Operation-Aware Arithmetic (OAA) I: Foundational Axioms and the Information-Preservation Criteria
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2026
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| _version_ | 1866901420620382208 |
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| author | ueda, takashi |
| author_facet | ueda, takashi |
| contents | <p>This paper formalizes the core axioms of Operation-Aware Arithmetic (OAA). We redefine</p> <p>mathematical expressions as dynamic command sequences where information is preserved</p> <p>within the operational history. The solvability of an equation is determined strictly by</p> <p>the bijectivity of its operators or the sequential protection of solution data. We conclude</p> <p>that for degree n ≥ 5, algebraic solvability is possible if and only if the solution formula is</p> <p>encapsulated as a command argument before the application of non-bijective power operators.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19858043 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Operation-Aware Arithmetic (OAA) I: Foundational Axioms and the Information-Preservation Criteria ueda, takashi <p>This paper formalizes the core axioms of Operation-Aware Arithmetic (OAA). We redefine</p> <p>mathematical expressions as dynamic command sequences where information is preserved</p> <p>within the operational history. The solvability of an equation is determined strictly by</p> <p>the bijectivity of its operators or the sequential protection of solution data. We conclude</p> <p>that for degree n ≥ 5, algebraic solvability is possible if and only if the solution formula is</p> <p>encapsulated as a command argument before the application of non-bijective power operators.</p> |
| title | Operation-Aware Arithmetic (OAA) I: Foundational Axioms and the Information-Preservation Criteria |
| url | https://doi.org/10.5281/zenodo.19858043 |