Intrinsic Quantum Geometry and the Emergence of General Relativity Gravitation

We propose a unified geometric framework in which each quantum particle is endowed with an intrinsic spatial geometry governed by a universal stiffness constant A₀ and sourced by its wavefunction. This geometry gives rise to a repulsive self-interaction that prevents gravitational collapse. When multiple particles are present, their individual geometries combine through local interactions, forming a collective structure whose dynamics, in the continuum limit, reproduce 4-dimensional GR gravity. Newton’s constant emerges as G = c⁴/(8πA₀). The framework provides a geometric account of quantum interference and entanglement, eliminating the need for a separate configuration space. Extending the formalism to the vacuum, interpreted as a compound of virtual geometric excitations, yields a constant harmonic field ΦH whose scale is set by the Hubble radius, leading to a vacuum energy density ρ_vac ∼ 3c²H²/(8πG) in agreement with observations. This approach offers a deterministic, unified model for quantum mechanics, gravity, and cosmology, with testable predictions for precision measurements.