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It also means you are using your 7th policy to finish Liberty, instead of opening one of the other trees. This means your GE for the NC is delayed—not necessarily the worst, as it’s not uncommon to get through Liberty faster than I can get libraries up in all my cities (especially if I ally a culture CS, get a culture pantheon, or have to build other stuff, like triremes or archers).

I must say that it's a very common mistake to build library and NC too early as Liberty. library is a very ineffecient building in low pop cities, so in general do not build library before aqueduct. NC is also not necessary as Liberty.

Tradition opener is a very valuable policy for it's border expansion (usually the most valuable policy besides Collective Rule), but Collective Rule speed is also very important, so my suggestion is to pick it after Collective Rule, or after one another policy like citizenship or piety opener. If you get an early culture ruin and are planning to build an early Wonder (like ToA), pick Tradition opener first is also a good idea. On island maps where faster border expansion usually means more useless sea tiles, just skip it.
 
library is a very ineffecient building in low pop cities
Libraries are very inefficient buildings compared to external trade routes. Some games you don’t have access to science from trade routes due to geography/war.

Liberty finisher -> GE -> NC between turn 90-100 is pretty standard sequence on Deity imo.
 
Libraries are very inefficient buildings compared to external trade routes. Some games you don’t have access to science from trade routes due to geography/war.

Liberty finisher -> GE -> NC between turn 90-100 is pretty standard sequence on Deity imo.

growth your pop is more effecient for science in the long term, so if you don't want some certains techs immediately, granary, watermill and aqueduct are always better than library.
if you check out the tech tree, you will find that all techs in classical era only unlock buildings and units, the first tech that provide immediate effect is civil service. As long as your tech is not too far behind that you don't have any efficient production options, increasing your tech speed during classical era is meaningless. and science from your pops is more than enough to fulfill that, so you really don't need any extra science (even external trade routes are not necessary) during the entire classical era. If you are already near civil service, you should still only build libraries in big cities, because it's impossible to speed up Civil service for just 1 turns for a library in small cities.
 
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