What does Ky give to Cassia after they kiss on top of the hill?

On the last hike, she apologizes to Ky for doubting their love. The two break the rules together first by climbing to the top of the hill so they no longer feel like Sisyphus, then by truly kissing. Ky gives Cassia his artifact, showing that he knows his own future even if she does not. It will help her find him. For one brief moment, their world is perfect.