{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KVKNKDDG6Y2PDW7VNTOVPRISFA","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":"4798b399828c9e1eaae5ea8536f8a000a73e2bcf27c187a66d5de30623554673","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-27T15:49:35Z","title_canon_sha256":"507c5d936908fd8855cc9b173b996d4caa8f4362719f1ff86dd560e928981453"},"schema_version":"1.0","source":{"id":"1609.08505","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08505","created_at":"2026-05-18T00:13:07Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08505v1","created_at":"2026-05-18T00:13:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08505","created_at":"2026-05-18T00:13:07Z"},{"alias_kind":"pith_short_12","alias_value":"KVKNKDDG6Y2P","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KVKNKDDG6Y2PDW7V","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KVKNKDDG","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:0703e69d40ec0ba895983a11aae15a1200dc6cde43e05e515960c53920b9f7d7","target":"graph","created_at":"2026-05-18T00:13:07Z","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":"Let $(S,\\Phi)$ be a pair of a closed oriented surface and $\\Phi$ be a real analytic flow with finitely many singularities. Let $x$ be a point of $S$ with the polycycle $\\omega$-limit set $\\omega(x)$. In this paper we give topological classification of $\\omega(x)$. Our main theorem says that $\\omega(x)$ is diffeomorphic to the boundary of a cactus in the $2$-sphere $S^{2}$. Moreover $S$ is a connected sum of the above $S^{2}$ and a closed oriented surface along finitely many embedded circles which are disjoint from $\\omega(x)$. This gives a natural generalization to the higher genus of the main","authors_text":"Hahng-Yun Chu, Jaeyoo Choy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-27T15:49:35Z","title":"Polycycle omega-limit sets of flows on the compact Riemann surfaces and Eulerian path"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08505","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":"sha256:868d949b0f6a6338995ae9717fc123adcbc192ca00afcbe0c675dee16c4f0cac","target":"record","created_at":"2026-05-18T00:13:07Z","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":"4798b399828c9e1eaae5ea8536f8a000a73e2bcf27c187a66d5de30623554673","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-27T15:49:35Z","title_canon_sha256":"507c5d936908fd8855cc9b173b996d4caa8f4362719f1ff86dd560e928981453"},"schema_version":"1.0","source":{"id":"1609.08505","kind":"arxiv","version":1}},"canonical_sha256":"5554d50c66f634f1dbf56cdd57c5122825f8b69b4cfa8dde5357bdfbdc7d160b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5554d50c66f634f1dbf56cdd57c5122825f8b69b4cfa8dde5357bdfbdc7d160b","first_computed_at":"2026-05-18T00:13:07.959958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:07.959958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QK55fWFsX6gUxqp8PgSP9L7W9pApYoePX0Np/znAWQPTnC5IIMcGil9w7IwnWML1/kIz/Pri4gG0mXiceWrkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:07.960875Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08505","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:868d949b0f6a6338995ae9717fc123adcbc192ca00afcbe0c675dee16c4f0cac","sha256:0703e69d40ec0ba895983a11aae15a1200dc6cde43e05e515960c53920b9f7d7"],"state_sha256":"46890f9ccaa62e128a1d5fa587a4904e1d9e68fc55ca336d585343b24240b2e5"}