Starting from the mathematical structure of Taiji, the Two Modes, Four Images, and Eight Trigrams in the Book of Changes, this article systematically explores the information-carrying capacity of Bazi and Qimen Dunjia as divinatory systems. Through analysis of Yin-Yang, the Five Phases, the Hetu and Luoshu, and other classical mathematical foundations, it seeks to provide a unified perspective for measuring and comparing the information volume of these two arts.

An in-depth analysis of the philosophical core, the detailed procedure of the Four Operations and Eighteen Transformations, and the mathematical mysteries of non-uniform probability in the Yijing's Great Expansion milfoil divination method, combined with the classic case of Duke Mu of Qin's campaign against Jin from the Zuo Zhuan (Duke Xi, Year 15) to reconstruct the hexagram-interpretation logic of the pre-Qin perspective.

Argued across four dimensions — the judgment text, the line's position, cross-verification between the Classic and its Commentary, and philosophical meaning — this essay shows why the top nine of Hexagram Dayou (Great Possession) stands first among the 384 lines of the Book of Changes: 'Aided by Heaven, fortune — nothing unfavorable' is the only unconditional, supreme judgment in the entire classic, while the Great Treatise, speaking in the Master's own voice, supplies the operative mechanism for attaining such fortune — 'treading on trust, cherishing compliance, and honoring the worthy.'

This article offers an in-depth interpretation of Xiaoman (Grain Full), one of the twenty-four solar terms, drawing on pre-Qin Confucian and Daoist philosophy, philology, astronomy, and phenology. Through the etymology of "full yet not overflowing," and the phenological signs of bitter herbs flourishing and wheat's autumn arriving, it reveals the deep meaning behind why the twenty-four solar terms include a "small fullness" (Xiaoman) but no "great fullness"—illuminating the ancient Chinese wisdom of guarding against excess, prizing humility, of loss following fullness and gain following modesty, of completeness found even in imperfection, and the venerable cosmology of the unity of Heaven and humanity.

A line-by-line reading of the second chapter of the Upper Xici. The sage's four acts -- establishing the hexagrams, observing the images, appending the statements, clarifying fortune and misfortune -- run in exact reverse order to the noble person's four acts -- observing the images, savoring the statements, observing the changes, savoring the divination. The four clauses "is the image of..." form a chain tracing effect back to cause; "the repose in which he dwells" echoes the Doctrine of the Mean's "dwelling in ease, awaiting the Mandate"; and the chapter closes by quoting the top line of hexagram Da You, "From Heaven comes its aid," gathering the whole into the two words compliance and good faith. Grounded in Confucian and Daoist thought, and drawing on the Analects, Mencius, Laozi, Zhuangzi, Xunzi, and the Zuo Tradition, it explores how the noble person finds repose between Heaven and Earth and acts amid change.

This study offers a profound analysis of the *Zhengming* chapter in the *Xunzi*, specifically examining the philosophical implications of "the perfected names of the later kings" and "dispersed names." By situating Xunzi’s theory within the broader discourse of Pre-Qin thought, the article elucidates how the rectification of names functions as a critical nexus for political governance, social order, and epistemological framework.