Cài Yuān 蔡淵 (1156–1236), zì Bójìng 伯靜, hào Jiézhāi 節齋, of Jiànyáng 建陽 (Fújiàn). CBDB id 10051. Sòngshǐ biography in juan 434, Rúlín zhuàn.
Eldest son of Cài Yuándìng 蔡元定 (1135–1198), Zhū Xī’s principal scholarly collaborator and the most important xiàngshù-and-numerology specialist of the Zhū-school inner circle (joint author with Zhū Xī of the Yì xué qǐméng 易學啟蒙). Elder brother of Cài Shěn 蔡沈 (1167–1230), author of the canonical Shàngshū jí zhuàn 書集傳.
The Cài family of Jiànyáng — Cài Fā 蔡發 → Cài Yuándìng → Cài Yuān / Cài Shěn / Cài Mò 蔡沕 / Cài Háng 蔡杭 — is the most important late-Sòng Dàoxué scholastic dynasty after the ZhūXī family proper. Cài Yuān succeeded his father as head of the Cài-family scholarly compound at Jiànyáng, presiding over a family-and-academy Yì-pedagogy network that long outlasted the ZhūXí circle proper.
Catalog-vs-external dating: the Kanripo catalog meta gives 1148–1236; CBDB id 10051 and the Sòngshǐ give 1156–1236. The 1156–1236 dating is followed here per the project rule. (The catalog 1148 birth year would have made Cài Yuándìng a father at age 13 — biologically possible but unusual; the standard 1156 leaves Cài Yuándìng at 21 at his eldest son’s birth, which is normal.)
Within the Kanripo corpus he is the author of KR1a0052 Zhōuyì jīngzhuàn xùnjiě 周易經傳訓解 (originally 4 juan; surviving in 2-juan abbreviated form titled Zhōuyì guàyáo jīngzhuàn xùnjiě by a book-dealer’s title-modification) and KR1a0053 Yì xiàng yì yán 易象意言 (1 juan).