NSk--Matter Matter Phases, Dark Sector, and Anchor Stabilisation in the NSk/ψ Program

NSk--Matter establishes the framework of matter phases, the dark sector, and material-carrier stabilisation in the NSk/ψ programme. The module formalises the materialisation field P, the distinction between background, dark matter, and ordinary matter, and the conditions under which a positive carrier becomes an admissible source-side carrier of mass for downstream modules. In the PRE-PURE and PURE layers, the module introduces the minimal language of materialisation: material classes, stabilisation statuses, stabilisation cost, materialisation threshold, and stabilisation margin. The CORE layer develops a full theorem-level framework for transitions between sectors, including promotion from the dark sector to the ordinary sector, degradation from ordinary to dark, the existence of a stabilisation barrier, and the structure of minimal-cost trajectories. The module also defines a source-side mass record that organises the relation between carrier materialisation and downstream mass-generation mechanisms. A major part of the paper is devoted to inter-module interfaces. NSk--Matter exports a source-side package to NSk--Gravity, a package compatible with partial and full materialisation models to NSk--VisGeom, a spinor-mass bridge to NSk--Dirac, a sectoral record to NSk--Cosmology, and a common input record for mass-branch modules, in particular NSk--MassLadders, NSk--Higgs, and NSk--Neutrino. In this form, NSk--Matter serves as the central module responsible for matter phases, the dark sector, and the source-side status of material mass carriers within the NSk/ψ architecture.