The Ramanujan-Hernández Packing Factor (ΦRH ): A Universal Regulator for Spacetime Information Density and Finite-State Physics

The reconciliation between General Relativity and Quantum Mechanics has historically been obstructed by the "Continuum Fallacy", the assumption of infinite spatial divisibility (ℝ3) that leads to non-renormalizable singularities and undecidable energy densities. We present a definitive resolution by formalizing the Ramanujan-Hernández Packing Factor (ΦRH). Derived from the fundamental ground state (n=0) of Ramanujan's 1914 modular series for 1/π, ΦRH is established as the topological stiffness coefficient governing the information density of the vacuum. We define the Hernández-Valdivia Limit (εHV ≈ 10-70 m2) as the intrinsic "hardware" resolution of the universe, preserving Lorentz invariance through isotropic modular geometry. We demonstrate that ΦRH acts as the universal regulator that resolves the Navier-Stokes singularity via adaptive hyperviscosity, explains the Yang-Mills Mass Gap as topological friction, and identifies Dark Energy as the emergent Bulk Viscosity (ζHV) of the modular vacuum. Finally, we predict the existence of Landau-Ramanujan Oscillations in the vorticity of the Quark-Gluon Plasma (LHC Run 4) as empirical evidence that spacetime operates as a finite-state machine.