Electron mass m_e
The electron mass m_e is, in the τ-framework, the τ-effective Layer-2 readout m_e = m_n / R, where R = ι_τ⁻⁷ − (√3 + π³ α²) ι_τ⁻² is the τ-predicted neutron-to-electron mass ratio. It is the flagship precision result of the τ-cascade, agreeing with CODATA to 0.025 ppm (Tier A).
τ-Definition
The electron mass m_e is, in the τ-framework, the τ-effective Layer-2 readout m_e = m_n / R, where R = ι_τ⁻⁷ − (√3 + π³ α²) ι_τ⁻² is the τ-predicted neutron-to-electron mass ratio. It is the flagship precision result of the τ-cascade, agreeing with CODATA to 0.025 ppm (Tier A).
Categorical invariant. m_e = m_n / R(ι_τ, α) — the lightest charged-lepton sector readout, anchored to m_n.
Primary registry anchor:
IV.T218
τ-Derivation Chain
-
I.K0— Universe Postulate -
IV.D255— Master constant ι_τ -
IV.D407— α = (11/15)² ι_τ⁴ -
IV.P274— Electron Mass — proposition R = m_n/m_e from τ-cascade -
IV.T218— Electron Mass theorem: R = ι_τ⁻⁷ − (√3 + π³ α²) ι_τ⁻² ≈ 1838.684 (0.025 ppm) -
V.T142— E₁ Completeness — m_e is the most precisely τ-predicted constant
Lean modules referenced:
TauLib.BookIV.Calibration.MassRatioFormula,
TauLib.BookV.Coda.ConstantsLedger
SI Translation
Numerical value: 9.1093837015e-31 ± 2.8e-40 kg
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math)
- Layer 1: R = m_n/m_e = ι_τ⁻⁷ − (√3 + π³ α²) ι_τ⁻² ≈ 1838.684
- Layer 2: m_e = m_n / R = 9.109 383 70 × 10⁻³¹ kg
- τ-predicted vs CODATA: 0.025 ppm (Tier A — flagship precision)
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex