Method

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Ordinal-Positional Conservation as the Pivot of P/Z Dual Formalization: With Ordinal Position Unifying Principle and the Isomorphic Identities

• September 2026

• DOI: 

• 10.13140/RG.2.2.11942.69446

• Xiaohui Zou

• Shunpeng Zou

P/Z dual formalization is a complete classification of formalization capacity: the P-base handles direct formalization for small, enumerable character sets, while the Z-base handles indirect formalization for large, structured, and open symbol domains. This paper argues that the theoretical pivot of P/Z dual formalization is indirect formalization, and that the invariant which makes indirect formalization computationally and semantically stable is OP Logic-Ordinal-Positional Logic. The decisive claim is that neither ordinal nor positional conservation alone is sufficient: ordinal preservation without positional preservation loses the identity of symbols; positional preservation without ordinal preservation loses the structure of relations. Only their conjunction-OP Logic-makes possible the third conservation, meaning conservation. But meaning itself is composite. The Chinese term for meaning, yiyi, is composed of yi (intention, selection) and yi (ordinal position). This yields the core Abstract identity of Synergistic Intelligence: Meaning = Intention + Ordinal Position. (1) The machine conserves ordinal position (L1/L2); the human selects intention (L3); their conjunction yields meaning. This is isomorphic to the formula Intelligence = Information Processing + Intention Selection. (2) Together they define the new era of human-machine mutual assistance. We prove a con-junctive theorem: OP Logic holds if and only if the ordinal-positional invariant I(x) = (op(x), id(x), ge(x)) is preserved under generation. Ordinal position is shown to unify principle , meaning, and law within a single formal field. We situate this result in dialogue with Gödel's incompleteness, Leibniz's characteristica universalis, the three AI schools, and contemporary large language models. The layered architecture of the Indirect Formal Method and Indirect Computing Model-a decidable substrate plus open-ended invocation-circumvents rather than avoids Gödelian limits. Engineering evidence includes Chinese patent CN00109380.0 (2000), the 2001 China Patent Expo Gold Award, and the thirteen tables exhibited in 2002. The paper concludes that OP Logic is the unique contribution of Synergistic Intelligence to dual formalization: no other formal system in the world combines ordinal and positional conservation as the foundation of meaning, unifies principle, meaning, and law through ordinal position, decomposes meaning into intention and ordinal position, and defines intelligence as information processing plus intention selection.

Data

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Anonymous Peer Review Compilation.pdf

• September 2026

• Xiaohui Zou

• Shunpeng Zou

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