Not the complete answer, but one ohio code (maybe repealed? hard to follow )
Quote:
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(A) No person who is eighteen years of age or older shall engage in sexual conduct with another, who is not the spouse of the offender, ehen the offender knows the other person is thirteen years of age or older but less than sixteen years of age, or the offender is reckless in that regard.
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I added the bold. The word "knows" is in there, and that sounds like it wouldn't match up to a strict liability view of the world.
However, that is the sideline to the bigger circus... the one sexsearch is getting dragged into.