{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:KJDUOEPGU7DM7XKLTMUFCT5NA7","short_pith_number":"pith:KJDUOEPG","schema_version":"1.0","canonical_sha256":"52474711e6a7c6cfdd4b9b28514fad07deaa2ab3efb5f91fdf64775c443b800c","source":{"kind":"arxiv","id":"1801.09014","version":1},"attestation_state":"computed","paper":{"title":"Poincar\\'e-Bendixson Theorem for Hybrid Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC","nlin.CD"],"primary_cat":"math.DS","authors_text":"Anthony Bloch, Leonardo Colombo, William Clark","submitted_at":"2018-01-27T00:48:09Z","abstract_excerpt":"The Poincar\\'e-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincar\\'e-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincar\\'e return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincar\\'e-Bendixson Theorem for a class of one dimensional hybrid dynamical systems."},"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":"1801.09014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-01-27T00:48:09Z","cross_cats_sorted":["cs.SY","math.OC","nlin.CD"],"title_canon_sha256":"f6a1313dfb84c73db64ff24c94e6545c76276c9df89c5eef70c25c48b0a32b8e","abstract_canon_sha256":"a98b719c789a3800e4c961bb4e58209d8da97944c139e7dac78dfe50d2e26fba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:58.879656Z","signature_b64":"8vQKymhJ8PVO0aMLKLWIikuANlwHsaIY1Zqf6asLXOplG64DP9pV/sBNwwUMkoBA4dxUI7DOocN1w9nKi3joAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52474711e6a7c6cfdd4b9b28514fad07deaa2ab3efb5f91fdf64775c443b800c","last_reissued_at":"2026-05-18T00:24:58.879018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:58.879018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e-Bendixson Theorem for Hybrid Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.OC","nlin.CD"],"primary_cat":"math.DS","authors_text":"Anthony Bloch, Leonardo Colombo, William Clark","submitted_at":"2018-01-27T00:48:09Z","abstract_excerpt":"The Poincar\\'e-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincar\\'e-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincar\\'e return map, a useful object for the stability analysis of hybrid systems. We also prove a Poincar\\'e-Bendixson Theorem for a class of one dimensional hybrid dynamical systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09014","kind":"arxiv","version":1},"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":"1801.09014","created_at":"2026-05-18T00:24:58.879126+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.09014v1","created_at":"2026-05-18T00:24:58.879126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09014","created_at":"2026-05-18T00:24:58.879126+00:00"},{"alias_kind":"pith_short_12","alias_value":"KJDUOEPGU7DM","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_16","alias_value":"KJDUOEPGU7DM7XKL","created_at":"2026-05-18T12:32:33.847187+00:00"},{"alias_kind":"pith_short_8","alias_value":"KJDUOEPG","created_at":"2026-05-18T12:32:33.847187+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/KJDUOEPGU7DM7XKLTMUFCT5NA7","json":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7.json","graph_json":"https://pith.science/api/pith-number/KJDUOEPGU7DM7XKLTMUFCT5NA7/graph.json","events_json":"https://pith.science/api/pith-number/KJDUOEPGU7DM7XKLTMUFCT5NA7/events.json","paper":"https://pith.science/paper/KJDUOEPG"},"agent_actions":{"view_html":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7","download_json":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7.json","view_paper":"https://pith.science/paper/KJDUOEPG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.09014&json=true","fetch_graph":"https://pith.science/api/pith-number/KJDUOEPGU7DM7XKLTMUFCT5NA7/graph.json","fetch_events":"https://pith.science/api/pith-number/KJDUOEPGU7DM7XKLTMUFCT5NA7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7/action/storage_attestation","attest_author":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7/action/author_attestation","sign_citation":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7/action/citation_signature","submit_replication":"https://pith.science/pith/KJDUOEPGU7DM7XKLTMUFCT5NA7/action/replication_record"}},"created_at":"2026-05-18T00:24:58.879126+00:00","updated_at":"2026-05-18T00:24:58.879126+00:00"}