BUR #4527 has been rejected.
create implication side_braid -> side_braids
Unless we want to merge them? In any case this seems like another one of those "we used to have X tag but people realized it wasn't broad enough so they created a broader one that now is needlessly separated from the first".
Another alternative would be to nuke it into twin_braids + side_braid, though I'm not a big fan of that.