Well...
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I am not sure which one could be considered as the "Chinese Emperor". I prefer that the off-map power should be unavailable since East Asia was just a region with several independent countries in 936, just like Europe.
While the "one Empire" narrative was wrong for all practical purposes throughout most of history, having multiple actual emperors which were recognized by reasonably large groups of Han Chinese (the Emperor's main power base, even under Yuan and Qing rule) was pretty rare. So I'd argue that if you tried to contact "China", someone would answer.