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The views that history is continuous, and that the dynasties are a succession of legitimate reign with the Mandate of Heaven regardless of ethnicities of the rulers, and an unified Zhong Yuan under the rule of a legitimate regime, appear to be Confucian.
This is a product of Han Imperial Confucianism, a la Dong Zhongshu, rather than the original thought of Kong Qiu/Confucius, who spoke hardly anything about the dynastic cycle, the Mandate of Heaven, or a unified regime. Indeed Confucius shied away from any discussion of cosmology or metaphysics. He said only that rulers gain legitimacy through moral authority. The part about ethnicity being irrelevant is even more recent, being developed by the Qing dynasty. The Neo-Confucians had earlier reversed Sima Guang's judgment on the Age of Fragmentation and declared the Northern Dynasties to be illegitimate compared to the Southern Dynasties because the Northern rulers were 'barbarians' - this was of course also a reaction to the claims of the Jurchen and then the Mongols to have inherited the Mandate of Heaven. It took some time for the Qing to convince its Neo-Confucian elite that culture, and not ethnicity, was the determinant of political legitimacy in Chinese civilization.
Confucian political thought is highly moralistic and, in a sense, puritanically conservative. Any ruler who engaged in behaviour considered self-indulgent and pleasure-seeking, and spent a great deal on projects of little public utility, was considered fatuous and decadent. Any ruler who spent a lot on expansionist military campaigns without any clear moral purpose was considered overly ambitious and inconsiderate to the livelihood of the people. Any ruler who sought to rule through strict laws and harsh punishments was considered to be undermining his moral authority by treating the people like criminals rather than educating them about right and wrong. Thus the ideal ruler practices an austere lifestyle, maintains the status quo and refrains from offensive warfare unless the cause is just, sets an example of moral virtue for everyone he rules, selects ministers who are themselves moral exemplars, and promotes education as the best means of maintaining public order and gaining the loyalty of his subjects.
Confucian political thought also had a strong misogynistic (i.e. anti-woman) streak. Women, including the emperor's women, have only two roles - to bear children, and to educate children. Sometimes, an exceptional empress or concubine may have enough moral virtue to counsel the emperor against immoral or unwise behaviour. But most of the time, it is bad news for women to be involved in matters of state, or for a ruler to listen too much to a woman, whether it is his wife or his mother. Women were routinely seen as fickle, unprincipled, superficial, short-sighted, driven by emotions, and lacking in a sense of the greater good. Thus Confucian historians had few good things to say about rulers who liked their women too much, or for women who meddled in politics.