NNLO Correction Parameter δ

τ-Formula

δ = 1/W₃(4)² = 1/25 = 0.04

Derivation

The NNLO correction to the muon-to-electron mass ratio involves the parameter

where $W_3(4) = 5$ is the third Waring number at four summands. This correction brings the winding exponent from $5.00$ to $4.96$, producing the $+307$ ppm agreement cited above. At the $τ$-native NNLO level, the mass ratio formula becomes

m_μm_e = ι_τ^-(W_3(4) - 1/W_3(4)^2) = ι_τ^-(5 - 1/25) = ι_τ^-4.96.

Source

This prediction is derived in the Physics Ledger (Chapter 60 — mass-spectrum), Books IV–V of Panta Rhei.