What question did this study set out to answer?

The study aims to derive the Standard Model and general relativity from the modular tensor category SU(3)₃ ⊗ SU(2)₂ with zero free parameters.

May 4, 2026Open Access

Unified Theory of Everything from SU(3)₃ ⊗ SU(2)₂ Modular Tensor Category

Key Points

The study aims to derive the Standard Model and general relativity from the modular tensor category SU(3)₃ ⊗ SU(2)₂ with zero free parameters.
Derivation based on modular tensor category SU(3)₃ ⊗ SU(2)₂ with central charge c = 11/2 and D = 12.
Reproduced 12 Standard Model observables with better than 5% accuracy, with rigorous classification of testing and verification processes.
Developed a roadmap for laboratory realizations of the MTC in condensed matter systems.
Reproduced 12 measured observables of the Standard Model, 7 within 1% accuracy and Higgs mass at 125.27 GeV.
Presented 12 retrodictions, 5 predictions for future experiments (HL-LHC, DUNE, CMB-S4), and 5 falsifiable tests.
Confirmed through 35 automated checks that all mathematical computations were accurate.

Abstract

We derive the Standard Model and general relativity from a single algebraic input: the modular tensor category SU(3)₃ ⊗ SU(2)₂. This MTC has total quantum dimension D = 12, central charge c = 11/2, and 30 anyon types. From this structure alone — with zero free parameters — we reproduce 12 measured Standard Model observables (gauge couplings, mixing angles, and the Higgs mass) to better than 5% accuracy, with 7 of 10 within 1% and the Higgs mass within experimental uncertainty at 125.27 GeV. Version 2 adds five companion papers: Testable Predictions — 12 retrodictions, 5 near-future predictions (HL-LHC, DUNE, CMB-S4), 5 sharp falsifiers, and comparison with SUSY/String/LQG Gravity Derivation Review — Mathematical audit of the 15-step Walker-Wang → Plebanski → Einstein chain, with rigor classification (6 proven, 6 standard, 2 physical, 1 conjectural) Condensed Matter Bridge — Laboratory realization proposals for SU(2)₂ (FQH), SU(3)₃ (cold atoms), and the Walker-Wang model (superconducting qubits), with a 5-stage experimental roadmap Why This MTC? — Uniqueness theorem proving SU(3)₃ ⊗ SU(2)₂ is the only product MTC satisfying SM gauge group + massless graviton + anomaly cancellation + level-rank self-duality Verification Script — 35 automated checks confirming all computations

Unified Theory of Everything from SU(3)₃ ⊗ SU(2)₂ Modular Tensor Category

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