Wilhelmus, Ted and Ben - thanks for your encouraging reactions.
Have downloaded your essays, but so far only had the opportunity to briefly scan through them.聽
Wlihelmus and Ted - at first glance it seems you don't shy away from "the final frontier" aka the physical basis for consciousness, and you both do dare to tread into territories that emerge would I have gone beyond the point where I decided to end my essay. Ben - I also notice that your essay addresses topics similar to the ones I discuss. Interestingly, you turn this into a proposal (causal metric) quite different from mine.
Will need to read each of your essays in more detail to make more meaningful comments.
Ben - thanks for asking some very relevant questions that allow me to address some points not discussed in the essay.
On local causality: in this model, just like unitarity, also causality loses its status as fundamental principle. The toy model replaces both with a locally isotopic correlation (i.e. color balance). Notice that unitarity and causality both re-emerge as local phenomena on a larger (emergent) scale. For unitarity this is discussed in the article, for causality this can be seen as in the late-time/large distance limit the two nearby patches A and B will share the same color evolution.
Not sure if I fully understand your question about the binary weights. The presence of a binary field (nodal coloring) is essential to the whole proposal. One can work with more than three links per node, but this would not eliminate the requirement of a field defined by a local relationship.聽
Causal set theory starts from the assumption of a (partial) ordering between the nodes. The toy model presented here does not assume such an ordering, but rather assumes a field (node coloring) with nearest neighbor correlations.
Your question on a non-commutative angle emerging in this toy model is intriguing. The 'color addition algebra' (i.e. the colorings resulting from specific choices) indeed doesn't commute. However, I don't immediately see whether this has any direct physical consequences. I probably need to think a bit more about this.
