On the $\Sigma^0_1$-Completeness of Cubic Diophantine Systems and their Consequences for Equations

arXiv:2510.00759v5 Announce Type: replace-cross Abstract: We prove that $\mathrm{H}\mathbb{N}(3,n)=\mathrm{U}$ for some fixed $n$. The core result is a uniform primitive recursive compiler from sentence codes to finite cubic Diophantine systems over $\mathbb{N}$, such that ari...

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