Surviving Southern Song?

In my TL, Temujin (Genghis Khan) dies in 1201. So he doesn't unite the Mongols. (Jamukha does, but is quickly defeated by the Jurchens after he starts raiding their border cities.) And so China isn't conquered by the Mongols, either.

But I was wondering what the consequences of having the Southern Song Empire survive in China might be. Might it be able to industrialize? Might it become a major naval power in the area (or even discover America by 1350)? Might it be able to reconquer the North?

How might things be different with a surviving Southern Song?
 
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