Ordinary and Dark Matter as Phase Regimes of the ψ Field in the NSk Energy–Spectral Anchor Formalism

We develop a mathematical definition of ordinary matter and dark matter in the language of an existence density field psi and the NSk energy-spectral anchor, on a class of manifolds with bounded geometry. Building on the NSk anchor operator H = hbar c sqrt (-Deltag), spectral windows satisfying assumptions (A1) - (A4), and the Anchor-Strong Theorem for the anchoring function F (Gammaₑff), we define ordinary matter as regions of full stabilisation (P = |psi|² = 1) that are locally compatible with the anchor equation, and dark matter as semi-stable regions (0 This preprint contains the original formulation of the NSk-based definition of ordinary and dark matter as phase regimes of the ψ field.