Why are you assuming that S[n+1] takes S[n] as an input, rather than being completely unaffected by S[n]? Is n here a discretization of time or a "meta-time" that captures state progression?

If the former, then you are treating time as a primitive, whereas the representation or even existence of time can be part of state and vary over state changes, so this does not work.

If the latter, are you assuming S[n] is an input because a universe where that is not the case and state "transitions" are completely independent from each other is indistinguishable from a multiverse with inaccessible sub-universes and should be called as such? In the latter, you are also assuming linearity and discreteness of state changes, whereas it could be a DAG or more complex structure.

Edit: On further reflection, I think you are proceeding with the standard post-Renaissance assumption that a universe must always be governed by fundamental rule(s) at the "lowest level," rather than a more chaotic or unstructured universe that behaves more like a disjoint set than an orderly structure. I think it makes sense to constrain to that assumption as departing from it makes reasoning difficult but it is worth stating explicitly as an axiom.