The mainstream theory is that whatever reality is, its consequences on measurable length-scales are as-yet indistinguishable from an almost-everywhere-continuou

The mainstream theory is that whatever reality is, its consequences on measurable length-scales are as-yet indistinguishable from an almost-everywhere-continuous medium. (I.e. away from black hole singularities.). Until we have the ability to measure not just deviations of reality from theory, but deviations from what any continuum theory might predict, the question of whether hypergraphs have the correct asymptotic continuum behavior is largely moot. Wolfram has been pushing an atomistic program of cellular automata as models of physical systems for many years. They are beautiful, but so far they are only useful insofar as they approximate continuum mechanics-- which is to say, they are of limited application. The thing about continuous media is that they involve dynamics on all length scales: .1 meters, .1 nanometers, 1e-10 nm, etc. Because of wave-particle duality, length scales and energy scales run inversely: a low energy experiment just does not exhibit any measurable dependence on extremely short-range behavior of the universe. Only high-energy experiments have a wavelength short enough to be sensitive to this unknown sector. Low energy physics is “well understood” in the sense that any experiment with a modest number of component particles can be totally predicted from theory, to the limits of experimental accuracy. Granted that many real-world problems involve stupendous numbers of particles, and exhibit challenging-to-explain emergent behavior: but this is not evidence of unexplained fundamental phenomena, just of the limits of our mathematical insight into finding good abstractions for many-body problems, and evidence of the limits of our computational power to try and work around the lack of good abstractions. It is known that the most generous interpretation of current theories is that they are self-consistent to arbitrary high energies (renormalizable is the term). That does not mean they are consistent with actual reality, just with themselves. So... hypergraphs are a big lift, an unneeded multiplication of entities. Until an experiment reveals non-continuum behavior of space-time, what we have here is a solution to a non-issue.