Universality of the Modal Stability Function f(n)

This paper introduces the modal stability function f(n) as a universal operator governing which mathematically allowed modes persist as physically observable, long-lived structures. It is intended as a foundational companion to The ψ Framework: Emergent Geometry, Quantization, and Cosmological Dynamics, where stability-selected ψ configurations generate quantization, mass hierarchies, and large-scale dynamics. By making the stability criterion explicit, this work identifies the single principle that prevents ad hoc, sector-dependent constructions within the ψ framework.