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(non-mathematical) Implication doesn't mean certainty, which is where I stand with that. But I would posit that it (mathematically) implies that joining two knots with under to ove…

I'm not saying I could have come up with the example. I'm saying looking at the example, and seeing how the two unders are connected togther, and the two overs connected together, …

This example seems obvious to me - Joining the under to the under, and the over to the over would obviously give more freedom to the knot than the reverse.