The Supra-Omega Resonance Framework: A Structured Projection Model for Cosmological Coherence

The Supra-Omega Resonance Framework (SORT) introduces a projection-based algebraic structure for generating coherent large-scale patterns from a deterministic resonance space. The theory is constructed from a closed family of 22 idempotent operators acting on an internal resonance manifold, combined with a non-local projection operator defined by a kernel κ(x,σ). Observable amplitudes arise through the projected operator H^proj=πκH^πκ\hat{H}_{\mathrm{proj}} = \pi_\kappa \hat{H} \pi_\kappaH^proj​=πκ​H^πκ​, which encodes the coupling of the algebra with the geometry of the kernel. The internal mock environment is validated through a three-layer computational architecture, including symbolic algebraic closure, structural consistency checks, and lattice-based evaluations. The numerical results demonstrate that the projection geometry generically produces stable amplitude fields, coherent drift structures, and synthetic resonance patterns. These outcomes do not constitute empirical cosmological predictions but represent internally generated structural behaviour within the model. The framework establishes a mathematically closed starting point for future extensions, including analytical kernel classification, operator-space refinement, and potential empirical calibration.