Northern-Sòng 北宋 Yìjīng 易經 numerologist of the Sānqú 三衢 (modern Qúzhōu 衢州, Zhèjiāng) school, zì Xiānzhī 先之 (also 長民 Chángmín). With his contemporary Shào Yōng 邵雍 (1011–1077), Liú Mù is the only member of the early-Sòng 圖書 (“School of Charts and Writings”) Yì-numerology lineage whose works have come down to us in complete form. Active under Sòng Rénzōng 宋仁宗 (r. 1023–1064), Liú Mù was a transmitter of a chart-tradition reportedly received from Fàn Èchāng 范諤昌 ← Xǔ Jiān 許堅 ← Lǐ Gài 李漑 ← Chōng Fàng 种放 ← Chén Tuán 陳摶 (陳摶) — i.e., from the legendary patriarch of the Sòng Yì-tú 易圖 tradition.
His principal works are the Yìshù gōuyǐn tú 易數鉤隱圖 (KR5a0160, DZ 159 / CT 159; “Charts for Probing the Hidden Meaning of the Figures of the Book of Changes”), recorded in the Jùnzhāi dúshū zhì 郡齋讀書志 1.33–34 and abstracted in the Sìkù quánshū zǒngmù tíyào 四庫全書總目提要 2.1a–b, with an editor’s preface in the Tōngzhìtáng jīngjiě 通志堂經解 edition that describes the text’s Sòng transmission; and a posthumous supplement, the Yìshù gōuyǐn tú yílùn jiǔshì 易數鉤隱圖遺論九事 (KR5a0161, DZ 160 / CT 160), which was already incorporated as an appendix in Southern-Sòng editions (Jùnzhāi dúshū zhì 1.134). Old editions of the Yìshù gōuyǐn tú once carried a preface by Ōuyáng Xiū 歐陽修 (1007–1072), later excised because considered likely spurious.
Liú Mù’s contribution to the Sòng Yì-tradition was to produce an integrated chart-commentary on every step of the cosmogonic sequence — tàijí 太極 → liǎngyí 兩儀 → sìxiàng 四象 → bāguà 八卦 — anchored in his “fifty-five charts” (the number of the Hétú 河圖 + Luòshū 洛書 cosmic numerology). His chart-corpus and explanatory technique influenced Zhū Zhèn 朱震 (1072–1138), Zhū Xī 朱熹 (1130–1200), and the entire later xiàngshù 象數 tradition. Pseudonymously, his name was attached to several later chart-compilations, including the [[KR5a0159|Dàyì xiàngshù gōushēn tú]] (DZ 158).
CBDB: 1216. Dates 1011–1064 follow CBDB; biographical sources include Zhèjiāng tōngzhì 浙江通志 123.22b, Xù zīzhì tōngjiàn chángbiān 續資治通鑑長編 197.1b, Guǎngxī tōngzhì 廣西通志 21.15b, and Wáng Ānshí’s 王安石 Wángjīng wén gōng wénjí 王臨川文集 97.1001–1002.