Physics Ledger · Prediction
Particle Physics
τ-Effective
10–1000 ppm
Proton–Neutron Mass Splitting
Proton–Neutron Mass Splitting: τ-value 1.38!×!10⁻³, observed 1.378!×!10⁻³, deviation +33~ppm.
Prediction
τ-Formula
τ-Value
1.38!×!10⁻³
Observed
1.378!×!10⁻³
Deviation
+33~ppm
τ-Formula
Δm / mₙ = (3/16)√3 · ι_τ⁵ − (3/20)α · ι_τ²
Derivation
The proton–neutron mass splitting is given by the two-sector formula:
where $α ≈ 1/137.036$ is the fine-structure constant and $ι_τ = 2/(π + e)$. The first term is the strong-sector (C-sector) contribution; the second is the electromagnetic correction (B-sector). Numerically:
in agreement with the measured value at $+33$ ppm. (Registry: IV.T142, Wave 1.)
Structural anatomy. The two-sector formula (eq:ch60-pn-formula) has a transparent structure:
Source
This prediction is derived in the Physics Ledger (Chapter 60 — mass-spectrum), Books IV–V of Panta Rhei.