The Geometric Basis of the Fine-Structure Constant and Neutrino Hierarchy

Overview This collection (TN-125–129) develops the particle-sector derivation chain within Elastic Spacetime Theory (EST). The goal is to show that a small closure parameter—numerically close to the electromagnetic coupling scale—can emerge from geometry and stability of topological defects, rather than being inserted as an empirical input. What this bundle does The notes form a modular sequence: TN-125 — Geometric Origin of βIntroduces the nonlinear coupling as a geometric property of defect closure. TN-126 — Euler–Lagrange and Pohozaev Derivation of βDerives the key scaling relations from a reduced field-theoretic treatment. TN-127 — Consistency Conditions for the Nonlinear SectorEstablishes conserved quantities and internal consistency of the construction. TN-128 — Helical Braid Locking and Phase ClosureModels the electron as a braided structure with competing bend, twist, and locking energies. TN-129 — Curvature-Limited Soliton Geometry and Closure Ratio rShows how a finite loop radius and braid thickness produce a small, nonzero closure excess. Key result (scope-limited) Together, these notes provide a reduced derivation chain: β → geometry → ϵ=r−1 → r linking nonlinear defect structure to the closure ratio used in the EST neutrino hierarchy. This does not claim a final derivation of α but demonstrates a concrete mechanism by which a parameter of that scale can arise from first-principles geometry. Status and falsifiability This is a derivation scaffold, not a completed theory. It remains testable: the geometric chain must extend to full EST field solutions, and the associated neutrino predictions must match observation. Authorship note Conceptual framework: Jonathan E. WilsonMathematical derivation support and LaTeX: LLM-assisted (OpenAI, Google, DeepSeek) The author takes full responsibility for all physical claims.