Final answer:
The core of the Chinese state government from the Song dynasty to the early 20th century centered on the ideological debate between small and powerful government, the commandery-county system, and the civil service examination system, all under the mandate of the Mandate of Heaven.
Step-by-step explanation:
At the heart of Chinese state government from the Song dynasty to the twentieth century was the balance between governance ideas: a smaller government versus a more involved, effective one. The Song Dynasty debate on state ideology brought forth differing views from historical figures like Sima Guang, who advocated for minimal government, and Wang Anshi, who pushed for major reforms. This period also solidified the structure of Chinese governance through the commandery-county system, the Mandate of Heaven, and the civil service examination system, which recruited scholar-officials and mandarins based on their knowledge of Confucianism.
The success and legitimacy of a dynasty were encapsulated in the Mandate of Heaven, a concept which justified the ruler's sovereignty. It posited that the dynastic founder earned this mandate through superiority over rivals and that later rulers were caretakers of the state, tasked with maintaining its structures. Despite various dynastic changes, the system of governance endured, emphasizing ritual, moral virtues, and the selection of officials through exams, which remained until the fall of the monarchy in the early twentieth century.