Mechanism of left–right symmetry breaking from 14D split bioctonionic space to 6D split biquaternionic spacetime

Determine the underlying mathematical and physical mechanism by which left–right symmetry breaking in the 14-dimensional split bioctonionic pre-spacetime with signature (7,7) yields a 6-dimensional spacetime generated by complex split biquaternions with signature (3,3), and explain why the remaining eight Euclidean directions organize into two copies of 4-dimensional vector bundles associated with the unbroken gauge symmetries SU(3)_color and SU(3)_grav.

Background

The framework employs split bioctonions to define a 14-dimensional non-commutative pre-spacetime whose gradient (Dirac) operator squares to the Klein–Gordon operator in signature (7,7).

After a left–right symmetry breaking (identified with electroweak breaking in this program), the authors assert that the 14D structure reduces to a 6D (3,3) spacetime described by complex split biquaternions, while the remaining eight Euclidean directions serve as two 4D internal vector bundles associated with SU(3)_color and SU(3)_grav. The detailed reason for this reduction and assignment is not yet understood and is identified as an open issue.