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--the stopper is tied as a double overhand, but it hasn't been dressed and set in the normal manner. I have seen it dressed and set like this before, but I don't know how secure it is compared to a properly dressed and set double overhand. I always make sure the turn is seated across the entire knot, as Jman described. See the article in my post above that Chris mentioned .
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Fiddling around with Paul's stopper, I can't see it giving up under load. It could have the potential to loosen and fall apart if the tail is too short and it's not set properly. After it's set I don't think it's coming apart on its own.
Paul's stopper is very easy to break after loading, same as the Anchor Bend.
Double overhand has a kind of self-locking feature which is probably why it's become the default stopper for tree climbers.
-AJ