My thinking about Geometric Unity has been centered on 14 dimensions for a long time. That is, I thought of the physics unfolding in 14 dimensions as primary, and of the 4-dimensional world as akin to a defect or a braneworld located in that background.
However, I have found my way to a perspective centered on 4 dimensions. The reason is the multi-time metric signature of Y. Multi-time backgrounds usually spell trouble, and yet GU prefers a (7,7) signature for Y, so I thought I'd just have to deal with it.
However, eventually I noticed that the preferred metric signature for X is (1,3), the usual Lorentzian signature with one time dimension. At the same time, I finally understood the dependence of Y's metric on X - you use a canonical metric within each vertical fiber, and then you stitch those fibers together horizontally, using X's Levi-Civita connection as the template.
This opens the possibility of grounding everything in single-time evolution on X. Possibly the other timelike directions in the fibers can then be dealt with, through a combination of gauge-fixing and constraints.
I've also been consolidating my understanding of other aspects of GU. For example, I've noticed that the equations of motion for the spin-1 component of the unified field on Y are basically "curvature = torsion", except that (1) the curvature is sheared of its Weyl-tensor-like component by the shiab operator (2) the resulting "swervature" and the torsion are then made gauge-invariant.
At the other end of the scale in terms of complexity, I'm getting to know what happens to every component of the 14-dimensional spin-1/2 and spin-3/2 fields. Diagram 11.6 in the GU paper depicts how they end up in "F", "Q", and "Z" multiplets, but I want to know the implied interaction terms as well, e.g. 12.28 tells us that the 4-dimensional yukawa couplings are supposed to descend from the VEVs of certain 14-dimensional bifermion operators.
