{"paper":{"title":"An organizing principle in the study of the Jacobian Conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Frederico Xavier","submitted_at":"2026-06-20T13:43:19Z","abstract_excerpt":"Let $\\Omega$ be an irreducible component of the locus of polynomial maps $ F:\\mathbb C^n \\to \\mathbb C^n$ satisfying $\\text{\\rm deg} F\\leq k$ and $\\text{det}DF=1$. It is shown that either $\\Omega \\subset \\text{\\rm Aut} (\\mathbb C^n)$, as claimed by the Jacobian Conjecture, or the {\\em general} $F\\in \\Omega$ is not an automorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22041","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/2606.22041/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"}