you right,but caoyijin age is mistake,too small,So tayangu it makes sense to show up early,At least he was probably born in 1268.The tayangu wasn't a person, it was a office. The tayangu who fought against the Ghurids in 1198 was so relevant that we don't even know his actual name, not to mention he was only notable 20 years after the start date.
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Most importantly, there are few records of Khitan lords.