Select the Clifford algebra best fitting the Standard Model and observed physics

Ascertain which Clifford algebra—Cl(6,0), Cl(5,1), Cl(2,4), Cl(1,5), or Cl(3,3)—best models the Standard Model and observed physics within the quaternionic extension of Dirac matrices proposed in the paper, providing explicit criteria and validations for the choice.

Background

The paper discusses framing the 4×4 quaternionic matrix algebra as a Clifford algebra for various six-dimensional signatures and notes multiple candidate frameworks (including twistor-based approaches).

While several models have been proposed in the literature, the author explicitly states that it is not clear which Clifford algebra provides the closest fit, leaving a selection problem to be resolved.

References

Models of this type have also been proposed [40], as have models based on Cl(3,3), and it is not at all clear which of these Clifford algebras provides the closest fit to the Standard Model, and/or to observed physics.

— A discrete model for Gell-Mann matrices (2401.13000 - Wilson, 22 Jan 2024) in Section 6.4