By doing a bit of searching I found that the chaos crystal will allow you to get some weapons. However, I talked to hope in Academia 4XX and he didn't mention anything, I also have all the graviton cores. Do I have to close the gate and try again?
Do you believe that your consciousness can affect the behavior of subatomic particles? ~ Nathaniel Sr. from 'Six Feet Under'
You shouldn't have to. If you have a chaos crystal, you just speak to him in Academia 4XX and give it to him, if you have one it will automatically open up a dialog. After that, he says it will be ready at the front desk in a bit, so you just walk out there and collect it. Whichever one you choose, Serah's or Noel's, the other will be available in Serendipity to purchase in a shop.