I have been working on something similar; although not with cubes. Right now it explains proton to eletron mass ratio, and it gives very stong indications of "why" we will never have more than 3 generations of matter in any form and predicts the fine structure constant. Please message me I would...
Would a geometrical structure following a single set of simple rules when it tessellates that:
1) Predicts the mass ratio of the electron to the proton
2) Derives and explains the fine structure constant
3) Explains the reason for only 3 generations of matter
4) Predicts the electron...
Any way that you could refactor or refit Bell's experiment in a way that would limit or reduce the size of his observed violations by introducing a piece of what you have in mind, in a way that incremental introductions of your theory displace his results. And with those observations then...
Forward your infomation to Stephan Wolfram re:NKS maybe he could get the quantum folks off his back :)
That is if I'm grasping your papers, seems a good fit.