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

Topological Soliton Theory — Paper VII Topological Solitons vs. the Standard Model: Twenty Anomalies, Twelve Predictions, Zero Free Parameters Alexander Novickis · [email protected] Abstract 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. Twelve quantitative predictions achieve median accuracy 0.19% 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 = 137.18 GB-structural (0.105%, correction open; canonical value: Paper LXX, 137.0363, 2.2 ppm) — 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 GeV (structural: m_H = √(2λ)·v, with the electroweak vev derived and λ near-critical; the 125.82 GeV volume-weighted Coleman-Weinberg value is a geometrically-motivated estimate lying 5.6σ above the measured mass) — 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 = 1.145 (14.5%) — 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 μ_p/μ_n = −1.46 (6.7% from experiment) — from mixture states (Paper X) Λ_QCD = 0.232 GeV (7% from experiment) — from soliton confinement scale (Paper XXI) Additional anomalies resolved topologically: Charge quantization from Hopf linking number H ∈ ℤ (Paper I) Spin-1/2 from Finkelstein-Rubinstein mechanism (Paper I) Three-generation count from N = 3 Casimir/triality uniqueness (conditional on the division-algebra input; geometric realisation open) (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. Keywords Standard Model topological soliton unification fine structure constant Weinberg angle Higgs mass PMNS mixing lepton mass ratios dark energy charge quantization Faddeev-Niemi model zero free parameters Koide formula Hopf fibration Type Preprint License CC BY 4.0 Date 2026-03-10 Subject Theoretical Physics Paper Series: Topological Soliton Theory The Toroidal Electron (Paper I) Fine Structure Constant as Soliton Aspect Ratio (Paper II) Quarks and Confinement from Multi-Sector Hopf Solitons (Paper III) Neutrinos as SU(2) Skyrmions (Paper IV) Entanglement as Topology (Paper V) Dark Matter as Topological EM Structures (Paper VI) Topological Solitons vs. the Standard Model (Paper VII) Strong CP Problem Dissolved (Paper VIII) Topological Baryogenesis (Paper IX) From the Hopf Bundle to the Standard Model (Paper X) Dark Energy from Topological Vacuum Constraints (Paper XI) Speed of Light from Vacuum Topology (Paper XII) Antenna Impedance and Topological Mode Conversion (Paper XIII) Two Roads to 137 (Paper XIV) Quantum Foam from Hopf-Linked Fluctuations (Paper XV) Detecting Electron Topology via Precision Spectroscopy (Paper XVI) © 2026 Alexander Novickis. Licensed under Creative Commons Attribution 4.0 International.