An Exceptional Lie Algebra Representation Ansatz for the Fine-Structure Constant: (E₈ → F₄ → G₂) Branching and Octonionic Topological Scars in G-MaTT

Abstract

We present a structural geometric ansatz for the electromagnetic fine-structure constant (α) within the Generalized Mass as Twisted Time (G-MaTT) framework. Rather than searching for an isolated scalar invariant, we model α as the geometric transparency (cross-sectional flux ratio) of the fundamental G₂ root core traversing an anisotropic topological defect manifold left by the symmetry-breaking cascade E₈ → F₄ → G₂. Combining the fundamental-to-residual representation ratio (7/78) with a global Cartan rank-suppression factor (15/16) yields the closed-form geometric ratio

√α_shape = (7/78) × (15/16) = 35/416 ≈ 0.08413,

corresponding to α⁻¹ ≈ 141.22 (approximately 97% of the empirical value). Modulation by a non-associative octonionic 1-cycle phase factor W₀ = 1 + 1/(24π) improves the agreement to α⁻¹ ≈ 137.59 (99.6% of the empirical value). We formulate an explicit, falsifiable prediction for anisotropic phase shifts in neutron interferometry and state the open mathematical requirements (uniqueness of the representation projector and an independent Chern–Simons derivation of the 24π factor) needed to elevate the ansatz to a theorem.