Mass Relations in the Z3 ×Z3 ×Z2 Topology: Proton, Delta, and Pion from a Common Cascade

A unified derivation of three hadronic masses — the proton, the Δ(1232) baryon, and the charged pion — from a single topological structure with one mass scale (M_Pl) and one dimensionless coupling (α). The common cascade is m = M_Pl · 3^(k/4) · α⁹ with the α exponent 9 being half the gravity topology exponent 18 = |Z₃ × Z₃ × Z₂| (one-body mass amplitude versus two-body gravitational intensity), and the Z₃ amplification factor 3^(k/4) discriminating baryon spin configuration: k = 1 (3^(1/4)) for the J = 1/2 proton in mixed-symmetric Pauli combination, k = 2 (√3) for the fully symmetric J = 3/2 Δ. The pion follows through the dimensional scaling observable fraction: m_π/m_p = (d/N)² · (1/N) = 4/27 for N = 3, d = 2. Numerical results, all parameter-free: m_p = M_Pl · 3^(1/4) · α⁹ — error 0.49% m_Δ/m_p = 3^(1/4) — error 0.23% m_π/m_p = 4/27 — error 0.41% m_Δ − m_p = 296.6 MeV/c² — error 0.97% (replacing the fitted hyperfine coupling of constituent-quark models) The framework predicts a Z₃ exponent ladder of baryon-like states indexed by integer k. The k = 1, 2 entries are the proton and Δ; higher k entries (1.6 – 2.1 GeV range) are predictions to be matched against measured baryon resonances. The strangeness-broken Z₃ symmetry is verified in Σ*, Ξ* mass ratios, which deviate from 3^(1/4) proportionally to m_s/m_q. The lepton sector is closed in the companion paper "The Proton-Electron Mass Ratio from Quaternion Phase Space" via m_e = m_p / (6π⁵).