The Foundations of General Relativity as a Quantum Theory: Providing the Microstate Substrate for Entropic Gravity and Holography

In this ontological-applicative paper, we examine how recent formulations of emergent gravity, notably the Gravity from Entropy framework (Bianconi, 2025), successfully describe the gravitational interaction as a dynamic driven by the minimization of quantum relative entropy, aligning with black hole thermodynamics. However, such thermodynamic approaches face a fundamental ontological deficit, often termed the "Abstraction Problem": they treat information as a floating scalar entity, lacking a rigorous definition of the microscopic physical substrate that carries these local degrees of freedom. In this work, we establish General Relativity as a Quantum Theory, (RGTQ) as the necessary discrete geometry underlying this thermodynamic description. By formalizing the breakdown of continuous simultaneity in Special Relativity as a Covariant Sampling Lattice (Vol. V), we identify the fundamental element of gravitational information not as an algebraic abstraction, but as a physical Topological Knot (Chern-Simons soliton) in the affine connection of the manifold. We analytically demonstrate that Bianconi's entropic gravity emerges rigorously as the statistical limit of the elastodynamics of this lattice, where the Geometric Impedance of the vacuum ($\alpha$) acts as the natural regulator of the density of states. Consequently, the Bekenstein-Hawking entropy law ($S_{BH} = A/4 l_P^2$) ceases to be a thermodynamic postulate and is derived, from first principles, as the direct counting of topological invariants anchored on the saturation surface of the event horizon. The present unification resolves the ontological divergence, integrating the discrete mechanics of RGTQ with the informational thermodynamics of gravity.