I feel like this question has a good chance of having been asked here before, but the first ten-odd "similar questions" listed by the site when I composed the title didn't cover what I'm aiming for, so I'm not sure. Will delete if it turns out to be a duplicate, anyway.
Also, the only SEP article I refreshed my memory of before composing this question is one about time in general. Could easily be addressed in e.g. the article about the metaphysics of causation. For now, my incomplete memory of the latter does not testify on behalf of said address, however.
So "caveat emptor," so to say...
Definition of causal determination at issue. Assume that the past and "half" the present function as constants relative to a variable future. The past/part of the present determine the future mathematically in the sense of "solving for" the variable of the future.
The four-dimensionalism consideration. Imagine a world consisting in a single tesseract whose fourth coordinate slot is timelike. Without supposing an absolute past, present, or future, we have all facets of the tesseract "given" in atemporal simultaneity.
It seems as if no facet, taken to be pastwise, "solves for" other facets as variables, since no facet is a variable as such. All facets are determined "at once" by whatever function projects the whole tesseract "at a glance." We can't step outside the tesseract (if we're inside of it) to say that the unit cause of the entire structure is itself an effect of a prior cause, etc. Perhaps this is possible in general, but for reasons of local empirical-causal closure, this fact transcends our possible empirical knowledge. And logically, it is impossible to predetermine the content of an information powerset from prior information sets; there is always underdeterminately more in an indefinite powerset than is in its base. So there is no a priori guarantee of determination either.
Question: so what use is the concept of causal determination in a four-dimensionalist closed world? A unit circle could be determined from x2 + y2 = 1 but no infinitesimal side of the circle "causes" the other sides to be so. And we have no knowledge that the formula for the unit circle must be an effect, so to say, of another formula, and so on "backwards in time." So is the notion of temporal determination, as A-series determination, required at all to interpret four-dimensionalism as such? Because it seems, here, not to be required at all.