This is a discussion on New Bodhum -700AF- Fragments 4+5? within the Final Fantasy XIII-2 forum, part of the F; I read somewhere that they appear after you complete the game, I've done so and still there's nothing there. Anyone ...
You need to complete the Paradox Ending: Beneath a Timeless Sky.
1. Turn on Paradox scope and go to Academia 4XX AF.
2. Follow the Storyline and accept the artifact.
3. Proceed through the Story and defeat Caius.
4. If the Paradox scope is on you will be able to watch the Ending and then go back to New Bodhum 700 AF and pick up the green crystals. (one by the boat on the west side of the map and one by the dark crystal on the southeast portion of the map).