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    $\begingroup$ I recently found a way to modify Terry's argument to show that it suffices to check speed vectors in $\mathbb Z^7$ with $l^2$ norm up to $56^6/\text{vol}_6$ (that is the reciprocal of the volume of a ball of radius 1/56 in $\mathbb R^6$). This bound is slightly less than 6 billion which still leaves far too many cases to check without some clever idea. $\endgroup$ Commented Dec 7, 2017 at 23:22
  • $\begingroup$ @Anthony: That's quite encouraging! Certainly that is still too large for a brute force search, but I'd imagine that one could whittle the search space down substantially through elementary arguments (congruence considerations, etc) which was the spirit of the polymath proposal. It might be also worth trying to re-frame these argument in terms of Freiman isomorphism classes instead of bounding the size of the largest element. This might also yield a substantial reduction in the size of the search space. $\endgroup$ Commented Dec 11, 2017 at 1:17