Topological Solitons vs. the Standard Model: Twenty Anomalies, Ten Predictions, Zero Free Parameters

The Standard Model contains 19 free parameters and leaves foundational questions — charge quantization, spin origin, wave-particle duality, dark matter, neutrino masses — unanswered. We audit 20 major anomalies, organized as unexplained parameters (8), missing physics (6), and conceptual gaps (6), against a sixteen-paper programme in which all fundamental particles are topological solitons in nonlinear field theories of the Faddeev-Niemi type. The programme closes 18 of 20 anomalies with zero or few free parameters. Ten quantitative predictions achieve median accuracy 0.12% with zero free parameters: mμ/mₑ = 206.768 (0.001% from experiment) — from Casimir ratio δ = C₂(3)/C₂(Sym³(3)) = 2/9, with N = 3 as unique solution to (N+1)/(2N²) = 2/9 mτ/mₑ = 1776.86 (0.007% from experiment) — same Casimir mechanism 1/α = 137.09 (0.04% from experiment) — five-step algebraic chain: α̂_GB = 1/56 from Riemann operator eigenvalue on Λ²(ℝ⁸), multiplicity 3 from S³ internal geometry sin²θ_W = 3/13 = 0.2308 (0.19% from experiment) — from horizontal Ricci flatness Ric_horiz = 0 at λ = √2 m_H = 125.82 GeV (0.46% from experiment) — from volume-weighted Coleman-Weinberg Rayleigh quotient + R_scalar = 0 cutoff + APS η-invariant species count n_sp = 5/4 θ₂₃ = 49.0° (within 1σ) — Wigner-Eckart + level repulsion + Berry-phase cross-metric ξ_geo = 0.325 θ₁₂ = 33.10° (−0.44σ from experiment) — e² = 2√2 from Berger sphere; full KK derivation e² = 4(λ²−1)/λ θ₁₃ = 8.5° (structural prediction from 2+1 framework) ρ_Λ/ρ_obs = 1.014 (1.4%) — virtual pair multiplicity N_eff = 8; ρ = 8α¹⁶c_geom⁴mₑ⁴ (noteworthy coincidence; systematic uncertainties span orders of magnitude) Σmν = 62 ± 5 meV — at CMB-S4 detection threshold Additional anomalies resolved topologically: Charge quantization from Hopf linking number H ∈ ℤ (Paper I) Spin-1/2 from Finkelstein-Rubinstein mechanism (Paper I) Three generations from N = 3 uniqueness of Casimir ratio (Paper I) Strong CP problem dissolved: π₃(U(1)) = 0 eliminates θ-vacuum (Paper VIII) Gravity from 7D Einstein-Gauss-Bonnet on Hopf bundle (Paper X) Baryogenesis from CP-odd soliton nucleation at T ~ MeV (Paper IX) Entanglement from Hopf fiber linking (Paper V) Dark matter as H = 0 knotted solitons (Paper VI) Two anomalies remain partial: quark masses (Casimir mechanism is lepton-specific; quarks require F₂ dynamics) and strong-coupling confinement (flag manifold saddle-point problem). Four self-generated tensions are identified, three resolved. A prioritized research queue addresses each remaining gap.