Relativistic Geometry under Spectral Superposition. A stability criterion, minimal variational formulation, and general physical consequences.

The formulation of a consistent theory of quantum gravity remains an open problem, often approached through attempts at the direct quantization of geometry. In this work, we propose a conceptual reformulation of the problem, interpreting it as a question of spectral stability under relativistic superposition. We introduce the Geometric Spectral Stability Principle (GSSP), formulated as a general criterion of physical consistency whereby only geometric configurations compatible with spectral stability under relativistic superposition are physically admissible. We show that the unrestricted extrapolation of a continuous geometric manifold becomes structurally fragile when subjected to relativistic spectral superposition, motivating the need for a selection criterion independent of specific dynamic models. The GSSP is formulated as a minimal variational principle, without introducing new fields or free parameters, restricting the set of admissible geometric descriptions. We argue that this criterion imposes structural limits on the validity of the continuous description, manifesting in different physical regimes as a loss of coherence in relativistic superpositions, residual contributions in rotating systems, and effective constraints in cosmological scenarios, in agreement with known experimental and observational results. Existing spectral and geometric formulations can be evaluated in light of this criterion, without the principle depending on any specific theoretical realization. The GSSP does not modify General Relativity nor Quantum Mechanics, nor does it introduce new dynamic mechanisms. It acts as a falsifiable principle of consistency, delimiting the domain in which continuous geometric descriptions remain compatible with coherent spectral superposition in quantum-relativistic regimes.