Probability that six random numbers between 0 and 1 are the lengths of a tetrahedron's edges

This is Part 3 of Problem No. 81 of the Missouri State University's Advanced Problem Archive.

The website seems to have been last updated in 2015 and states that this problem is "still unsolved." Has this problem been solved since then?

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Probability that six random numbers between 0 and 1 are the lengths of a tetrahedron's edges

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