Full SU(3) Flavour Breaking from F₂ — scale-independent decomposition

Title: Full SU(3) Flavour Breaking from F₂ — scale-independent decomposition

Author: Alexander Novickis (alex.novickis@gmail.com)

The strange-quark-mass coefficient $c_{\rm sp}$ in the Gell-Mann-Okubo linear vector-meson mass formula $m_{K^*} - m_\rho = m_s \cdot c_{\rm sp}$ has an observed value $c_{\rm sp}(\mu = 2\,\text{GeV}) = 1.23 \pm 0.05$. This paper derives $c_{\rm sp}$ as a four-factor decomposition at the soliton scale plus QCD running to the observational scale:

$$ c_{\rm sp}(\mu) = c_{\rm sp}^{\rm LO}(\mu_{\rm sol}) \cdot R_{\rm run}(\mu_{\rm sol} \to \mu) \cdot R_{\rm dyn} \cdot R_{\rm mix}, $$

with $c_{\rm sp}^{\rm LO} = 1$ exact (SU(3) Gell-Mann-Okubo, group theory, derived); $R_{\rm run}$ from standard four-loop QCD $m_s$ running (derived external); $R_{\rm dyn} = 1$ in the SU(3)-symmetric limit (verified via F₂ eigenmode matrix elements on Paper I's canonical axial-2D soliton profile, derived); and $R_{\rm mix} \approx 1$ from physical φ-ω ideal mixing (small, bounded). At the choice $\mu_{\rm sol} = 1\,\text{GeV}$, the prediction is $c_{\rm sp}(2\,\text{GeV}) = 1.247$, within 1.4% of PDG $1.23 \pm 0.05$. The one remaining open element is the first-principles derivation of $\mu_{\rm sol} = 1\,\text{GeV}$ — documented in `Provisional_Choices_Ledger` entry `L2026-04-20-03` (Branch F, the naive F₂-Laplace-Beltrami-scale interpretation, ruled out 2026-04-20 session 2; Branch C, the chiral cutoff $4\pi f_\pi \approx 1.17\,\text{GeV}$, is the strongest programme-derived candidate).

This is a structural derivation of $c_{\rm sp}$: the retracted v0.2 numerology (`c_sp = 1.232` from a calibrated $V_0$ · $r_0$ combination) and the v0.3 "dimensionless combination that needs calibration" have been replaced by a three-derived-plus-one-empirical-scale framework. The paper makes explicit which pieces are derived (three out of four factors) and which is empirical (the scale identification $\mu_{\rm sol}$).

Series: Paper CXXXIII in the Hopf Soliton Programme