Spectral Quantum Gravity: A Falsifiable Single-Scale Modification of General Relativity

This paper introduces Spectral Quantum Gravity (SQG), a novel theoretical framework that derives spacetime, matter, and gravitation from a pre-geometric, two-dimensional resonant spectral substrate (Q). Unlike traditional models that treat spacetime as a fundamental background, SQG describes the emergence of 3+1-dimensional Lorentzian geometry as a spontaneous coherence phase transition characterized by a spectral order parameter O(x). Key Highlights of the Theory: Origin of Mass: Particles emerge as topological vortices (spectral condensates) within the substrate. Mass is identified as the stored rotational spectral energy of these vortices. Non-local Gravity: The gravitational interaction is mediated by a ghost-free non-local kernel K⁽k), which ensures stability (positive Källén-Lehmann representation) and recovers General Relativity in the ultraviolet limit (kL 1). Resolution of Cosmological Tensions: The theory provides a natural explanation for the S₈ tension through infrared suppression of gravitational coupling and addresses late-time acceleration via global coherence relaxation of the substrate. Standard Model Integration: A prospective mapping is provided, suggesting that gauge symmetries (SU(3) × SU(2) × U(1)) and spinorial structures emerge from the topological and oscillatory degrees of freedom of the 2D substrate without requiring extra spatial dimensions. Falsifiability: SQG remains strictly falsifiable by predicting scale-dependent violations of the lensing consistency relation Σ(k,z), which can be tested by upcoming surveys such as Euclid and LSST.