Here’s a concept that seems useful, but that I don’t remember ever hearing explicitly referred to (with my own tentative name for it—if it turns out to not already have one in some extensive philosophical literature, I might think more about whether it is a good name):
Normative reductionism: The value of a world history is equal to the value of its parts (for some definition of relevant parts).
For instance, if two world histories only differ between time t and time t’, according to NR you do not need to know what happened at other times to evaluate them in full. Similarly, the value of Alice’s life, or the value of Alice enjoying a nap, depend on the nature of her life or the nap, and not for instance on other people’s lives or events that took place before she was born with no effect on her (unless perhaps she has preferences about those events or they involve people having preferences about her, but still the total value can be decomposed into the value of different preferences being fulfilled or not). Straightforward hedonistic utilitarianism probably implies normative reductionism.
My impression is that people have different intuitions about this and vary in how much they assume it, and that it mostly isn’t entirely aligned with other axes of ethical view, either logically or sociologically, though is related to them. So it seems maybe worth noting explicitly.
Meteuphoric 
I think you’re implying that all the parts that follow t’ are identical to the parts that follow t. Wouldn’t that automatically prove that part t’ is insignificant and therefore it won’t affect the value of the world history? I’m thinking that in any case where t and t’ are the only difference, and the parts that follow are identical, then the value of the two world histories will always be equal. For example, if in part t Betty published a novel, and in t’ she didn’t (and that was the only difference), but in part t+1, possibly 1000 years later, nobody’s life is being impacted by it in both cases, then the value of part t is equal in both cases, and we can disregard this difference, meaning that both histories have identical value. The values will only differ if later parts are non-identical, which means that you do need to know what happened in other parts. Right?
What is t is the moment when Alice stubs her toe? It has no permanent consequences, but it still hurts in t.
The only way that you’d know it had no permanent consequences was if you observed >t, yet the claim is that you don’t need to know >t to evaluate t.
Normative reductionism is normally used for a position in meta-ethics: that normative properties can be reduced entirely to descriptive properties. The idea you’re discussing is known in the literature as ‘separability’. John Broome discusses separability over times and separability over lives in ‘Weighing Lives’ if you’re interested.
I think this is normally called “additivity” in population ethics. You would say additivity across time for your first example, and additivity across lives for your second example, or objects, or spaces, or whatever. Philosophers also argue about additivity over experiences within lives.