Geometric Formulation of Gravitation in Phase Space with Quantized Volume Elements

We propose a geometric framework for gravitation in which the fundamental degrees of freedom are encoded in a distribution function over phase space, replacing the concept of point mass with a probabilistic description. This approach enables a regularization of gravitational self-energy via vacuum polarization, analogous to Debye screening in plasmas. We show that gravitational interactions arise as statistical responses of a structured vacuum populated by mass dipoles , leading to a quantized field without divergence. A covariant variational principle is formulated, combining the Einstein-Hilbert action with a kinetic term in phase space. The resulting field equations describe the curvature as sourced by averaged energy-momentum derived from . A geometric quantization condition on phase-space volume replaces standard operator methods and recovers the uncertainty principle as a topological constraint. This framework paves the way for a theory of Quantum Gravito-Dynamics (QGD), wherein gravitation is quantized not via field excitations (gravitons) but as an emergent property of phase-space geometry. The model is naturally compatible with bimetric and Janus cosmologies exhibiting CPT symmetry.