This is a discussion on Paradox Professor glitch? within the Final Fantasy XIII-2 forum, part of the F; I have 100% map completion for all zones, however Miss Horizon won't give me the fragment for Academia. I have ...
Just play through the game and unlock all the other timelines inorder to make sure. Make sure you have the majority of the Artifacts then return and see if she gives you the Artifact. Never heard of any glitches so I'm sure your just missing 1 unexplored map.
Here this might actually be a bit faster. Check the Final Fantasy XIII-2 Trophy Guide and the Defragmented section and Academia 400AF for all the areas and timeline you'll need.
You'll be able to tell which timeline you haven't been to yet. But for us it's a complete guessing game unfortunately. Sorry I can't be more helpful. Good luck with getting your trophies. If your needing any other help then let me know and I'll try and help as best as I can.