The point I was referring to was the check after the e.p. Some engines fail to look for check after e.p. It's very rare that it has any effect, like 1:15,000. You are correct, Pg4 has no bearing on the 3-move mate.
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I doubt any engine will miss seeing a check after an e.p. or else their PERFT test would fail.
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I totally agree, this is a very rare issue and so rare it's often overlooked and ignored; however, if you want to be perfect it shows where to correct your engine.