What is the 'arm' at the rear of the X-29?
Two X-29's were built, and the only difference between the two is that #2 has an externally mounted spin recovery chute attached to the tail. That is what you are seeing in this picture. The chute is packed in the tube structure and the "arms" are structural to distribute load.

Source


  The only significant difference between the two aircraft was an emergency spin chute deployment system mounted at the base of the rudder on aircraft No. 2.


Here is a video of the chute deployed

And here are more details from NASA on the chute system

The reason that #2 needed this and #1 did not is that #2 was going to be conducting experiments at up to 67° angle of attack, where entering a spin was much more likely. #1's AOA was limited to about 21° and was considered the "phase-1" flight dynamics platform, while #2 was the "phase-2" platform.