I've read the first few pages. Looks like an interesting paper and I'll read it further. Only flaw is that it doesn't cover Steve Russell being the first to discover/invent continuations. Steve Russell was the first implementor of LISP, and gave it its final syntax after McCarthy did his design work on it.
Are you confusing continuations with closures? McCarthy credits Russell with inventing the FUNARG device to achieve lexical scoping.
page 6 of the PDF, a continuation is essentially the return address of a subroutine call. But then there are scoping rules that interact with that simplicity.
Well, I'm not sure what that's about, besides possibly being mathematical. The title alone isn't enough to get me to download a pdf. (And I've downloaded 100s of mathematical PDFs)