{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:T4L3GMLHPRGTNW5FNL2KPR233K","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":"21232c857bf3a66f5dffeaef436668f8979275f4babae7206bbdc9fa39935f8d","cross_cats_sorted":["math.DG","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-22T18:36:50Z","title_canon_sha256":"41a6b0479a2af6cbb0d2c5deef3d197bb85c52a0b2ec4e314cc7067da6c9338b"},"schema_version":"1.0","source":{"id":"1111.5277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5277","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5277v1","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5277","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"pith_short_12","alias_value":"T4L3GMLHPRGT","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"T4L3GMLHPRGTNW5F","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"T4L3GMLH","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:0885f7bf9947a0d5b350560c738a674fad08d6432efae5de67ae11c78966f313","target":"graph","created_at":"2026-05-18T01:23:10Z","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":"The problem on the minimal number (with respect to deformation) of intersection points of two closed curves on a surface is solved. Following the Nielsen approach, we define classes of intersection points and essential classes of intersection points, which \"are preserved under deformation\" and whose total number is called the Nielsen number. If each Nielsen class consists of a unique point and has a non-vanishing index after a suitable deformation of the pair of curves, one says that {\\it the Wecken property holds}. We compute the minimal number of intersection points in terms of the Nielsen n","authors_text":"Elena A. Kudryavtseva, Heiner Zieschang, Semeon A. Bogatyi","cross_cats":["math.DG","math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-22T18:36:50Z","title":"On intersections of closed curves on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5277","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":"sha256:31e65f7fe2a260412fc8e3060e1a8bb61cffb6f0a2abb17a9a94e5d5c7c208e6","target":"record","created_at":"2026-05-18T01:23:10Z","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":"21232c857bf3a66f5dffeaef436668f8979275f4babae7206bbdc9fa39935f8d","cross_cats_sorted":["math.DG","math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-22T18:36:50Z","title_canon_sha256":"41a6b0479a2af6cbb0d2c5deef3d197bb85c52a0b2ec4e314cc7067da6c9338b"},"schema_version":"1.0","source":{"id":"1111.5277","kind":"arxiv","version":1}},"canonical_sha256":"9f17b331677c4d36dba56af4a7c75bda91ce97b28f07ea592d272c7400e8faac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f17b331677c4d36dba56af4a7c75bda91ce97b28f07ea592d272c7400e8faac","first_computed_at":"2026-05-18T01:23:10.758070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:10.758070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C1avH0MYgdBRgngbDTuFJ34bYliV88c6+CzJJOOPU6J9HGbS7EzvAJqEUN1SbqdZuSXalw5GtyQtJEtYKBXSCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:10.758557Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31e65f7fe2a260412fc8e3060e1a8bb61cffb6f0a2abb17a9a94e5d5c7c208e6","sha256:0885f7bf9947a0d5b350560c738a674fad08d6432efae5de67ae11c78966f313"],"state_sha256":"953a17df005bfa3d2d6c4e76ee27fec9c8ba67a5f01cd60f2ce9e504206d8e22"}