I'm pretty sure someone with more mathematical knowledge than me can prove it is not possible.
That's pretty much the point I'm at too (except someone would need a LOT more math than me). I've fiddled with the problem for a while, and everything I try ends up either: (1) not locking, (2) as an eye splice, (3) as a double loop, or (4) unsatisfactory in some other way (bulk and/or strength).
Regards,
Eric