In a comment at the sub-reddit /r/ThePortal, a forum originally devoted to Eric Weinstein's podcast of that name, I mentioned how uplifting well-known physical solutions like electromagnetic plane waves and black hole metrics, to their 14-D counterparts in GU, would be a way to advance the (classical bosonic) theory.
Meanwhile, a Youtube discussion led to the idea that quantum GU would be advanced by trying to embed processes like QCD confinement and the Higgs mechanism into the GU framework.
I'll also note that in a slide on his talk in April, "From Dark to Geometric Energy", Eric provides the most concrete explanation we have yet seen, as to how the Seiberg-Witten equations relate to GU. See the bottom of the screen at 2:30 - a Rosetta stone relating general relativity, Geometric Unity, and the Seiberg-Witten equations.
Another important part of the lecture, is where he motivates the use of the Hodge star operator and the shiab operator, to construct a higher-dimensional gauge-invariant analogue of the tensor contraction used to define the Einstein tensor in general relativity.
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