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 t

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!