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The content of this note isn't particularly new: it seems to me that I've always known the main result and treated it as kind of obvious. But when challenged about it (during discussions with Selene Makarios and others during the IKRIS project) I realized that I had never seen a proof; and trying to write the proof down forced me to isolate the necessary assumptions. This, and the surprisingly trickiness of the proof itself, suggested that the topic, although rather detailed, might be of wider interest.
The 'nest' technique used is not original, either, of course (in fact it goes back to A. N. Whitehead, I believe.) I learned the basics of it as an undergraduate, and have used a version of it previously to show that any interval model of time can be re-cast as a theory of time-points.
The original version of the paper contained a few more diagrams, and used slightly different axioms. This version is clearer, I think.
One reviewer wanted me to mention Situation Theory. He was probably right, but I havn't done (sorry) largely because I don't trust my grasp of Situation Theory well enough to be sure I don't say something silly. And in any case, the real focus of this Note is not on the calculus so much as the mathematical structure of the space of contexts/situations/whatever you want to call them.
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