τ-Electron
The τ-electron is the lightest stable lepton-class T²-defect: a charged, spin-½ winding bundle whose mass is generated by the τ-Yukawa overlap integral on the linkage modes of the neutron, fixing it as the proton's β-decay complement and the lightest charged matter defect in the τ-atlas.
τ-Definition
The τ-electron is the lightest stable lepton-class T²-defect: a charged, spin-½ winding bundle whose mass is generated by the τ-Yukawa overlap integral on the linkage modes of the neutron, fixing it as the proton's β-decay complement and the lightest charged matter defect in the τ-atlas.
Categorical invariant. Lightest lepton-class T²-defect; charge −1 winding; mass set by τ-Yukawa overlap integral.
Primary registry anchor:
IV.D460
Supporting items:
IV.D461,
IV.D143,
IV.D117,
IV.T257,
IV.P255,
IV.D474
τ-Derivation Chain
-
IV.D12— Particle Kind: a particle is a stable defect bundle on the T² fiber -
IV.D474— Fundamental Fermion Atlas establishes the lepton/quark mode taxonomy -
IV.D117— Left-Handed Doublets organize charged leptons under EW chirality -
IV.D460— Electron — lightest lepton-class T²-defect with charge −1 -
IV.D461— Electron Linkage Principle ties the electron to neutron-defect linkage modes -
IV.D143— τ-Yukawa overlap integral generates the electron rest mass from ι_τ -
IV.T257— Electron charge Q = −1 from conservation in β-decay -
IV.P255— Proton-Electron Complementarity — joint earning under β-decay
Lean modules referenced:
TauLib.BookIV.MassDerivation.ElectronMass
SI Translation
Numerical value: 9.1093837015e-31 ± 2.8e-40 kg
Calibration anchor: PG-P01-neutron
Calibration chain:
- m_n (anchor)
- ι_τ ≈ 0.341304 (master constant)
- τ-Yukawa overlap integral (IV.D143)
- m_e = m_n × (Yukawa-overlap ratio)
Manuscript reference: manuscript-sources/book-04/part02/ch20-electron-mass-prediction.tex
Lean Coverage
Status: Formalized
Module: TauLib.BookIV.MassDerivation.ElectronMass
Lean kind: theorem
Lean symbol: ElectronMass