FRACTIONAL WINDING AND THE ORIGIN OF ELECTRON MASS

Three papers complete the rigorous derivation of the electron’s spin and mass from
vacuum geometry. (I) The Fractional Winding paper closes the gap flagged in the previous manuscript by applying the White-Franks theorem SL = W + Tw to the right-handed T2,3 trefoil. The minimal writhe W = +3 forces a Seifert twist T Sei f ert w = −3 to maintain SLSei f ert = 0. The physical Mobius phase-lock injects exactly ¨ +1/2 twist, giving T Mobius ¨ w = −5/2. Evaluated mod 1: s = (−5/2) (mod 1) = 1/2. The electron’s spin1/2 is the exact fractional residue of the Mobius framing on the Seifert surface of ¨ T2,3. (II)
The −1/12 paper provides the rigorous hydrodynamic derivation of the Casimir residue from the Euler-Maclaurin formula applied to the discrete mode spectrum of the 861-node lattice. The total energy functional Etot(N) = AN2 − BN ln(N) − κ/(12N) has a unique stable minimum at N ≈ 861 determined by the dimensionless variable x = N/N0 with N0 = (κ/24A) 1/3. The stability criterion d2Etot/dN2 > 0 at N = 861 is verified analytically. (III) The mean nearest-neighbor pairwise interaction energy ⟨Epair⟩ = 3Γ 2/(16πr) from the 1985 Biot-Savart kernel provides the physical scale for A, B, κ in the energy functional, completing the chain from vacuum fluid parameters to the observed electron mass me ≈ 0.511 MeV.