~10^-12 rad, accessible to state-of-the-art cryogenic technology. Crucially, our falsification protocol establishes clear experimental signatures for definitive validation or invalidation of the theory, positioning this work within Popper's scientific methodology. While experimental verification remains technically demanding, our framework provides a rigorous theoretical foundation for future quantum gravity phenomenology.