This seems equivalent to assuming that time is a converging series in the sense that minor changes in the inputs will have only certain types of effects but the

This seems equivalent to assuming that time is a converging series in the sense that minor changes in the inputs will have only certain types of effects but the end result is fixed. For example, using newton's method to compute square-roots always converges on the correct value, pretty much regardless of the initial guess. (It doesn't work for "potato".) The initial guess does influence how many iterations are necessary but that's it. While that may be true wrt time travel, it's unclear why it should be true.