Afolabi Unified Framework Applications to the Millennium Prize Problems: Yang–Mills Mass Gap and Navier–Stokes Regularity via Z_M Field Impedance and Kuramoto Collective Coherence

We apply the mathematical framework of the Afolabi Unified Framework (AUF) — specifically the Field Impedance operator Z_M from Afolabi Field Theory (AFT), the N² Collective Coherence Scaling Law from Resonance Physics (RP), and the Dimensional Algebra Type System from APLO — to two Clay Mathematics Institute Millennium Prize Problems: Yang–Mills Existence and Mass Gap, and Navier–Stokes Existence and Smoothness. For Yang–Mills: the mass gap emerges as the minimum value of Z_M · E_c above the AUF vacuum, protected by topological Chern C=±1 structure. The E₈ root system at APLO dimension 7D provides the geometric realisation of the gap. Confinement is reinterpreted as a Z_M stability condition via IFA vacuum…