{"paper":{"title":"Genus two embedded minimal surfaces in $\\mathbb{S}^3$ with dihedral symmetry","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Joaqu\\'in P\\'erez, Jos\\'e M. Espinar","submitted_at":"2025-11-20T12:18:23Z","abstract_excerpt":"We prove that the Lawson surface $\\xi_{2,1}$ is the unique closed embedded minimal surface of genus $2$ in $\\mathbb{S}^3$ whose isometry group contains the dihedral group $D_4$ generated by two reflections across orthogonal totally geodesic two-spheres and a half-turn about a great circle. This weakens the full-symmetry hypotheses in previous characterizations of Lawson surfaces and leads to a substantially different geometric problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.16295","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/2511.16295/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"}