{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:LZVJHUHRKGBB54L4NO652QUNOS","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a613dadbf16a74176089c8688a372d1702da329f7aba36673ce400a158590812","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.DG","submitted_at":"2004-02-04T23:21:56Z","title_canon_sha256":"48dabc0310cc4e95a51235e5b844865dbde10907c0a4bd3baaf7b3e299ec6cb5"},"schema_version":"1.0","source":{"id":"math/0402070","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0402070","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0402070v1","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0402070","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"LZVJHUHRKGBB","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"LZVJHUHRKGBB54L4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"LZVJHUHR","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:8a87a0339dd32f2316fd223c33cd60ef81ba47ef9f7120dc099965766f762bcb","target":"graph","created_at":"2026-05-18T02:35:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In the 3-dimensional Riemannian geometry, contact structures equipped with an adapted Riemannian metric are divergence-free, nondegenerate eigenforms of the Laplace-Beltrami operator. We trace out a 2-d analogue of this fact: there is a close relationship between the topology of the contact structure on a convex surface in the 3-manifold (the dividing curves) and the nodal curves of Laplacian eigenfunctions on that surface. Motivated by this relationship, we consider a topological version of Payne's conjecture for the free membrane problem. We construct counterexamples to Payne's conjecture fo","authors_text":"R. Komendarczyk","cross_cats":["math.SP"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2004-02-04T23:21:56Z","title":"On the contact geometry of nodal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0402070","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4822373da22855192141526a93410d41125b0dfa3953f005efe993443ca67848","target":"record","created_at":"2026-05-18T02:35:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a613dadbf16a74176089c8688a372d1702da329f7aba36673ce400a158590812","cross_cats_sorted":["math.SP"],"license":"","primary_cat":"math.DG","submitted_at":"2004-02-04T23:21:56Z","title_canon_sha256":"48dabc0310cc4e95a51235e5b844865dbde10907c0a4bd3baaf7b3e299ec6cb5"},"schema_version":"1.0","source":{"id":"math/0402070","kind":"arxiv","version":1}},"canonical_sha256":"5e6a93d0f151821ef17c6bbddd428d748593d62bef9829e234ac7f01e2d61059","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e6a93d0f151821ef17c6bbddd428d748593d62bef9829e234ac7f01e2d61059","first_computed_at":"2026-05-18T02:35:38.540773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:38.540773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/mp/hfOItUG2XjWm/JCgqAY0n0CPYI/UjTx52Ph4Ca+7zCU0Dox5HjWGtbf2nzJnTqE3dcyTyWv6+CmNDQ2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:38.541467Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0402070","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4822373da22855192141526a93410d41125b0dfa3953f005efe993443ca67848","sha256:8a87a0339dd32f2316fd223c33cd60ef81ba47ef9f7120dc099965766f762bcb"],"state_sha256":"d2a76ea97a00a29d82c05cc00931cc3cabf33d34ca00b232b19d5f8a5e431986"}