FYI: If you want to do something with his theory, then up to octonions supported here (but not sedenions):
I recall sedenions also mentioned in some of his papers, here from the first link, at least sedenionic:
Quantum worlds vs. Classical worlds
Our universe, as it is today, is dominated by classical bodies, which produce, and live in, a classical spacetime. This is the substrate shown in Fig. 7. […]
The octonionic theory achieves a formulation of the upper quantum level, relating quantum systems to a quantum spacetime, i.e. the octonionic spacetime.In the octonionic theory, the transition from the classical substrate to the upper quantum level is very elegant and is reflected in the simplicity of the action principle of the theory.
[…]
the action principle of the theory is [an atom of spacetime-matter (STM)][Formula (66)]
where the degrees of freedom are on sedenionic space. This action is nothing but a refined form of the action of a relativistic particle in curved classical spacetime
[…]
and obey the Fano plane multiplication rules.
[…]
Equation (68) defines an octonion, whose eight direction vectors define the underlying physical space in which the ‘atom of spacetime-matter’ [the Q matrices = elementary particles] lives. The form of the matrix is shown in Eqn. (69). The elementary particles are defined by different directions of octonions.Our fundamental action is a relativistic matrix-particle in higher dimensions. The universe is made of enormously many such STM atoms which interact through ‘collisions’ and entanglement. From their interactions emerges the low-energy universe we see. There perhaps cannot be a simpler description of unification than this action principle.
[…]
Once again, we see the great importance of Connes time τ. The universe is a higher-dimensional spacetime manifold filled with matter, all evolving in an absolute Connes time.
There he referenced from other people:
[1904.03186] Three fermion generations with two unbroken gauge symmetries from the complex sedenions
can be described using the algebra of complexified sedenions C⊗S
I had never seen sedenions mentioned in any (physics) paper, at the time I wrote this post (after seeing them used for the first time in neural networks):