Registry · Proposition IV.P187 tau-effective formalized

IV.P187 — Quark-Lepton Universality: Exponent Step ≈ −2.7

The ι_τ-exponent step between second and third generation (relative to m_n) is approximately −2.7 in both the quark s/d sector and the lepton τ/μ sector. Quark: p_s−p_d=log(m_s/m_d)/log(ι_τ)=−2.797 (m_s=95, m_d=4.7 MeV PDG). Lepton: p_τ−p_μ=−2.626. Difference 0.171 exceeds the strict universality threshold of 0.1, so universality is approximate. The ~6.5% discrepancy may arise from different sector couplings (C-sector strong vs B-sector EM), consistent with the conjectural scope. Both steps lie near −2.7 ≈ −(ι_τ⁻² − ι_τ⁻¹), suggesting a shared winding-number increment structure across fermion families.

Book IV Part 5 Ch. 36

Dependency Graph

Depends on (1)

Lean Formalization

Module: TauLib.BookIV.Particles.ThreeGenerations

Symbol: Tau.BookIV.Particles.quark_lepton_universality_hint