Curious about your paper (assuming you are the author). Clarify if I misunderstood.
Doesn't introducing separate time slices automatically forces you into a continuum of time and therefore the "Instantaneous" requirement "I" become meaningless.
One can't evaluate physical state transitions without continuous time or atleast some form of mathematical ordering.
But if you strip away continuous time and keep only the abstract "ordering", you are again back in the world of pure mathematics where states never decay and memory never fades.
I wouldn’t call an instant as meaningless in a continuum. It is indeed, though, non primitive and idealised as traditionally in physics (the physical state at time t, given as the limit of arbitrarily fine time resolution). If I understand your question correctly, the interesting issue is not whether instants exist as an idealisation, but how independent observations can be synchronised well enough to assess a physical implementation of an abstract mapping. That is a genuinely difficult problem, and one that appears even if time is discrete. It is one of my current work subjects. Anyone who has worked on distributed systems will recognise that ordering events is one thing, establishing a common notion of “now” is another. Once again, no “grand conclusions“ from me!
Doesn't introducing separate time slices automatically forces you into a continuum of time and therefore the "Instantaneous" requirement "I" become meaningless.
One can't evaluate physical state transitions without continuous time or atleast some form of mathematical ordering.
But if you strip away continuous time and keep only the abstract "ordering", you are again back in the world of pure mathematics where states never decay and memory never fades.