NSk--Spin Global Spin Structure and Globalization of the Local Dirac Framework

NSk--Spin closes the global spin layer of the Einstein--Dirac track developed within the NSk/ψ program. The module globalizes the local Dirac framework by constructing global Lorentzian data, frame reductions, spin structures, the spinor bundle, the global Clifford action, the spin connection, and the global Dirac operator. The main result identifies the existence of a spin structure with the vanishing of the second Stiefel--Whitney class. When this obstruction vanishes, local Dirac data glue into a global spinor bundle and a global Dirac operator. The module also controls the dependence on the choice of spin structure, spinor holonomy, global geometric chirality, the flat Minkowski spin certificate, a physically natural Cauchy class, and gauge-twisted spinor bundles. At the export level, NSk--Spin provides the global input required by downstream Einstein--Dirac, Dirac/gauge, Yang--Mills, Wightman, and future fermionic modules. Its purpose is to separate the local Dirac apparatus from global spinorial legality and to determine when local spinor physics can be assembled into a globally coherent geometric package.