Your system of grand unification has similarities with Kaluza-Klein theory, but the tiling idea is relatively novel -- brane tilings are a current research topic. They are, however, used in a completely different way to ath you suggest.
Besides the issue of Higgs Debye screening, I think one of the big problems is that in order to "fit" such tilings in GR, you would need incredibly large local curvatures which, although not ruled out (because they are in the fuzzy bits of conformal diagrams) are inelegant.
It's easier and more elegant to attempt to couple gravity directly to scalar fields (TeVeS or f(R) models), or to go for one of the full critical string/M-theories involving supergravity.
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Besides the issue of Higgs Debye screening, I think one of the big problems is that in order to "fit" such tilings in GR, you would need incredibly large local curvatures which, although not ruled out (because they are in the fuzzy bits of conformal diagrams) are inelegant.
It's easier and more elegant to attempt to couple gravity directly to scalar fields (TeVeS or f(R) models), or to go for one of the full critical string/M-theories involving supergravity.
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