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arXiv · 2510.00759

Considering The Satisfiability of Cubic Diophantine Equations

Milan Rosko
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Abstract

Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every emitted equation has degree at most 3. Degree-3 terms arise only when a linear selector variable activates a quadratic verification obligation. Earlier versions of this manuscript claimed a reduction from unbounded theoremhood to satisfiability of a fixed bounded-domain cubic polynomial instance. That claim is withdrawn. The error and its source are identified precisely. The bounded construction, the degree bookkeeping, and the Zeckendorf-based carryless encoding stand independently of the withdrawn claim. The note closes by identifying the uniformization gap that separates a family of decidable bounded slices from a single many-one reduction target, and records why closing that gap would require a compression principle not supplied here.

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BibTeXRIS

Milan Rosko. 2025-10-01. Considering The Satisfiability of Cubic Diophantine Equations. https://arxiv.org/abs/2510.00759

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