Complete R-Matrix Braiding Catalog for SU(3)_3 Modular Tensor Category

Adam Bazih

Published Apr 17, 2026• 0 citations

Abstract

[NOTE, June 2026: This paper is part of the AME(4,6)/TOE series whose headline claims were partially retracted. In particular the "zero free parameters" framing and several numerical predictions are withdrawn; see the Status Note at DOI 10.5281/zenodo.20618848 and the maintained mathematics at DOI 10.5281/zenodo.20128951. The text below is unchanged and remains as the record of the programme's history.] We present the complete R-matrix braiding catalog for SU(3)_3 modular tensor category, comprising all 144 eigenvalues across 55 anyon pairs. Each eigenvalue takes the form exp(in*pi/18) where n is an integer, establishing that pi/18 serves as the universal phase quantum. The catalog is obtained through direct Sage computation (127 eigenvalues), charge conjugation symmetry (15 eigenvalues), and a novel Hopf link derivation for the multiplicity-2 channel (1,1) x (1,1) -> (1,1) (2 eigenvalues). We verify consistency through the Verlinde formula (144/144 channels confirmed) and charge conjugation symmetry (71/71 pairs, zero failures). Universal patterns discovered include: (i) the adjoint anyon (1,1) produces a universal elastic phase of -pi/2 for all non-simple-current anyons, (ii) adjoint self-braiding yields exclusively fourth roots of unity, and (iii) the simple current (3,0) generates phases that are exact multiples of pi/3. This catalog provides the foundational braiding data for the AME(4,6) theory of everything based on the Walker-Wang model.

DOI: 10.5281/zenodo.19627068

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