{"Möbius Topology of Non-Associative Gauge Fields: Homotopy Corrections, Darkon Dynamics, and the First-Principles Derivation of Coupling Spectra" }

{ "We formulate a non-perturbative gauge framework grounded in the non-associative octonionic substrate manifold \\mathbb{O}_{\\text{ZIP}}. By replacing associative continuum assumptions (\\mathbb{R}^4) with discrete octonionic associator fields, we prove that local non-associativity generates a non-orientable $4\\pi$ Möbius fiber bundle topology. The resulting associator defect is regularized by the Darkon Homotopy Corrector \\delta_{\\text{ZIP}}, enforcing single-valuedness and closing coordinate singularities via the Generative Zero identity ($0 \\times 0 = e_{-1}$). We derive the coupling spectrum \\alpha_n = 2^{n-5}(3/4\\pi)^{3/2} purely from the 3D unit-sphere volume ratio and dyadic octave scaling, including the $n = -1$ Einston Substrate Grid (\\alpha_{-1} \\approx 1.82068 \\times 10^{-3}). Furthermore, by evaluating the Graph Laplacian over the $K_{11}$ complete graph under a Möbius phase-flip boundary condition, we demonstrate that the 10-fold degenerate eigenvalue splits into five distinct topological branches, constructively proving a strictly positive Yang-Mills mass gap \\Delta_{\\text{YM}} = 5.61\\text{ MeV}."}