{"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 _{}. By replacing associative continuum assumptions (^4) with discrete octonionic associator fields, we prove that local non-associativity generates a non-orientable 4\π Möbius fiber bundle topology. The resulting associator defect is regularized by the Darkon Homotopy Corrector \δ_{}, enforcing single-valuedness and closing coordinate singularities via the Generative Zero identity (0 \× 0 = e₋₁). We derive the coupling spectrum \α_n = 2ⁿ⁻⁵(3/4\π)3/2 purely from the 3D unit-sphere volume ratio and dyadic octave scaling, including the $n = -1$ Einston Substrate Grid (\α₋₁ \≈ 1.82068 \× 10⁻³). Furthermore, by evaluating the Graph Laplacian over the K₁₁ 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 \Δ_{} = 5.61\ MeV."}