{"paper":{"title":"An autonomous Lipschitz fast dynamo on the three-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Lukas Niebel","submitted_at":"2026-08-03T17:55:29Z","abstract_excerpt":"We construct a single real-valued, divergence-free, time-independent velocity field $u\\in\\mathrm{W}^{1,\\infty}(\\mathbb{T}^3;\\mathbb{R}^3) $ that is a fast dynamo for the kinematic induction equation on the flat three-torus. For every sufficiently small positive magnetic diffusivity, the corresponding induction operator has an eigenvalue whose real part is bounded below by a positive constant independent of the diffusivity. For each such diffusivity, there is a non-zero real-valued, divergence-free solution of the induction equation whose $\\mathrm{L}^2 $-norm obeys an exact exponential growth l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02586","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/2608.02586/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"}