NSk--Dirac First-Order Dirac Framework in the NSk/ψ Program

The NSk--Dirac module constructs a local first-order spinor framework on a pseudo-Riemannian manifold with metric and tetrad provided by NSk--Einstein. It defines the Dirac operator, the compatible spinor covariant derivative, and the full second-order structure via the Lichnerowicz identity. The module establishes the spinor current, the symmetric Belinfante–Rosenfeld energy–momentum tensor, and the corresponding balance law in the presence of a variable mass field, with the conserved case recovered for constant mass. The evolution parameter is inherited contractually from NSk--Einstein, and the Hamiltonian regime is treated only in the weak-field approximation. The module does not define geometry, time, or the mechanism of mass generation; instead, it operates on an abstract mass input interface. The resulting construction provides a closed local spinor sector ready for downstream use within the NSk/ψ program, in particular for quantum, gauge, and particle-structure modules.