NSk--Geo Admissible Geometry Class and Elliptic Operator Framework for the NSk/ψ Program

NSk--Geo establishes the geometric and analytic layer of the NSk/ψ program. The module defines an admissible geometry class, a hierarchy of geometric classes, an elliptic-operator framework, and an output-data adapter that exports geometry, measure, the Laplace--Beltrami operator, spectrum, spectral counting data, heat-kernel data, functional constants, topology, holonomy, and twisted boundary conditions to downstream modules. The PRE-PURE layer defines the admissible geometry class and the spectral-refinement axis. The PURE layer develops the analytic apparatus: the Dirichlet form, Laplacian, heat semigroup, heat kernel, functional inequalities, Hodge decomposition, and holonomy. The CORE layer defines the output data package and its named export records for modules such as Anchor, Windows, Weyl, PLS, and Einstein. The EXEC layer provides the q3D torus as a reference geometric-operator model with explicit metric, spectrum, spectral counting function, heat data, and holonomy data. The module serves as a common geometric interface for later operator-theoretic and physical constructions in the NSk/psi program. Its main role is to organize the passage from admissible geometry to downstream-consumable records while keeping source-side geometric data separated from observational or executable readouts.