Variational Formalization of the Geometric Spectral Stability Principle

We present a rigorous mathematical formulation of the Geometric Spectral Stability Principle (GSSP), originally introduced in the context of General Relativity as a Quantum Theory (GRQT). The principle is formulated as a variational functional defined over a functional space of effective metrics and covariantly sampled spectral densities. We demonstrate coercivity, the existence of a global minimum, and stability against unbounded spectral growth. The construction is independent of phenomenological interpretations and is compatible with relativistic covariant sampling theories, geometric flows with torsion, and quantum non-locality theories.