The classical framework was only the beginning; the Song dynasty synthesis is a later development in its own right. That later development is Zhu Xi's, and its institutional reach eventually dwarfed anything the classical texts achieved on their own.
Working in the twelfth century, Zhu Xi drew together the metaphysics of earlier Song thinkers, organizing the cosmos around li, an ordering principle, and qi, the vital or material force that principle takes shape through, and used that framework to reinterpret ren, li in its ritual sense, and the other classical virtues as expressions of a single underlying moral principle running through the cosmos and through human nature alike. He also made an editorial decision that mattered as much as his metaphysics: selecting the Analects, the Mencius, and two chapters drawn out of the older Book of Rites, the Great Learning and the Doctrine of the Mean, as a unified curriculum he called the Four Books, arranged with his own extensive commentary and, with a colleague, Lu Zuqian, distilled further into a teaching anthology, Reflections on Things at Hand.
Zhu Xi's Four Books, read through his commentary specifically rather than on their own, became the official basis of the Chinese imperial civil service examinations from the early fourteenth century onward, a curriculum every aspiring official across the empire had to master to hold office, and it held that position for centuries, longer than almost any other single interpretive framework has governed a state's own selection of its administrators anywhere.