City growth limit?

Your city size is limited by food mainly though if your running negative you only need to ship in food from another city to refill your ques, you can still send caravans and units with 0 food

Yes Sov is limited by your research/resource/gold production, you can ship in supplies from other cities if you are negative but if you run out of a resource your Sov structures/squs will de-level until your production goes positive

I know you are up to your eye-balls in works on v2 etc., but I have a questions about city growth limits.

I would like to acquire more sov squares for my capitol, but my research production is topped out. I assume I am at the limit of growth. Maybe I'm missing something...

1. Is a city size limited to the amount of research it produces?
2. If gaining sovereignty negatively effects research production, are the number of sov squares limited by research going into the negative?
3. If the library is at level 20, is the only way to raise research production to lower the tax rate (until it goes negative, at which point a growth limit has been reached.)?

Any help will be appreciated.

When you gotta grow, you gotta grow!

Kelis