{"paper":{"title":"On defectless unibranched simple extensions, complete distinguished chains and certain stability results","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Arpan Dutta, Rumi Ghosh","submitted_at":"2025-03-10T20:23:05Z","abstract_excerpt":"Let $(K,v)$ be a valued field. Take an extension of $v$ to a fixed algebraic closure $L$ of $K$. In this paper we show that an element $a\\in L$ admits a complete distinguished chain over $K$ if and only if the extension $(K(a)|K,v)$ is defectless and unibranched. This characterization generalizes the known result in the henselian case. In particular, our result shows that if $a$ admits a complete distinguished chain over $K$, then it also admits one over the henselization; however, the converse may not be true. The main tool employed in our analysis is the stability of the $j$-invariant associ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.07830","kind":"arxiv","version":3},"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/2503.07830/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"}