> Theorem: for every positive integer N, there is a TeX file which needs N > passes to be properly processed.
That's a special case of the stronger statement "One can construct a TeX file which does not converge." Using "normal" editting, the only way it is *likely* to occur involves many (or large font) page numbers and/or floats such that the n-th pass yields a forward reference page number ending in 1, which then on the (n+1)th pass is actually typeset and narrow enough that the reference itself ends up on the previous page ... which ends in 0, and is wider again, to bump it forward. This is more of a TUG-level theoretical concern, I've never seen a non-contrived example (and it is easy to avoid) but I might suggest that in practice, just make sure that any clever iterative hack will *give up* after some small number of iterations to let a human tweak it (and save the non-contrived example for submission to one of the TeX journals :-) [I suspect that this is actually a property of *any* sufficiently advanced reference system, but I haven't kept up with the computer typesetting literature in the last 10 years or so...]
