S^1_2 is consistent with EXP not in P/poly, via separations of V^1_2 from T and Gödel-style consistency statements; analogous results hold for PSPACE but require unknown separations.
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From G\"odel incompleteness to the consistency of circuit lower bounds
S^1_2 is consistent with EXP not in P/poly, via separations of V^1_2 from T and Gödel-style consistency statements; analogous results hold for PSPACE but require unknown separations.