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After the fall of the Tibetan Empire, things went quite downhill in Tibet which knew a long era of decline known as the Era of Fragmentation.
It tended to be better after the Yuan conquests, but between mid IXth century and mid-XIIIth century, the region was a mess of small dynasties which can reach some hegemonic control on Central Tibet, but not much long.
Your mission, should you choose to accept it, is to manage to shorten the Era of Fragmentation by having a relatively unifed Tibetan entity emerging after the fall of the Tibetan Empire (as early as the early Xth century), and to describe what most important changes does it implies ITTL Asia.
It doesn't have to be ruled by a Tibetan-issued dynasty, but must be based on a Tibetan structure and court.