Paper CXXI (v2) · One-Octonion Brane-Bulk Framework · Predictions P204–P205 Spin-½ from the Half-Möbius Boundary, and the Electron Mass from Quark–Lepton Twist Traversal

The electron mass formula mₑ = (αm_π/2) (1 + 2α√7) = 0. 51150 MeV was established in Paper CXXI v1, where the factor 2 was attributed to "two chiralities traversing the boundary. " This paper provides the deeper derivation: the factor 2, the spin quantum number ½, and the requirement that mass and charge waves make two traversals of the quark–lepton boundary B (1, 4) per oscillation cycle all have a single topological origin — the half-Möbius (anti-periodic) spin structure of B (1, 4) in the Klein quartic pants decomposition. The boundary B (1, 4) carries an odd Arf invariant: a fermionic wave making one circuit of B (1, 4) picks up a factor of −1 (anti-periodic boundary condition). Two circuits restore the wave to +1. This is precisely the spin-½ property. The Dirac mass, as a standing wave between the quark and lepton sectors, must close on itself, requiring two traversals of B (1, 4). Each traversal costs α × sec (τ) = α√7 (electromagnetic coupling times the Fano secant). The total correction 2α√7 = 3. 86% follows. The same anti-periodic structure applies to the charge wave, setting the renormalisation point of α at the quark–lepton boundary. Two predictions: P204, the electron mass formula (same as v1) ; P205, the spin-½ property of all first-generation leptons is a theorem from the Arf invariant of B (1, 4), not an assumption. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.