What is the minimum required depth of reductions for NP-hardness of SAT?
Reposting my comment:

From a quick look, it seems like your question should be answered by "Manindra Agrawal, Eric Allender, Steven Rudich, Reductions in Circuit Complexity: An Isomorphism Theorem and a Gap Theorem, JCSS 57: 127-143, 1999." They say "we prove that all sets complete for NP under AC0 reductions are complete under reductions that are computable via depth two AC0 circuits." But I may be missing something.