Method

File available

From 0 to 1: Generating the Sub-Universe and Reconstructing Number Systems via the Hyper-Subdomain Order-Position Logic, Linkage Functions, and Five Broad Selections

• September 2026

• DOI: 

• 10.13140/RG.2.2.34411.71203

• Xiaohui Zou

This paper proposes a generative reconstruction of number systems within Rongzhiology order-position logic. Starting from the Dao-function zero point Φ(0), one unit invocation +1 yields the minimal sub-universe S 0 = {0, 1}. The sub-universe is then lifted vertically into layered tuples L n = {0, 1} n , L = ∪ n≥0 L n , and classified horizontally by a classification set Ω that records physical markers, intentional attributes, textual features, and the eight-form carriers. Their joint structure is the hyper-subdomain H = S hier ⊕ S class. The dynamics are carried by three order-position morphisms: µ as tuple morphism for positioning , ϕ as layer functor for precision lifting, and η as cross-domain natural transformation for translation and disambiguation. A linkage function Λ generates sequences and formulas from atomic "speech" units, while the Five Broad Selections (broad language, broad text, broad bilingual , broad translation, broad interpretation) are converted into an order-position selector χ. On this basis, we outline a route from S 0 to N, Z, Q, R, C, and to infinity/continuum discussions. The paper does not claim to replace ZFC, Peano arithmetic, or standard real analysis; it claims only a translation-compatible, generative, layer-stoppable, and semantic-classification-friendly framework that can interface AI mathematics with HI mathematics. 1 Problem and Scope Classical single-brain mathematics usually gives number systems first and 0 later: Peano arithmetic starts from 0 as an initial object and generates natural numbers by succession; set theory defines 0 as the empty set; analytic geometry first gives the number axis and then chooses an origin. Two questions remain under-clarified: first, why can 0 serve as an origin rather than merely an empty symbol; second, how can numbers in different bases, precision layers, and semantic domains share the same order-position coordinates. Rongzhiology reverses the direction of generation: Φ(0) → +1 → S 0 = {0, 1} → ϕ-layer → class → η-cross-domain translation → universal number systems.

支持单位：