{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AATACZOI3GOQWGK6O5QLLQ3OB5","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":"3e5b487cc3fcc599e646a39d1f97c39b32f21261c3ad4b509d3f4181bda4dc0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-25T17:49:05Z","title_canon_sha256":"fdb7a356b0f576b3cbea1705050ad8f44f66d5a7007eda26747cfbe924b82fea"},"schema_version":"1.0","source":{"id":"1407.6986","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6986","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6986v1","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6986","created_at":"2026-05-18T02:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"AATACZOI3GOQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AATACZOI3GOQWGK6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AATACZOI","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:ce61d66abca36d1a43f0b8ad025fa9ac46f900d6259ea4579d733bbaa41a8e24","target":"graph","created_at":"2026-05-18T02:46:31Z","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 term \"hybrid system\" refers to a continuous time dynamical system that undergoes Markovian perturbations at discrete time intervals. In this paper, we find that under the right formulation, a hybrid system can be treated as a dynamical system on a compact space. This allows one to study its limit sets. We examine the Morse decompositions of hybrid systems, find a sufficient condition for the existence of a non-trivial Morse decomposition, and study the Morse sets of such a decomposition. Finally, we consider the case in which the Markovian perturbations are small, showing that trajectories","authors_text":"Anthony Sanchez, Emily Speranza, Jennifer Kunze, Kimberly Ayers, Sijing Shao, Thomas Rudelius, Xavier Garcia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-25T17:49:05Z","title":"Limit and Morse Sets for Deterministic Hybrid Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6986","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":"sha256:35ffcbd16cc1482329b0778ffabe9d5727188561c4fb319de85435425126acb9","target":"record","created_at":"2026-05-18T02:46:31Z","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":"3e5b487cc3fcc599e646a39d1f97c39b32f21261c3ad4b509d3f4181bda4dc0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-07-25T17:49:05Z","title_canon_sha256":"fdb7a356b0f576b3cbea1705050ad8f44f66d5a7007eda26747cfbe924b82fea"},"schema_version":"1.0","source":{"id":"1407.6986","kind":"arxiv","version":1}},"canonical_sha256":"00260165c8d99d0b195e7760b5c36e0f5d2c0d5401b027cb93aa87dbf33fa914","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00260165c8d99d0b195e7760b5c36e0f5d2c0d5401b027cb93aa87dbf33fa914","first_computed_at":"2026-05-18T02:46:31.933516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:31.933516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5GE+fePNeom6Lmn4XPmbFaoL3YnX87D80pKnNDEL6w5EEnBiPlhIKlXKNnLSoqiAvZdI5+d51RivRI3Gk820CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:31.933982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6986","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35ffcbd16cc1482329b0778ffabe9d5727188561c4fb319de85435425126acb9","sha256:ce61d66abca36d1a43f0b8ad025fa9ac46f900d6259ea4579d733bbaa41a8e24"],"state_sha256":"23753351f1b8abe733776ef9854c31b404cf368483268bd314e1da79823b870c"}