{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IYPDNTBCAVKMDJK3KNTNOTWKNF","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":"2f93b6792b0e1c251ea3b3a197393bcfefb3626b60aa3593168117b5dece7e51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-10T13:11:18Z","title_canon_sha256":"aac5bcd644fe009bbc4171c93edf7469c584c91789d0ce650fe57bb533adab22"},"schema_version":"1.0","source":{"id":"1303.2319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2319","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2319v1","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2319","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"IYPDNTBCAVKM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IYPDNTBCAVKMDJK3","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IYPDNTBC","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:5c54d6d44236dcd5e627355776dc250dec8f50bdd47f86f9a7b364d49894e363","target":"graph","created_at":"2026-05-18T03:31:19Z","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":"We study the finiteness of uniform sinks for flow. Precisely, we prove that, for $\\alpha>0$ $T>0$, if a vector field $X$ has only hyperbolic singularities or sectionally dissipative singularities, then $X$ can have only finitely many $(\\alpha,T)$-uniform sinks. This is a generalized version of a theorem of Liao","authors_text":"Dawei Yang, Yong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-10T13:11:18Z","title":"On the finiteness of uniform sinks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2319","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:ac688b3abc0444bb829d61430d4a05074f458a309d5a6d1acda096bc554db023","target":"record","created_at":"2026-05-18T03:31:19Z","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":"2f93b6792b0e1c251ea3b3a197393bcfefb3626b60aa3593168117b5dece7e51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-03-10T13:11:18Z","title_canon_sha256":"aac5bcd644fe009bbc4171c93edf7469c584c91789d0ce650fe57bb533adab22"},"schema_version":"1.0","source":{"id":"1303.2319","kind":"arxiv","version":1}},"canonical_sha256":"461e36cc220554c1a55b5366d74eca697f07e886992a8fd49c1343bf30840de4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"461e36cc220554c1a55b5366d74eca697f07e886992a8fd49c1343bf30840de4","first_computed_at":"2026-05-18T03:31:19.354819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:19.354819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oq2caFQ8+TylRrufLG0l2hDdhNyanC/jYrpCoGSsi//0JCU0wtfuZwQxRnwNQrZVaD7veiuzxHmUpeeC2OI7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:19.355515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac688b3abc0444bb829d61430d4a05074f458a309d5a6d1acda096bc554db023","sha256:5c54d6d44236dcd5e627355776dc250dec8f50bdd47f86f9a7b364d49894e363"],"state_sha256":"aab8d44a9156630f58393af505b69f33595ded36bd56a3003a21182edc82d713"}