A Proposal for a New Mathematical Framework: The Constant Decomposition Axiom and Asymptotic Point System
Year: 2026
Type: preprint
Abstract: This paper presents a foundational study of constant decomposition and directional state limits. The central expression is A = limA + lim0, where limA is not the standard limit operator, but a state-number symbol representing a value that approaches A without being identified with A itself. Likewise, lim0 is not zero itself, but a difference state number representing the remaining gap. The study introduces the N-th digit difference state number lim0_N, directional signs for approaches from below and above, and shows that the full binomial expansion of the state number and the difference state number restores A^m for natural-number exponents m. It also develops N-block digit laws describing how digit blocks appear in upper and lower approaches, with direct verifications for the square, cube, and fourth power. This work proposes a state-number framework for recording how constant decomposition is preserved and restored through arithmetic expansion and radix digit structures.
Author: Cha, Seungpyo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160252840
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