The South Capital thing is interesting, I had no idea.
During the en.wikipedia.org/wiki/Liao_dyn⦠or Khitan Empire, Beijing ("Nanjing")[0] was really in the far south of that empire, which covered Korea, Manchuria, the area around Beijing, most or all of Mongolia and maybe a third of Siberia.
It seems Beijing was never part of the Song Dynasty, I never realized that. After the Tang everything was a bit fractured until the Mongols unified most of Eurasia.
[0] ... or was it "Xijin" ... and Nanjing was the province? It's not clear on Wikipedia, the articles contradict the maps, or the maps and/or articles are unclear