Baryon Density Parameter ω_b

τ-Formula

ω_b from τ-native η_B = 0.02209

Derivation

m_s = m_b(τ) × ι_τ^53/15 = 4,174.4 × 0.02241 = 93.55\;MeV

at $+1,559$ ppm from PDG $m_s(MS, 2\;GeV) = 93.4 ± 0.8$ MeV (within $0.2σ$), where $m_b(τ) = m_t(τ) · ι_τ^45/13 = 4,174.4$ MeV.

The denominator $15 = (τ^3) · W_3(4)$ is the same product governing the $m_t/m_b$ fiber correction (Eq. (eq:iv-mt-mb-exponent)). The numerator $53 = 4\,a_3 + 1$ suggests a four-fold $a_3$ winding with unit offset—the ``confinement unit’’ carried by each of the $|non-ω generators| = 4$ boundary channels.

The charm-to-strange mass ratio from the $τ$-chain:

Source

This prediction is derived in the Physics Ledger (Chapter 36 — koide-mass-hierarChapter ies), Books IV–V of Panta Rhei.