Parameter-Free Derivation of 𝑚𝑝/𝑚𝑒 and 𝛼 from Spectral Geometry on 𝑇5 with SU(3)

We derive the proton-to-electron mass ratio and the fine-structure constant from a single geometric structure — with zero free parameters. Main Results mₚ/mₑ = 6π⁵ (1 + α²/√8) = 1836. 15268 — accuracy: 0. 002 ppm (CODATA: 1836. 15267) −2 ln α = π² − 4α + c₂α² — accuracy: 0. 009 ppm (CODATA: α = 1/137. 036) Δm (n−p) /mₑ = 8/π − 2α — neutron-proton mass splitting (354 ppm) Framework The computation uses spectral geometry on the isotropic five-torus T⁵ with SU (3) gauge field. The Hosotani mechanism stabilizes the Wilson-line vacuum at a = 1/2 (Ramond boundary conditions). The instanton action S₀ = π² and the Weyl group order |W (SU (3) ) | = 6 combine to give the exact identity 6π⁵ via the Weyl integration formula. No parameters are adjusted — all inputs are topological or group-theoretic. Proof Architecture: 4-Tier Classification (26 results, no open problems) Tier 0 (9 results): Known, cited — Hosotani mechanism, Georgi-Glashow sin²θW = 3/8, Epstein zeta, Clifford algebra dS = 4, Hurwitz ζ', quark charges ΣQ² = 1, R-independence, π⁷-bridge algebra. Tier 0+1 (5 results): Known methods, our specific application — Ramond BC from S₅-isotropy, c₂ = 5/2 ln 2 − 3/8, Gilkey-Seeley Gₑ/Gₚ = 6, Atiyah-Singer ind (Dₚ) = 6, the Matching Principle (Connes 1994). Tier 1 (12 results): Genuinely new, proved here — Weyl identity 6π⁵, d = 5 uniqueness theorem, bootstrap uniqueness, c₃ independent formula (6 ppm), δEW = 0 (exact), spectral entanglement identity, gap decomposition theorem, Weyl orbit theorem, β* = 13. 6 analytical, 1/√8 from 3 routes, toy model d = 1…5, GPU verification to 50 digits. Tier 2/3: None remaining. All formerly open problems resolved in v55. 33 Parameter-Free Consequences (V1–V33) Including: V1: mₚ/mₑ = 1836. 15268 (0. 002 ppm) ✓ V3: α = 1/137. 036 (0. 009 ppm) ✓ V22: θQCD = 0 exactly (no axion needed) — testable via nEDM V23: Proton stable (τ > 10¹⁰⁰⁰ yr) — testable at Hyper-K V30: Ngen = Nc = 3 ✓ V31: Neutrinos are Dirac particles — neutrinoless double beta decay (0νββ) is FORBIDDEN. Testable at LEGEND/nEXO/CUPID (2027–2028). A single 0νββ event would falsify SFST. V32: Σm_ν ≈ 3mₑ α² ≈ 0. 08 eV — within Planck/KATRIN window Standard Physics as Limits Maxwell equations and Einstein equations emerge as Kaluza-Klein zero-mode reductions (Tier 0). The Weinberg angle sin²θW = 3/8 at the compactification scale reproduces the Georgi-Glashow (1974) prediction. Known Limitations (stated explicitly) The Matching Principle (det'/det' → mₚ/mₑ) is Tier 0+1: standard method (Connes 1994), not derived from first principles for this specific bundle. Lepton mass hierarchy (μ, τ) not predicted. Absolute energy scale (R in Planck units) not determined. Computational Reproducibility 27 numbered Python scripts (Tier 0/0+1/1/Util), all executable with pip install mpmath numpy. Full repository: github. com/SFST-2026/Spectral-Geometry Package Contents Main paper (34 pages, complete step-by-step derivation in Appendix A) Supplement (55 pages, 20 appendices Z1–Z20) Reviewer roadmap (8 pages, 5 anticipated questions with answers) 27 Python scripts + results + data + figures