Paper VIII in the Vacuum Mechanics series. Derives the fine-structure constant alpha = MK/ (4pi) as a theorem of MacCullagh-Larmor elasticity theory, closing the foundational gap where Paper I postulated this relationship. Demonstrates that the hierarchy problem's seed (31. 6x) follows from Green's compression-to-shear coupling ratio. Shows 137 is the unique integer consistent with four independent observables (alphaₛ, mH, MPlanck, dark matter ratio). Confirms topological stability of fermions (B=1, pi₃ (S³) =Z) and predicts all classical null experiments (Michelson-Morley, Lodge, Fresnel drag) quantitatively. Synthesizes contributions from MacCullagh, Green, Larmor, Lorentz, Fresnel, Kelvin, Stokes, Poincare, and Dirac, showing the 19th-century aether programme was abandoned for the wrong reasons. Includes honest accounting of 7 failures and 7 open problems.
Luqman Omar Mahmood (2026) studied this question.