{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BLMNEPYEGRVRQHWXQBT6WSEVZI","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":"8e060fa427c9b9d84972a52d2c17967e8bbf41a3cb0b64077bce29a6b4e4ab9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-27T20:13:20Z","title_canon_sha256":"075a62e936fc62d59d021bb03106e3e69c2a855848a3b7e50209711551c761d1"},"schema_version":"1.0","source":{"id":"1107.5981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5981","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5981v1","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5981","created_at":"2026-05-18T04:16:40Z"},{"alias_kind":"pith_short_12","alias_value":"BLMNEPYEGRVR","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BLMNEPYEGRVRQHWX","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BLMNEPYE","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:8871991d933992863e26d76b7f1687bb8a5598f877a34ca3e3cbed9be2d2f086","target":"graph","created_at":"2026-05-18T04:16:40Z","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 aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the existence of complete Lyapunov functions for semiflows on separable metric spaces.","authors_text":"Mauro Patr\\~ao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-27T20:13:20Z","title":"Existence of complete Lyapunov functions for semiflows on separable metric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5981","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:df869bc75c8f9a83a0673620507aa4b73fc93b060803a1d9ce7cfc71e76ca420","target":"record","created_at":"2026-05-18T04:16:40Z","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":"8e060fa427c9b9d84972a52d2c17967e8bbf41a3cb0b64077bce29a6b4e4ab9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-27T20:13:20Z","title_canon_sha256":"075a62e936fc62d59d021bb03106e3e69c2a855848a3b7e50209711551c761d1"},"schema_version":"1.0","source":{"id":"1107.5981","kind":"arxiv","version":1}},"canonical_sha256":"0ad8d23f04346b181ed78067eb4895ca1b3e992fc3866715d0a0a52d60c12611","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ad8d23f04346b181ed78067eb4895ca1b3e992fc3866715d0a0a52d60c12611","first_computed_at":"2026-05-18T04:16:40.087366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:40.087366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sQqLvwYkxEYGD9noKNLrzAxpDjat5lpn6wPbH3H9fZVLX8DZnavW3ImoClIL9sLz/zBvSZt+GLCDHasN0TFOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:40.087961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df869bc75c8f9a83a0673620507aa4b73fc93b060803a1d9ce7cfc71e76ca420","sha256:8871991d933992863e26d76b7f1687bb8a5598f877a34ca3e3cbed9be2d2f086"],"state_sha256":"e49febcf6a75f7b411300acd4b6e69b5d26e5119baded9381643bf2fbf919ba2"}