Formal Algebraic Analysis of Classical Chinese Symbolic Systems (Yixue): Structural Correspondences and Boundary Statements

Abstract: This paper presents a formal algebraic analysis of classical Chinese symbolic systems (Yixue), identifying structural correspondences with quantum mechanics at the level of discrete group theory and combinatorics. Four propositions are verified at explicitly graded rigor levels. First, the Twelve Earthly Branches constitute a cyclic group Z₁₂ that embeds strictly in U(1) ⊂ SU(2), the rotation group of the Bloch sphere, via the chain Z₁₂ ⊂ U(1) ⊂ SU(2). Second, the Z₆₀ Theorem establishes three results concerning the sixty-jiazi cycle: parity preservation under branch opposition (algebraic proof); the distribution of stem differences across the five realizations of branch opposition (complete enumeration of 30 pairs from the Five-Stem Cycle, zero counterexamples); and the exclusion of cross-parity generative relations (direct corollary). Third, the outer ring of the Pre-Heaven hexagram diagram encodes a Gray code — a minimum-Hamming-distance ordering of {0,1}⁶ — verifiable by direct inspection. Fourth, the four trigram pairs listed in Chapter 3 of the Shuogua zhuan correspond exactly to the four body diagonals of the cube inscribed in the Bloch sphere. The paper further identifies a principled translation barrier between the process-ontological framing of Yixue and the state-ontological framing of quantum state formalism, constituting a concrete cross-cultural case study for structural realism and process ontology. All claims are explicitly graded by rigor level; no quantitative predictive claims are made.