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The stars?
The level?????
^
However, maybe I just don't know enough about the quests involved but I believe neither of the quests that reward Research Commission Tickets have Research Level requirements. (except indirectly, in the cases of unlocking optional quests like High Rank Kirin)
White Winds of the New World requires all Optional quests (including Special Arena stuff, so you need to capture most monsters in most ranks at least once then beat them in the special arena) to be completed.
And The Sapphire Star's Guidance requires HR100.
Maybe White Winds has a research level requirement I just don't know about (and in any case you should be trying to fully research every monster in the game anyway) but I'm pretty sure OP has been confused by something when it comes to unlocking Research Commission Tickets.
If there are no more empty stars next to the monster that means you've fully researched it.
As a general guide, all monsters will have a max research level of either 4 or 6.
If a monster's research level is 6, the first 3 levels are for its Low Rank version and the final 3 are for its High Rank version.
If a monster's research level is 4, that means it's High Rank exclusive, so all 4 levels are for High Rank.
Check your optional quests and compare your list to the quests listed on the wiki. Make sure you captured all monsters alive at least once to unlock their arena quests and talk to the master of the third fleet at the flying research base. She has some quests for you that also unlock a bunch of canteen ingredients after capturing a Great Girros for her.