What does this research mean for the field?

The Standard Model lepton sector can be completely derived from the topological self-confinement of electromagnetic radiation on $S^3$ with high precision in parameters such as charged lepton masses and the PMNS matrix. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

The aim is to provide a comprehensive zero-parameter derivation of the Standard Model's lepton sector through topological concepts.

March 10, 2026Open Access

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

Key Points

The aim is to provide a comprehensive zero-parameter derivation of the Standard Model's lepton sector through topological concepts.
Derivation of charged lepton properties and PMNS matrix
Mathematical frameworks using triadic axioms, helicity, and bosonic dimensions
Analysis of neutrino mass constraints and quark charges
Charged leptons show specific percentages aligned with PDG2024 standards
PMNS matrix angles measured at ≤1σ with a delta CP value of 202.5° (±0.2σ)
Neutrino mass sum estimated at approximately 59.7 meV, below established bounds

Abstract

**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.

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Coty Austin Trout (Sun,) studied this question.

www.synapsesocial.com/papers/69af953870916d39fea4c82c — DOI: https://doi.org/10.5281/zenodo.18916084

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

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