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

Title: Full SU(3) Flavour Breaking from F₂ — Triply-Derived Soliton-Scale Decomposition (novickis@gmail.com)

The strange-quark-mass coefficient c_sp in the Gell-Mann-Okubo linear vector-meson mass formula m_(K^*) - m_ρ = m_s · c_sp has an observed value c_sp(μ = 2 GeV) = 1.23 ± 0.05. This paper derives c_sp as a four-factor decomposition at the soliton scale plus QCD running to the observational scale:

c_sp(μ) = c_sp^LO(μ_sol) · R_run(μ_sol → μ) · R_dyn · R_mix,

with c_sp^LO = 1 exact (SU(3) Gell-Mann-Okubo group theory, derived); R_run from standard four-loop overlineMS QCD m_s running (derived external); R_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_mix ≈ 1 from physical φ-ω ideal mixing (small, bounded).

The remaining open element of v0.4 — the first-principles identification of the soliton scale μ_sol — is closed in v0.7 by three converging independent derivations: (1) NDA chiral cutoff μ_sol = 4π f_π ≈ 1.17 GeV (Manohar-Georgi 1984, canonical from v0.5); (2) F₂ Berger-sphere Laplace-Beltrami spectral cutoff μ_sol = sqrtλ_(max)^F₂ = 4π f_π (Paper LXIII §6, canonical from v0.6); (3) lattice MC cross-check (b52+ closure 2026-04-30, §9) giving μ_sol^lattice = 1.20 ± 0.007, consistent with the analytical target within the expected single-cell lattice systematic. With f_π = m_e · α^(-18/17) = 93.5 MeV (Paper LXIII, zero free parameters), c_sp(2 GeV) ≈ 1.17–1.19 is fully programme-derived, within 5% of PDG 1.23 ± 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.

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