TL;DR - replace one big singularity with multiple singularities.
As in last sentence there is "The only difference between this work and the standard model is that the temporal singularity occurred only once in the latter, but more than once in the former."
> The geometric product is just the quaternion product broken up into scaler and vector parts.
The geometric product works in any dimensions. They have a clear geometric intepretation. Rotations and translations can done using the same algebraic operations.
I saw the show in London. As a show it was brilliant and an unforgettable night. As live music performances better around then were The Cure and Mike Oldfield.
p281 for Dirac equation. But I suggest you start at least from the beginning of Chapter 8. Earlier, obviously if you don't know Geometric Algebra. It's worth it; many examples but one is that the four Maxwell equations are expressed as one compact equation with geometric intuition.
Complex numbers and (Pauli/Dirac) matrices not required if you use Geometric Algebra. I highly recommend the book by Doran and Lasenby [0], or you can get the details from their papers, notably [1].