CAT'S THEORY: THE COMPLETE FRAMEWORK — Topological Emergence of the Standard Model from the Triadic Invariant

**CAT’S Theory Capstone (Nov2025-Mar2026): ** Complete zero-parameter derivation of the Standard Model lepton sector from topological self-confinement of EM radiation on S³. **Key Results: ** - Charged leptons: muon 0. 13%, tau 0. 02% PDG2024 (post-QED dressing) - PMNS matrix: all angles ≤1σ, delta₂₏=202. 5ᶜirc (0. 2σ) - Neutrino sum: sum m_ u approx 59. 7 meV (factor 2 below bounds) - Quark charges: 2/3, -1/3 from T (3, q) writhe (no color invented) **Core Math: ** - Triadic axiom mathcalR=PsiIP eq0 → E-L coupling - Mass exponent n=26/7 via **4 routes**: spectral zeta (Bar/APS), triadic dims, bosonic Dₘathrmcrit, QCD (b₁/b₀) - Hopf solitons T (p, q): helicity/dual-gate stable (Cho/Niemi/Witten) **Falsifiables (8): ** 1. Normal hierarchy only (DUNE) 2. m ₔ䂰=0. 82 meV (KATRIN) 3. delta₂₏=202. 5ᶜirc (HyperK) 4. GW proxy 8. 37 Hz (LIGO). . . full list in paper **Full registry** Appendix tracks every claim to proof/DOI. Builds: 10. 5281/zenodo. 18905443 (https: //doi. org/10. 5281/zenodo. 18905443), 10. 5281/zenodo. 18911645 (https: //doi. org/10. 5281/zenodo. 18911645). **Code/CSVs** in repo. hep-ph/arXiv ready.