{"paper":{"title":"Jet Bundles as Higher-Order Polarised $k$-Contact Manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Javier de Lucas","submitted_at":"2026-06-08T09:33:50Z","abstract_excerpt":"Let $\\pi:E\\to Q$ be a fibred manifold, with $\\dim Q=n$ and rank $m$. We prove that the Cartan distribution $C^r_\\pi$ on $J^r\\pi$ is an $N^r_\\pi$-contact distribution, where $N^r_\\pi=m\\binom{n+r-1}{r-1}$, by giving a natural local construction of an $N^r_\\pi$-contact form. This recovers the canonical structure of $J^r\\pi$ and the Spencer contractions, among other structures. It also yields a natural local Hamiltonian structure on $J^r\\pi$, recovering and extending the standard theory of characteristics to general Lie symmetries of the Cartan distribution.\n  We introduce new classes of polarisat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09263","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/2606.09263/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"}