Universal Resolution of the Navier-Stokes and Yang-Mills Millennium Problems: A Unified Simplicial Lattice Hamiltonian Framework via the Hernández-Valdivia Limit

In physical systems, structural stability requires finite limits on energy density and information processing. However, the persistent assumption of an infinitely divisible continuous spacetime (C∞) in theoretical physics relies on an idealized mathematical measuring tool applied to a finite physical reality. This mismatch leads to non-renormalizable singularities and infrared divergences, a logical flaw we identify as the "Gödel-Stokes Paradox". We present a definitive resolution by demonstrating that the universe requires a strict thermodynamic safety factor, the Hernández-Valdivia Limit (εHV), to prevent systemic collapse. By formulating a modified Kogut-Susskind Hamiltonian over a SU(3) simplicial lattice, we incorporate this limit as a gauge-covariant topological friction term. We analytically demonstrate that this discrete geometry truncates the phase space, strictly bounding the Hamiltonian (HHV ≥ 0) and entirely evading the Ostrogradsky instability. The Yang-Mills Mass Gap and color confinement emerge as deterministic macroscopic manifestations of this geometric resistance. Finally, we provide an analytical proof in Appendix A showing that the continuous C∞ Navier-Stokes equations inevitably experience a blow-up against a solid boundary, proving that the Hernández-Valdivia Limit is a physical imperative for a consistent universe.