Sai On in the context of Ryūkyū Kingdom

The Sanzan period (三山時代, Sanzan jidai; lit. 'three mountain period') is a period in the history of the Okinawa Islands when three lines of kings, namely Sanhoku (山北; lit. 'north of the mountain (island)'), Chūzan (中山; lit. 'middle mountain (island)') and Sannan (山南; lit. 'south of the mountain (island)'), are said to have co-existed on Okinawa Island. It is said to have started during King Tamagusuku's reign (traditional dates: 1314–1336) and, according to Sai On's edition of the Chūzan Seifu (1725), ended in 1429 when Shō Hashi unified the island. Historical records of the period are fragmentary and mutually conflicting. Some even question the co-existence of the three polities.

King of Sanhoku (山北王, Sanhoku-ō) was a title given to a line of local rulers on Okinawa Island from the late 14th century to the early 15th century. Contemporary sources on the Kings of Sanhoku are extremely scarce, and narratives on them have gradually been expanded over time. In historiography, the term Sanhoku conveniently refers to a realm supposedly under their control. Sanhoku is also known as Hokuzan (北山). The new term was coined in the 18th century by Sai On by flipping the two-character title.

King of Sannan (山南王, Sannan-ō) was a title given to a line of local rulers on Okinawa Island from the late 14th century to the early 15th century. Contemporary sources on the kings of Sannan are scarce and mutually conflicting. The narratives on the kings have gradually been expanded over time. In historiography, the term Sannan conventionally refers to a realm supposedly under their control. Sannan is also known as Nanzan (南山). The new term was coined in the 18th century by Sai On by flipping the two-character title.

The Chūzan Seifu (中山世譜, Okinawan:Chūzan shīfu; lit. “genealogies of the generations of Chūzan”) is an official history of the Ryūkyū Kingdom. It exists in two versions, the book of Sai Taku (蔡鐸本), compiled by Sai Taku Shitahaku Uēkata Tenshō (蔡鐸 志多伯親方天将) in 1701 and the book of Sai On (蔡溫本), compiled by his son Sai On Gushichan Uēkata Bunjaku (蔡温 具志頭親方文若) in 1725. The two books are integrally written in traditional Chinese characters.