Spectral Quantum Gravity (SQG): Fixed-Point Emergence and Non-Local Gravity

This paper presents Spectral Quantum Gravity (SQG), a novel theoretical framework that derives gravitational interaction as an emergent phenomenon from a timeless 2D resonant substrate. Within the minimal Eternal Universe Theory (mEUT) v8. 5, spacetime geometry is reinterpreted as a holographic projection of spectral correlations. Key Highlights: Derivation of Non-Local Gravity: Unlike phenomenological models, SQG derives a specific non-local kernel (Exponential Integral form) from the renormalization group flow of a Gaussian spectral measure. Resolution of Cosmological Tensions: The framework naturally recovers General Relativity in the ultraviolet (local) limit while providing a parameter-economical explanation for flat galactic rotation curves and the S₈ tension without the need for Dark Matter or Dark Energy particles. Fundamental Unification: The paper offers a suggestive geometric derivation of the fine-structure constant (₄₌ 137. 036) based on the topological stability of the 2D-to-3D spectral projection. Falsifiability: We predict a scale-dependent gravitational slip (r) with a characteristic peaked signature, offering a concrete target for upcoming large-scale structure surveys (e. g. , Euclid, Vera C. Rubin Observatory). Methodology: The framework utilizes tools from functional analysis, spectral geometry, and renormalization group theory to establish a structurally consistent theory that satisfies spectral positivity, energy-momentum conservation, and ultraviolet closure.