{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JAAVTJURLW7NMD5VEIQMQOABTF","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":"7c093661a2e919a99b029257200a210263851fe66d1bd0699c7476c2a5370637","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-06-09T09:10:57Z","title_canon_sha256":"61004db743e837bcdc60e345dc791460813993db1b2b901227b8b21ac8f86113"},"schema_version":"1.0","source":{"id":"1006.1749","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1749","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1749v3","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1749","created_at":"2026-05-18T03:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"JAAVTJURLW7N","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JAAVTJURLW7NMD5V","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JAAVTJUR","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:785169cbeb1b9f944c9fc0f51ee4735c1822c9f512292651be7935c412a61976","target":"graph","created_at":"2026-05-18T03:40:14Z","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 consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes.","authors_text":"Falk Hante (IECN, Inria Lorraine / Iecn / Mmas), Mario Sigalotti (IECN","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-06-09T09:10:57Z","title":"Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1749","kind":"arxiv","version":3},"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":"sha256:8cafbf9a1b64e7d2f065828af66f32869abba59d6ea946d658418d61a805db38","target":"record","created_at":"2026-05-18T03:40:14Z","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":"7c093661a2e919a99b029257200a210263851fe66d1bd0699c7476c2a5370637","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-06-09T09:10:57Z","title_canon_sha256":"61004db743e837bcdc60e345dc791460813993db1b2b901227b8b21ac8f86113"},"schema_version":"1.0","source":{"id":"1006.1749","kind":"arxiv","version":3}},"canonical_sha256":"480159a6915dbed60fb52220c83801996627b425c4b51cf98f7a107759e1525b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480159a6915dbed60fb52220c83801996627b425c4b51cf98f7a107759e1525b","first_computed_at":"2026-05-18T03:40:14.681816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:14.681816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"29SsSax4R+uVHoVCg/Q9NiWPNPnio2NX68z4E0QU4TbL9THSsV7YB1xLzaGeP/QhIboPgOr7fVr1dpKCSnHzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:14.684027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1749","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8cafbf9a1b64e7d2f065828af66f32869abba59d6ea946d658418d61a805db38","sha256:785169cbeb1b9f944c9fc0f51ee4735c1822c9f512292651be7935c412a61976"],"state_sha256":"7c6f7b9f4a2ac2cd7f49c551660fac2ddb180126bf05b63636a27afd33a00154"}