Geometric Spectral Stability Principle of General Relativity as a Quantum Theory

In this work, we establish the Geometric Spectral Stability Principle (GSSP) as the dynamic foundation of General Relativity as a Quantum Theory (GRQT). We propose an ontological inversion where non-local quantum fields (the Spectral Tensor) are primary, and geometry emerges as a filtering operator that maximizes informational stability. We demonstrate that the minimization of spectral divergence recovers the Einstein-Hilbert action in the low-energy limit. The phenomenological consistency of the theory is demonstrated through two quantitative tests free of adjustable parameters: (1) the analytical resolution of the Hubble Tension ($H_0 \approx 73$ km/s/Mpc) via an entropic horizon Ansatz (Appendix A); and (2) the exact recovery of the Hawking evaporation time for black holes, confirming thermodynamic correspondence in the semiclassical regime (Appendix B). Additionally, we qualitatively discuss how the emergent topological structure offers a new framework for interpreting the muon anomaly ($g-2$) and the geometric nature of the fine-structure constant.