Physics Ledger · Prediction
Cosmology
τ-Effective
1–5%
Matter-to-Baryon Ratio ω_m/ω_b
Matter-to-Baryon Ratio ω_m/ω_b: τ-value 6.655, observed 6.37, deviation +4.1%.
Prediction
τ-Formula
τ-Value
6.655
Observed
6.37
Deviation
+4.1%
τ-Formula
ω_m/ω_b = 1 + (1 − ι_τ)/ι_τ² ≈ 6.655
Derivation
m_c = m_t(τ) × ι_τ^105/23 = 172,440 × 0.007391 = 1,274.5\;MeV
at $+1,150$ ppm from PDG $m_c(MS, m_c) = 1,273 ± 4$ MeV (within $0.4σ$).
Exponent decomposition. The exponent $105/23$ factorises intrinsically:
10523 = (τ^3) · W_3(4) · n_Ha_3 + 2\,W_3(4) = 3 × 5 × 713 + 10,
Source
This prediction is derived in the Physics Ledger (Chapter 36 — koide-mass-hierarChapter ies), Books IV–V of Panta Rhei.