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

Title: Full SU(3) Flavour Breaking from F₂ — Triply-Derived Soliton-Scale Decomposition (v0.8)

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 $\overline{\rm MS}$ 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).

The remaining open element of v0.4 — the first-principles identification of the soliton scale $\mu_{\rm sol}$ — is closed in v0.7 by three converging independent derivations: (1) NDA chiral cutoff $\mu_{\rm sol} = 4\pi f_\pi \approx 1.17$ GeV (Manohar-Georgi 1984, canonical from v0.5); (2) F₂ Berger-sphere Laplace-Beltrami spectral cutoff $\mu_{\rm sol} = \sqrt{\lambda_{\max}^{F_2}} = 4\pi f_\pi$ (Paper LXIII §6, canonical from v0.6); (3) lattice MC cross-check (b52+ closure 2026-04-30, §9) giving $\mu_{\rm sol}^{\rm lattice} = 1.20 \pm 0.007$, consistent with the analytical target within the expected single-cell lattice systematic. With $f_\pi = m_e \cdot \alpha^{-18/17} = 93.5$ MeV (Paper LXIII, zero free parameters), $c_{\rm sp}(2\,\text{GeV}) \approx 1.17$–$1.19$ is fully programme-derived, within 5% of PDG $1.23 \pm 0.05$.

Grade A per §8.2 (b52+ promotion 2026-04-30; A− → A bookkeeping propagated 2026-05-15). Closes Provisional Choices Ledger entry L2026-04-20-03. Oxford review v2: CLEAR-TO-REPUBLISH at A.

v0.8 update (2026-05-17): References list expanded 7 → 17 (numbered, three categories) with full bibliographic data for previously informal canonical citations: PDG 2024 (full DOI), FLAG 2021, Gell-Mann (1962), Okubo (1962), Manohar-Georgi (1984, Branch C Path 1 NDA load-bearing), Skyrme (1962), Faddeev-Niemi (1997), Berger (1961, Branch C Path 2 spectral load-bearing). The previously untitled bullet for Ledger L2026-04-20-03 is now a properly cited programme record entry. Four "TBD" entries in the §9.7 forward-work placeholder table re-labelled "pending" for publication-ready placeholder hygiene.

Series: Paper CXXXIII in the Hopf Soliton Programme