Electron Mass at 0.025 ppm: 10-Link Derivation from K0–K6

Overview

V.T54 establishes that the electron mass m_e = 0.510998937 MeV can be derived from a 10-link chain starting at the axioms K0–K6. The derivation passes through ι_τ, the sector couplings, the mass ratio formula, and ultimately reaches the electron mass with 0.025 ppm agreement with CODATA — the highest precision of any mass prediction in the framework. The single calibration anchor is m_n (neutron mass); no other experimental input is used. The chain consumes α (the fine-structure constant) as an upstream intermediate, but α is itself kernel-derived from ι_τ alone (α = (11/15)²·ι<sub>τ</sub>⁴ at LO; full multi-loop via IV.T107) — so the m_e derivation is acyclic on the kernel, not circular.

Detail

The electron mass m_e = 0.510998950 MeV (CODATA 2022) is the lightest charged particle mass and the reference scale for atomic and molecular physics. In the Standard Model, m_e is a free parameter with no theoretical prediction. Book V proves the electron mass as a 10-link derivation chain from the axioms K0–K6, achieving 0.025 ppm precision.

The derivation chain (V.T54) runs: K0–K6 → generators {α, π, γ, η, ω} → ι_τ = 2/(π+e) → κ_D = 1–ι_τ → α_em (fine structure) → R_∞ (Rydberg) → mass ratio R = m_n/m_e → m_e = m_n/R. The mass ratio R = ι_τ^{–7} – (√3 + π³α²)ι_τ^{–2} is derived in V.T07 at 0.025 ppm. With calibration anchor m_n, the electron mass follows at 0.025 ppm.

The 0.025 ppm precision makes this the framework’s most precise mass prediction, equal to the neutron-to-electron mass ratio (V.T07/IV.T110, also 0.025 ppm) and the Rydberg constant (IV.T86, 0.026 ppm). Together these three predictions constitute the sub-1 ppm precision core of the framework.

Noting that the Book IV reference lists the electron mass as IV.R184 with ‘conjectural scope’ because the calibration identification (identifying the formula output with the physical electron mass) is unproved, while V.T54 is the full Book V statement. For catalogue purposes V.T54 is used as the primary registry ID.

Result Statement

V.T54: Electron mass m_e = 0.510998937 MeV at 0.025 ppm (CODATA 0.510998950 MeV). 10-link derivation chain from K0–K6 via ι_τ, couplings, mass ratio R. Single calibration anchor: m_n.