A Mathematical Unification of the Helix–Light–Vortex (HLV) Framework: Discrete Geometry, Spiral Time, Unified Lagrangians, and TOE-Level Structure

We present a unified mathematical formulation of the Helix–Light–Vortex (HLV) framework as a candidate for a geometric theory of everything. The core ingredients are: (i) a triadic spiral-time operator ψ(t) = t + iϕ(t) + jχ(t) with coherent, memory, and retrocausal components; (ii) a discrete golden-ratio quasicrystal lattice (G-lattice) as the geometric substrate of spacetime; (iii) a symbolic operator grammar GHLV organizing allowed field, lattice, and information processes; and (iv) a master Lagrangian whose limiting cases reproduce General Relativity, Quantum Field Theory, and the Standard Model. We construct the effective HLV Laplacian and propagators, derive modified dispersion relations, and show how known relativistic field equations emerge as limits. Topological entanglement invariants and geometric phase shifts arise naturally from the triadic time geometry. Finally, we prove that in a well-defined set of recovery limits (ε → 0, ϕ̇ → 0, a → 0, U₃ → 0), the entire Standard Model and conventional QFT are recovered, while HLV-specific corrections remain experimentally testable in precision measurements of g−2, King-plot nonlinearity, QGP observables, and quantum information experiments.