When you people accepted in wearing pants instead of traditional wrap around clothes and hair style like soncoho. Culinary culture had also changed assimilating various Mongol dishes as well.
By the way your original quote was "continuing civilization" in which lineage had been broken countless times.
So changing garments and culinary practise is thus indicative of one culture "taking over" another? That makes it sound like one culture is absorbing and erasing the other.
By your example, then you can say no civilisation on earth is not absorbed by western civilisation due to the penetrance of western clothing, food, media and brands.
Regarding your Mongolia example, do you seriously think your examples are sufficient evidence to say that it was the invading Mongolians whose culture absorbed the chinese, rather than vice versa? Social-political framework, language, and "civilisation" ambition. Do you think the Mongolians absorbed the chinese culture in that regard?
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As for continuity of civilisation, the onus is on you to provide what you perceive as incidences of it being broken.
Personally, i think that apart from measuring civilisation on the basis of physical structures locations and use of a said structures and locations, it is the idea of the civilisation and its physical boundaries that is important. The Roman Empire (and more importantly , its boundaries) is dead because no one believes in it. Same for the mongol empire. Can you provide an example for where no one chinese credibly didn't believe in the idea of china (note not the "chinese empire," but rather simply china, the self titled "Middle Kingdom" ) and its boundaries? Indeed, that was the entire basis of the KMT and CCP, both believed themselves to be the true inheritors of the chinese civilisation, that even after the century of foreign domination, the idea of china had not yet died.
In China's history there have been countless incidences of civil war, foreign invasion (and in more distant times, that was followed up with chinese cultural assimilation of the invader), and more recently, with the century of western and Japanese invasion. But in that time, has the idea of china ever been broken?
Edit: there are also specific philosophies, texts, and practises that also add up to the definition of a civilisation, of course. But I'd argue that due to today's more rapid exchange of ideas and information, the most concrete and undisputable signifiers of a civilisation is both the idea of it (which I understand can be vague and is self reported), and the (more objectively measured) claim of borders and land.