{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:U3NFTCXTR7LAAE7Z6TWVIZM3PM","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":"415b52174114b51aae6b206711a9eae7c19b52ad54052e6bb8e36c22ba3eadfa","cross_cats_sorted":["math.AP","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-07T16:50:45Z","title_canon_sha256":"03c36ce4f1913ea33e6cc7ae14e29cc908566f31bdfe9aa5400797b3528d027e"},"schema_version":"1.0","source":{"id":"1806.02779","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.02779","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.02779v2","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.02779","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"U3NFTCXTR7LA","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"U3NFTCXTR7LAAE7Z","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"U3NFTCXT","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:83746665d91508a3c52a370891838bab7eeebedb270ab9462d2d01865ed9bacc","target":"graph","created_at":"2026-05-18T00:13:09Z","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 this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic stability. We prove that also the converse statement holds without any further requirements on regularity of the system.\n  Furthermore, we give a characterization of uniform global asymptotic stability in terms of the integral stability properties and","authors_text":"Andrii Mironchenko, Fabian Wirth","cross_cats":["math.AP","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-07T16:50:45Z","title":"Existence of non-coercive Lyapunov functions is equivalent to integral uniform global asymptotic stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02779","kind":"arxiv","version":2},"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":"sha256:280f9b1d83205cbad2d0f89bd8fec0aef0bf859fca2be072fb7ff0d058bb8df4","target":"record","created_at":"2026-05-18T00:13:09Z","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":"415b52174114b51aae6b206711a9eae7c19b52ad54052e6bb8e36c22ba3eadfa","cross_cats_sorted":["math.AP","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-07T16:50:45Z","title_canon_sha256":"03c36ce4f1913ea33e6cc7ae14e29cc908566f31bdfe9aa5400797b3528d027e"},"schema_version":"1.0","source":{"id":"1806.02779","kind":"arxiv","version":2}},"canonical_sha256":"a6da598af38fd60013f9f4ed54659b7b29381cd91ea4ecc8331c50f633ff9a68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6da598af38fd60013f9f4ed54659b7b29381cd91ea4ecc8331c50f633ff9a68","first_computed_at":"2026-05-18T00:13:09.898970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:09.898970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bPNpmM95qXEw/12V3pf3TEHOS71lz1yfPNHllrM0LL2KggmDK8JrgTpC4N7XQtRQLvFwcmJpdj7ZFag1fuJsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:09.899599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.02779","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:280f9b1d83205cbad2d0f89bd8fec0aef0bf859fca2be072fb7ff0d058bb8df4","sha256:83746665d91508a3c52a370891838bab7eeebedb270ab9462d2d01865ed9bacc"],"state_sha256":"b8aa843edce25f000c65a1dde52c4161a568b48bd74f87e08d2b0297d163fc6a"}