The Information-Topological Unified Field Theory: Resolving Gravity, Quantum Mechanics, and Cosmological Expansion via the Modular Ramanujan-Hernández-Valdivia Limit

Major Update (v2): Incorporates the rigorous derivation of the topological limit via Ramanujan's Modular Geometry and establishes the connection with Conformal Field Theory (CFT) twist operators. Corrects dimensional coupling in the unified field equation. The reconciliation of General Relativity with Quantum Mechanics remains obstructed by the "Continuum Fallacy"—the assumption of infinite spatial divisibility that leads to non-renormalizable singularities. We propose a definitive resolution by introducing the Ramanujan-Hernández-Valdivia Limit (εHV), a fundamental quantization of topological area derived directly from the modular geometry of Ramanujan’s generalized hypergeometric series. Unlike arbitrary cutoff scales, εHV is defined by the Ramanujan Packing Factor (ΦRam), ensuring the preservation of rotational invariance in a discrete spacetime. We construct a fully covariant framework within Deformed Special Relativity (DSR), where εHV functions as a Lorentz-invariant topological scalar. The resulting field equations demonstrate that gravity emerges not as a fundamental force, but as the hydrodynamic pressure of information processing on this modular lattice. Furthermore, we identify Dark Energy as the emergent Bulk Viscosity (ζHV) of the superfluid vacuum, generated by the geometric rigidity of the modular cells. The theory resolves the "Gödel-Stokes Paradox" and predicts a falsifiable "Viscosity Saturation Plateau" observable in high-energy Quark-Gluon Plasma experiments (LHC Run 4), where fluid vorticity is bounded by the modular efficiency of spacetime.