A Pictorial Doubt about a Form of Determinism

There is a past state and a present state:

[past] [now]

A common determinist claim is that the whole state of the world at moment t (the past moment) entails a given state at t' (the present moment):

[past] -> [now]

However, we might ask how it is that anything in the past logically entails anything in the present. The events of the past as such don't appear to yield such an entailment. Therefore, it must be the union of the past state with some supposition or set of suppositions that overarch both the past and the present. This supposition cannot, however, be simply general (for the most part) in its application, because that introduces something less than an entailment:

~~~~~~~~~~~
[past] ~> [now]

So it must be one that is much stronger:

___________
[past] -> [now]

In other words, it has to be a universal and necessary [that should read: non-probabilistic--ed.] supposition. Now the question is: we are supposed to believe

__________
[past] [now]

rather than the weaker

~~~~~~~~~~
[past] [now]

But it seems this could not be established by empirical evidence without begging the question. And it does not seem there is any necessary truth that overarches past and present in such a way that it requires us to say that the present state is logically entailed by the past state, at least none that wouldn't highly controversial. So what could it be?