Separation of two-query-adaptive from two-query-non-adaptive completeness if NP is not small

Under the hypothesis that NP does not have p-measure O (roughly, that NP contains more than a negligible subset of exponential time), it is shown that there is a language that is ≤ P/2-T complete but not ≤ P/2-tt complete for NP. This conclusion, widely believed to be true, is not known to follow from P ≠ NP or other traditional complexity-theoretic hypotheses. This is a very preliminar version