I can’t immediately answer your questions; partly because I haven’t got my head around which inifinities we are working with. As you say we have an irrational twist, but I am not sure that means we have an *un*countable number of “loops”. If the twist was rational wrt the circumference we would have a finite number of loops; going up to an irrational loop might only give us a countable number of loops. That feels like a significant point to me …

Andrew

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