{"paper":{"title":"On the additive structure of algebraic valuations of polynomial semirings II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Alan Yao, Felix Gotti, Timothy Chen, Tony Lu","submitted_at":"2026-07-03T02:20:56Z","abstract_excerpt":"For $\\alpha \\in \\mathbb{C}$, let $\\mathbb{N}_0[\\alpha]$ be the subsemiring of~$\\mathbb{C}$ obtained as a homomorphic image of the $\\alpha$-evaluation map $\\mathbb{N}_0[x] \\to \\mathbb{C}$ defined as $p(x) \\mapsto p(\\alpha)$ for each polynomial $p(x) \\in \\mathbb{N}_0[x]$. Fundamental arithmetic and atomic aspects of the additive structure of $\\mathbb{N}_0[\\alpha]$ were first studied by the second author and Correa-Morris (2022). In this paper, we continue the investigation, now from the valuation-theoretic perspective.\n  We show that for any algebraic number $\\alpha$, the additive monoid of $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02874","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.02874/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}