{"paper":{"title":"Zoll magnetic structures and ruled surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.DG","authors_text":"Gabriel P. Paternain, Jan Bohr","submitted_at":"2026-06-23T21:05:42Z","abstract_excerpt":"A Zoll magnetic system on an oriented closed surface $M$ is a Riemannian metric $g$ together with a function $\\lambda\\colon M\\to \\mathbb{R}$, such that every unit speed solution of the ODE $\\ddot \\gamma(t)=\\lambda(\\gamma(t))\\gamma(t)^\\perp$ is periodic and the minimal period depends continuously on $\\gamma$. The trivial example is given by $g$ with constant curvature $K$ and $\\lambda\\equiv {\\rm const.}$ such that $\\lambda^2+K>0$. This article exhibits non-trivial Zoll magnetic systems for every genus-for genus $\\ge 2$ these are the first such examples.\n  The approach is twistor theoretic: To a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25173","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/2606.25173/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"}