Coercivity_and_Kernel_Exclusion_for_Fluid_Dirac_Paths

Coercivity and Kernel Exclusion for Fluid Dirac Paths

Its role is not to prove Navier–Stokes regularity unconditionally. Instead, it starts from an exact splitting of the auxiliary fluid Dirac path and proves two precise consequences: first, that a kernel-level coercive dominance condition excludes wall crossing of the auxiliary path; second, that an auxiliary-gap smallness estimate yields the strict physical gap-domination hypothesis required by the earlier conditional spectral-gap criterion. In this sense, the paper converts the first remaining obstruction into a precise and auditable theorem package. It does not derive the coercive kernel inequality from the classical Navier–Stokes equation itself, and it does not prove the auxiliary-gap smallness estimate from first principles. Those analytic inputs remain external.