Spectral Quantum Gravity: Emergent Spacetime, Matter, and Gravity from a Timeless Two-Dimensional Spectral Substrate

This paper presents Spectral Quantum Gravity (SQG), a phenomenological framework in which classical spacetime, matter, and gravitation emerge from a timeless two-dimensional resonant spectral substrate Q. The central result is a spectral uniqueness theorem: the gravitational kernel J(a) = a·exp(a)·E₁(a) is the unique ghost-free single-scale non-local modification of General Relativity consistent with four physical axioms (ghost-freedom, single coherence scale, UV recovery of GR, and maximum spectral entropy via the Jaynes principle). Key results include: A rigorous spectral uniqueness theorem for the gravitational propagator modification Parameter-free derivation of the microscopic coherence scale L_micro = 2√(ln2) · l_P ≈ 1.665 l_P from the Bekenstein–Hawking entropy Reproduction of the Hawking temperature from a vortex-dissociation mechanism Covariant field equations and Friedmann equations derived from the non-local action A full Einstein–Boltzmann perturbation hierarchy with three distinct CMB signatures Perturbative stability bound for vortex solutions (a < 1.25) With one fitted cosmological parameter L ≈ 46 Mpc, SQG potentially alleviates the S₈ tension, predicting S₈ ≈ 0.777 A falsifiable prediction for the lensing consistency parameter Σ(k) = J(k²L²) ≠ 1, with peak deviation near k ~ 1/L, testable by Euclid, LSST and DESI The third spatial dimension emerges via a Young-Laplace membrane mechanism driven by vortex pressure. Physical time emerges subsequently as a collective coherence ordering parameter. The Sine-Gordon model on the substrate yields fermions as topological solitons and provides a heuristic geometric motivation for baryon structure. The framework is ghost-free by construction through a positive Källén–Lehmann spectral representation. Dark energy is interpreted as residual global membrane tension. Many aspects remain prospective, and a full likelihood analysis against existing cosmological data is required before observational viability can be claimed.