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If Thetis exists (or existed- depending on your views on gods and goddesses) it seems logical that an Hyperthetis and an Hypothetis exist as well. What's that to do with exponential time, I don't know.

Not directly, afaik. Subexponential algorithms for NP problems, and revisiting a lot of what we have based on the ETH of course (including some stuff affecting standard cryptographic assumptions), but nothing as simple as collapse of standard complexity classes. (At least based on my recollection.)