NNP has it right about the connection - pin thru the arms. He's also on the mark about setting the angles, both with respect to the centerline of the tractor and tilt. When we got our first unit, I expected the adjusting nuts might vibrate loose but haven't seen anything in 5 yrs, including after heavy beating from a back blade clearing snow from a rocky gravel lane filled with #2's (did use Loctite).
Also, Pat's has extra-long pins, already cross-drilled, so that the stabilizer bars can fit on the outside of the hitches. If you do use the bars (I built some), then make one side adjustable, maybe like with a stubby cat 0 or cat 1 top link welded in. Then, you can match up to any implement width just by adjusting the stab link. As you know, fixed-length stab bars have the downside that implements aren't all the same width (same problem for fixed-width quick hitches like the u-shaped upside-down ones). It's great not having the 6' bush hog beating everything up swinging side to side. With stab bars, you don't need the optional spreader bar from Pat's (or just use a 2x4 like one guy did).
BTW, Northern Tool also carries Pat's, in case you're near one of their stores. Price might be a bit better. Reviews there are great (no, I'm not one of 'em - bought ours directly from Pat's). Link is below, for a Cat 1. The Northern stock # for the Cat 2 hitch is 12611-1451.
Since you've got a 4000 with more grunt than our 3000, if you have Cat 2 implements, then would suggest a Cat 2 unit, then use bushings on any Cat 1 implements.