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The Ordinal-Position Category: A Categorical Reconstruction of Wu-Xing for Information Ontology From Z-Encoding and Twin Turing Machines to the Three Fundamental Laws of SSS

• September 2026

• DOI: 

• 10.13140/RG.2.2.23250.93129

• Xiaohui Zou

Rongzhiology (SSS) proposes that sequencing and positioning is the primordial operation from which objecthood, relation, and cross-domain alignment are derived. This paper presents: (1) the equivalence theorem P≡Z, establishing Chinese characters as a single-collection universe under Z-encoding (twin Turing machine dual-lists); (2) the Three Fundamental Laws (A1-A3) as axioms of a new mathematics-Chinese-character mathematics (HanziShuxue)-formalized via ordinal-position category theory; (3) a containment thesis showing that Western mathematical category theory (Mac Lane, Lawvere, Grothendieck) and Aristotelian categorical thought are domain-restricted special cases (Wen and Yi projections respectively) of the ordinal-position category. The framework subsumes matter (M), intention (I), and text-sign (T) domains within a single computable system governed by the Dao-function Φ → 0.

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