The Dirac-Hernández-Valdivia Equation: Topological Friction and Finite-State Relativistic Quantum Mechanics

This paper extends the Hernández-Valdivia Modular Paradigm to the relativistic domain by reformulating the Dirac equation. We introduce the Dirac-Hernández-Valdivia (DHV) Equation, demonstrating that relativistic quantum superposition and infinite Hilbert space divergences are computational artifacts arising from the continuum fallacy (C∞). By incorporating the Ramanujan-Hernández Packing Factor (ΦRH) and the bulk viscosity (ζHV) of the modular vacuum, we introduce a non-linear Topological Friction term that forces a deterministic, local resolution of the spinor wavefunction. This framework naturally resolves long-standing anomalies such as the Klein Paradox and Zitterbewegung, reinterpreting them as fluid dynamic instabilities within the discrete processing network of the universe. Ultimately, we prove that relativistic quantum mechanics operates under strict hardware constraints as a self-regulating Finite-State Machine.