{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ALFSXVO6XXCT364HS3D5YDXZOS","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":"b327f152fde8bb8b8113dd53bd950c6d5716f5f8d9272281e8e3bc1fc9987829","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T15:09:05Z","title_canon_sha256":"b982ccb921898c07324659da11a5914c353d933a744fc59dc72667eb7c5500bb"},"schema_version":"1.0","source":{"id":"1601.05670","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05670","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05670v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05670","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"ALFSXVO6XXCT","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ALFSXVO6XXCT364H","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ALFSXVO6","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:3a972dbed288603322936b7f543f5983dbb3a2f45d28342ca013f084d42c474d","target":"graph","created_at":"2026-05-18T01:22:13Z","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 we study the global dynamics of piecewise smooth vector fields defined in the two dimensional torus and sphere. We provide conditions under these families exhibits periodic and dense trajectories and we describe some global bifurcations. We also study its minimal sets and characterize the chaotic behavior of the piecewise smooth vector fields defined in torus and sphere.","authors_text":"Durval Jos\\'e Tonon, Ricardo Miranda Martins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T15:09:05Z","title":"Chaos in Piecewise Smooth Vector Fields on Two Dimensional Torus and Sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05670","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:cfd531883aeef3c4ec4de25bf58a59c3d5818ff6b0c47ac91420fc1848dd7c33","target":"record","created_at":"2026-05-18T01:22:13Z","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":"b327f152fde8bb8b8113dd53bd950c6d5716f5f8d9272281e8e3bc1fc9987829","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-21T15:09:05Z","title_canon_sha256":"b982ccb921898c07324659da11a5914c353d933a744fc59dc72667eb7c5500bb"},"schema_version":"1.0","source":{"id":"1601.05670","kind":"arxiv","version":1}},"canonical_sha256":"02cb2bd5debdc53dfb8796c7dc0ef9748d62b96d1dd3e20900d574f401bda286","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02cb2bd5debdc53dfb8796c7dc0ef9748d62b96d1dd3e20900d574f401bda286","first_computed_at":"2026-05-18T01:22:13.266858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:13.266858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jMZkA8kmlkoVq/fyTBD6fl0WMMi1s+FVhGbDiEifgi83YTbEUnSvlYmqKRvfhbgZUGtlzx/pRSJGotpxbmSHAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:13.267229Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfd531883aeef3c4ec4de25bf58a59c3d5818ff6b0c47ac91420fc1848dd7c33","sha256:3a972dbed288603322936b7f543f5983dbb3a2f45d28342ca013f084d42c474d"],"state_sha256":"1102ebf44f295625d2443f062279f4a64b21a7c773250af6beaee0e1a5ad6c5b"}