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It's precisely this 'at any of those instances' and 'path' of causations that aren't sitting comfortably with me; primarily the first, but when it interacts with the latter and things are related by physics and derivatives w.r.t. time say, it's not any of more a causal factor than any other input?

If all we mean by 'x causes y' is that 'y is a function of (perhaps among other things) x', then.. fine?

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I made up these phrases to give a simple explanation instead of causal inference terms, and they are probably not good terms, so sorry for the confusion. If I describe it in more standard vocabulary, 'at any of those instances' refer to doing interventions (such as randomized controlled trials).

'causal path' refers to a path in a directed acyclic graph that models the causality. https://cran.r-project.org/web/packages/ggdag/vignettes/intr... has some examples.

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