The NSk--GapRelRol--CORE module provides a universal stability layer for the NSk/ψ program. It works in a spectral framework built on a non-negative self-adjoint operator with discrete spectrum on a Riemannian manifold of bounded geometry, equipped with a smooth spectral window calculus and a functional-analytic Dirichlet form setting. The analytic content is organized around four spectral ingredients: gap-type conditions that separate vacuum bands from matter bands, relative boundedness estimates for admissible perturbations, rolling bounds derived from Poincaré and log-Sobolev inequalities that control energy and entropy along the associated semigroup, and uniqueness and stability of the ground state. All these statements are formulated in a model-independent way, in terms of geometric and spectral data and standard tools from the theory of self-adjoint operators and Dirichlet forms. On the output side, NSk--GapRelRol--CORE exposes a compact stability API for higher-level NSk/ψ constructions in statics, dynamics, gauge theory, cosmology and number theory. In particular, it provides robust mass-gap-type constants for the semigroup, stability of spectral gaps under admissible perturbations, rolling estimates for energy and entropy on spectral bands, and a clean uniqueness statement for the NSk vacuum. In this way the module bridges microscopic spectral input with macroscopic stability and mass-gap applications. It is compatible with the global core interface formulated in NSk–MAIN–CORE–API (DOI: 10.5281/zenodo.17897274) and with the ontology of the ψ field presented in the NSk/ψ Manifest (DOI: 10.5281/zenodo.17782177).
Nowak et al. (Wed,) studied this question.