Negating ETH allows a separate 3-SAT algorithm for each positive exponent. Negating SETH gives one positive exponent improvement that works for every fixed clause width, with the algorithm allowed to depend on the width. Negating the 3-SUM Hypothesis gives a truly subquadratic solver. Negating the APSP assumption gives, for each fixed weight exponent, some truly subcubic solver; its improvement may depend on that weight exponent.

For each hypothesis, its randomized version implies its deterministic version. These are logical consequences of the specified algorithm classes; all four hypotheses themselves remain explicit premises.