The Supra-Omega Resonance Theory (SORT): A Mathematically Hardened Projection Framework for Large-Scale Cosmological Structure

TheSupra–OmegaResonanceTheory(SORT)isformulatedasanoperator–basedprojection framework designed to investigate structural coherence in cosmological settings without invoking dynamical evolution or empirical parameter fitting. The framework is built upon a set of twenty–two idempotent resonance operators forming a closed commutator algebra constrained by Jacobi consistency and a light–balance condition, ensuring algebraic stability and the absence of net structural distortion. Structural projection is implemented through a nonlocal Fourier–space kernel κ(k) characterized by a calibrated correlation scale σ0, obtained from purely internal consistency conditions. Numerical validation is performed within MOCKv3, a three–layer architecture comprising algebraic diagnostics, kernel construction, and semi–spectral evolution. The internal drift residual remains below 2 × 10−6, confirming the stability of the projection operator and the robustness of the kernel normalization. The framework involves no empirical fits, cosmological data comparisons, or dynamical assumptions, and is not intended as a replacement for ΛCDM. Instead, SORT provides a mathematically hardened foundation for future investigations of structural phenomena, including long–wavelength amplification, scale–dependent drift, and nonlocal coherence patterns.