What system served as the foundation of China's imperial political structure?

The foundation of China's imperial political structure was primarily Confucian-based. Confucianism, which emphasizes moral integrity, social harmony, and the importance of hierarchical relationships, shaped the political, social, and educational systems in imperial China. The loyalty to authority and emphasis on benevolent rulers who govern wisely were central tenets that guided the governance of the state.

Confucian principles influenced the selection of government officials through the civil service exam system, which prioritized merit over birthright, although access to these examinations was often limited to the elite. This system established a bureaucracy tasked with maintaining order and implementing the emperor's policies, thus reinforcing the idea that good governance was a moral duty rooted in Confucian ideals.

In contrast, while the feudal system was present in earlier dynasties, especially during the Zhou dynasty, it eventually evolved into a more centralized bureaucracy influenced heavily by Confucianism. Capitalism and socialism, though they have had significant impacts on China in different historical contexts, are not foundational to the imperial structure that was predominantly defined by Confucian thought. This makes the Confucian-based system the correct answer, as it fundamentally shaped the nature of governance throughout most of China's imperial history.