Chronoflux Research Initiative - Four-Dimensional Covariant Formulation for the Remaining Millennium Problems

This paper presents a four-dimensional covariant Chronoflux formulation for the remaining Millennium Prize Problems. Previous work established the temporal hydrodynamic continuity law and its application to spectral structure and fluid regularity. The present work reformulates the Yang–Mills mass gap, the Birch and Swinnerton–Dyer conjecture, the Hodge conjecture, the P versus NP problem, and geometrization within a single conserved temporal transport field defined on a four-dimensional spacetime manifold.

All constructions are derived from a covariantly conserved temporal current, a regulated norm constraint, and the associated temporal differential inertia tensor. Gauge dynamics, algebraic structures, and computational complexity are treated as effective projections of the same conserved flow. The formulation is written entirely in four dimensions and introduces no additional coordinates.

Each problem is reduced to properties of the same continuity law and its regulated dynamics, providing a unified invariant structure across spectral theory, gauge theory, algebraic geometry, topology, and computational complexity.

This work forms part of the Chronoflux Research Initiative.