Dear Ben,
Your comments have expanded my horizons somewhat.
Donatolle Dolce's essay adds flesh to the distribution-frequency idea in a very exciting manner.
Thank you for looking at my relational behaviour essay. It does indeed address many of the same issues as your causal metric hypothesis, though in a simpler, indirect way. And I hadn't realised the intimate connection between scale and volume that you point out.
I quote from your essay: "Conversely, it is impossible to prove the causal metric hypothesis, but it could be disproven by evidence of multiple independent relations on the power sets of universes." I don't know if it will be helpful to you (or if I am properly understanding you) but a more outrageous corollary I draw from the relational behaviour essay is that its two categories of relationship sometimes offer independent causalities and that our reality is an intersection of two possible causalities. (This is not mentioned in the essay, if you are interested I will pass the additional material to you - about 5 pages.) More so, one can be interpreted as a cyclic causality, in that its causal outcomes follow the logic say of a superposition rather than a volumetric collision. If one were to interpret your "causal cycles" in this way, then there is ample evidence of their existence.
One of the great difficulties I have, especially in relation to Donatelle's intrinsic periodicity, is what is it that changes a continuous behaviour to a discrete one? He speaks of "An elementary system constrained to have intrinsic periodicity......" Constrained by what? Yes, standing waves or resonances occur at particular frequencies, but why may they then hold those frequencies? Why not just pass on through them? We cannot invoke a fundamental interaction to also maintain a resonance in that interaction. There seems to be another fundamental mechanism anchoring relationships to integral wavelengths, and I don't think we are addressing it. (Unless, of course, I'm missing something.)
Mike