{"paper":{"title":"Nested nodal loops of biharmonic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Logunov, Javier G\\'omez-Serrano, Robert Koirala","submitted_at":"2026-05-18T17:36:21Z","abstract_excerpt":"Given any \\(n\\in\\mathbb{N}\\), we construct a real-valued biharmonic polynomial on \\(\\mathbb{R}^2\\) whose zero set contains a nest of \\(n\\) smooth, disjoint topological loops, meaning that the \\(k\\)-th loop lies inside the domain bounded by the \\((k+1)\\)-st loop for \\(k=1,\\ldots,n-1\\). The case \\(n=2\\), i.e., the existence of two nested loops, is related to the failure of the Boggio-Hadamard conjecture from the early 1900s."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18699","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/2605.18699/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.080917Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"00c793a0a76e9713d448103b23efc6427a47de33a7d15abc5975d967ab4ca225"},"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"}