{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GOVAQFN3E3QBHA4KKWBRPRJVDJ","short_pith_number":"pith:GOVAQFN3","schema_version":"1.0","canonical_sha256":"33aa0815bb26e013838a558317c5351a4910fc39f9dababbc8a812cc46bd9782","source":{"kind":"arxiv","id":"1702.06314","version":2},"attestation_state":"computed","paper":{"title":"Uniform weak attractivity and criteria for practical global asymptotic stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.OC","authors_text":"Andrii Mironchenko","submitted_at":"2017-02-21T10:14:58Z","abstract_excerpt":"A subset $A$ of the state space is called uniformly globally weakly attractive if for any neighborhood $S$ of $A$ and any bounded subset $B$ there is a uniform finite time $\\tau$ so that any trajectory starting in $B$ intersects $S$ within the time not larger than $\\tau$. We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attractive set. This result is valid for a wide class of distributed parameter systems, including time-delay systems, switched systems, many classes of PDEs and evolution differential equati"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.06314","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-21T10:14:58Z","cross_cats_sorted":["math.AP","math.DS"],"title_canon_sha256":"4fae76c37d9c26b34ec9c2df6722ebe834c04ad57f1808c8b7da05e6b7813d69","abstract_canon_sha256":"b0772b67339868a8a6a1b7ed744e544070f3fe975f736c99d3da151267fc1abf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:53.151567Z","signature_b64":"FY8EXgMMBnOkVJLdl5wTLg1PaiYUvDOrfr+9d3kGCpZnUPDFi1NOGs/IzelCRGMPfynnBPFgswEcbxKDy0IhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33aa0815bb26e013838a558317c5351a4910fc39f9dababbc8a812cc46bd9782","last_reissued_at":"2026-05-18T00:41:53.151048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:53.151048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform weak attractivity and criteria for practical global asymptotic stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS"],"primary_cat":"math.OC","authors_text":"Andrii Mironchenko","submitted_at":"2017-02-21T10:14:58Z","abstract_excerpt":"A subset $A$ of the state space is called uniformly globally weakly attractive if for any neighborhood $S$ of $A$ and any bounded subset $B$ there is a uniform finite time $\\tau$ so that any trajectory starting in $B$ intersects $S$ within the time not larger than $\\tau$. We show that practical uniform global asymptotic stability (pUGAS) is equivalent to the existence of a bounded uniformly globally weakly attractive set. This result is valid for a wide class of distributed parameter systems, including time-delay systems, switched systems, many classes of PDEs and evolution differential equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06314","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1702.06314","created_at":"2026-05-18T00:41:53.151125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.06314v2","created_at":"2026-05-18T00:41:53.151125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06314","created_at":"2026-05-18T00:41:53.151125+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOVAQFN3E3QB","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOVAQFN3E3QBHA4K","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOVAQFN3","created_at":"2026-05-18T12:31:18.294218+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ","json":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ.json","graph_json":"https://pith.science/api/pith-number/GOVAQFN3E3QBHA4KKWBRPRJVDJ/graph.json","events_json":"https://pith.science/api/pith-number/GOVAQFN3E3QBHA4KKWBRPRJVDJ/events.json","paper":"https://pith.science/paper/GOVAQFN3"},"agent_actions":{"view_html":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ","download_json":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ.json","view_paper":"https://pith.science/paper/GOVAQFN3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.06314&json=true","fetch_graph":"https://pith.science/api/pith-number/GOVAQFN3E3QBHA4KKWBRPRJVDJ/graph.json","fetch_events":"https://pith.science/api/pith-number/GOVAQFN3E3QBHA4KKWBRPRJVDJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ/action/storage_attestation","attest_author":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ/action/author_attestation","sign_citation":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ/action/citation_signature","submit_replication":"https://pith.science/pith/GOVAQFN3E3QBHA4KKWBRPRJVDJ/action/replication_record"}},"created_at":"2026-05-18T00:41:53.151125+00:00","updated_at":"2026-05-18T00:41:53.151125+00:00"}