The Visitor Event Guide/Discussion.

 Spoiler

...WHAT? @ The set gives bonuses? So much for me saying it's just cosmetic changes. I'm very interested to see about how "don't take damage from the cube" works. Probably related to Stage 3 or 4.

@ Erich, you can do the 5 OSSS Researcher quests 3 times a day for medals every time, as well as a quest to fame someone, a quest to clear a Party Quest, and log an hour into the OSSS Timer daily. The number of medals you get as a reward are level dependent (except for the Timer quest, as that only gives you one). As for the Medals themselves...

OSSS Medal
A medal issued by the OSSS. It can be used to purchase various core cells from Senior Researcher Jett.
Items per slot: 1000
Cannot resell to merchants
Tradeblock

EDIT: Dern you ninjas.