It seems sensible to have something like the permittivity of free space as a node in your map of the universe, which causes various relationships in electromagnetism (which then cause behavior of individual entities), but whose value is invariant, and thus does not have any inputs. (Your estimate of that node, of course, has inputs- but it doesn't seem reasonable to claim your estimate has any causal influence on the actual value.)

This becomes especially meaningful when you consider something like the fine structure constant, which we're not quite certain is a constant! If it's a node, then you can easily have arrows going into it or not, depending on what the experiments show.

EDIT:

Why not just call it a single tier universe then? Especially because your hypothesis is not distinguishable from the single-tier, which is simpler, so you have no good reason to ever have encountered it.

The tiers are a topological property of the graph- you can find a subset of nodes where the causal influences only flow out. The a priori statement that you expect to find that topological property does require special knowledge- but once you have a graph, noticing that the subset exists and identifying it as special doesn't require special knowledge.

Note also that this interpretation plays a big part in the question of "does something outside of my future selves' past light cones exist?", since the argument that conservation of energy applies everywhere rests on the premise that conservation of energy doesn't have any pertinent incoming causal links. It could be the case that there's an arrow from "is it in my future selves' past light cones?" to "conservation of energy," but we think that's implausible because "conservation of energy" is in this special subset of nodes that don't appear to take inputs from the physical universe where I and my future selves reside.