One extended Skyrme-type SU(11) Field Derives Full Standard Model, General Relativity, Fine-Construct Constant, Cosmological Constant, and more

The Self-Field Theory (SFT) extends the Skyrme model which began in 1958–1962 when Tony Skyrme proposed that baryons could emerge as topological solitons (“hedgehogs”) in a nonlinear pion field, with baryon number protected by a winding number — a radical idea largely ignored for two decades. The modern revival ignited in the early 1980s when Edward Witten connected the model to large-N_c QCD and supplied the crucial Wess-Zumino-Witten term, while Gerry Brown championed its nuclear phenomenology. Nick Manton, Paul Sutcliffe, and others then developed the rich moduli-space dynamics and multi-soliton solutions that turned Skyrmions into a precision tool for nuclei and hadrons.

SFT derives the Standard Model gauge sector, gravity, black-hole thermodynamics, precision cosmology, and the quantum measurement postulates from a single seven-term SU(11) Lagrangian and its unique physical-branch hedgehog solution. Every physical quantity in this work is derived from the Lagrangian and its unique physical-branch boundary-value problem; strict provenance enforcement via the ESP certification framework (below) guarantees that no empirical value enters any certified derivation chain, making parameter tuning structurally impossible rather than merely avoided.

The Lagrangian contains a kinetic (sigma-model) term, a Skyrme stabilizer, a Wess–Zumino–Witten term, a pion-mass term, a baryon–scalar interface coupling, a sextic coherence term, and an eta skin-dynamics term. The physical hedgehog branch is selected by six independent criteria — topological charge B = 1, virial balance, power-law tail, unique skin maximum, gauge unification (1/α_GUT = 24.711), and gravity closure — and is the sole solution consistent with all six simultaneously.

Derivations are machine-verified in Lean 4 (97+ files, 800+ theorems, zero sorry, standard axioms only) under the canonical normalization epoch 2M_WZW_LOCK_v1 on branch survivor_2M. Certification labels follow the Executable Scientific Provenance (ESP) taxonomy: CERTIFIED denotes full dependency traceability with no open lemmas; CONDITIONAL denotes a structurally sound derivation with an explicitly identified open surface; BOUNDED denotes a proved interval constraint; SYMBOLIC denotes a derived functional form awaiting one numerical closure (N_etebuda in the cosmological constant sector).

Selected results: α_s(m_Z) = 0.11801, sin²θ_W(m_Z) = 0.23119, 1/α_EM(m_Z) = 127.94, m_h = 125.10 GeV, m_p = 937.9 MeV, Ω_DM h² = 0.12002 — all within 0.1% of PDG or Planck values and none fitted. 21 of 22 PDG fermion observables match within 1%. The Bekenstein–Hawking area law is reproduced to 0.4%. The full periodic table is predicted to a mean relative error of 0.01% for Z ≥ 2.

SFT reproduces QED's high-precision predictions from first principles: the Schwinger term aμ(1)=α/2π emerges from the photon zero-mode structure on the hedgehog skin, all five QED loop orders (A1 through A5, covering 13,635 Feynman diagrams certified via IBP reduction) are derived geometrically from the soliton background without numerical integration tools, and the full muon anomalous magnetic moment — including hadronic vacuum polarization and hadronic light-by-light — is derived from the certified Lagrangian to within 0.09 sigma of experiment.

Additional falsifiable predictions include r ≈ 0.00357 (detectable at >3.5σ by CMB-S4), σ₈ = 0.797 with a specific high-k suppression signature, and a superheavy island of stability centered on Z = 126. A Gap Register (Appendix I) explicitly classifies every open derivation surface.

Repository contents: technical manual with full derivations · Appendices A–X (parameters, observables catalog, periodic table, gap register) · Lean 4 source (SFT_Full_Consolidated_Lean.zip) · companion methodology paper: T.M. Nguyen, Executable Scientific Provenance (2026)