Operation-Aware Arithmetic (OAA) I: Foundational Axioms and the Information-Preservation Criteria

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1. Verfasser: ueda, takashi
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Veröffentlicht: Zenodo 2026
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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