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Temrek

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Research speed depends mainly on the amount of ctiziens a province has and the civilization of the province.
 

Woody Man

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Use laws, or national ideas that up the rate of freemen -> citizen conversion
 

Kasimal

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the speed of research ist found by the number of research-points divided by the number of provinces. So if you conquer a lot provinces and so loose the civics in it, you will realy have much problems with research-speed.
Indeed, the research in VV is kinda messed up, as a little country, you can either chose to expand your country or research, but you can't have both, very sad that is.
 

Cheexsta

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Kasimal has the basics right.

I disagree with the assessment that a little country can't expand and research at the same time, though. It's a bit of a fine balance, but there are some things you can do to expand and research at the same time:
1. Restrict yourself to same-culture provinces. Conquering a province of the same culture will not reduce the number of citizens.
2. Enact laws and national ideas to increase Freedmen to Citizen growth. This is dangerous, though, since you may run low on Freedmen (and, therefore, manpower).
3. You can start by being expansionist, keeping high Freedmen numbers but low Citizen numbers, and then switching to research a little later with high Citizens and low Freedmen. Then you can balance everything out and be able to do both at the same time.

Hope that helps.