{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JAG6IWQPNKMC6IKRWUGASL4HVD","short_pith_number":"pith:JAG6IWQP","canonical_record":{"source":{"id":"1511.07200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-23T12:44:51Z","cross_cats_sorted":[],"title_canon_sha256":"8449e34819a340a852c6bac1aa14ff413353b2ed8732df2656d0dfeec0c3c6a7","abstract_canon_sha256":"0e4f5822569b7de64c82f8d8cd8ed467afe13573af97b0a1e6cdeba991671855"},"schema_version":"1.0"},"canonical_sha256":"480de45a0f6a982f2151b50c092f87a8d49d72c094698d7bdccceeb6d6d17b3c","source":{"kind":"arxiv","id":"1511.07200","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07200","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07200v1","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07200","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"JAG6IWQPNKMC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAG6IWQPNKMC6IKR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAG6IWQP","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JAG6IWQPNKMC6IKRWUGASL4HVD","target":"record","payload":{"canonical_record":{"source":{"id":"1511.07200","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-23T12:44:51Z","cross_cats_sorted":[],"title_canon_sha256":"8449e34819a340a852c6bac1aa14ff413353b2ed8732df2656d0dfeec0c3c6a7","abstract_canon_sha256":"0e4f5822569b7de64c82f8d8cd8ed467afe13573af97b0a1e6cdeba991671855"},"schema_version":"1.0"},"canonical_sha256":"480de45a0f6a982f2151b50c092f87a8d49d72c094698d7bdccceeb6d6d17b3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:11.977122Z","signature_b64":"oqGb3ydUAL8edJBttfrZrZlHfUXa1jww0vOE6/eFQTnvBxCamCSl2ycKH+t8JpWHeSmovl7R5Delv1NokBdjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480de45a0f6a982f2151b50c092f87a8d49d72c094698d7bdccceeb6d6d17b3c","last_reissued_at":"2026-05-18T01:26:11.976653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:11.976653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.07200","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvfrNpbFFXHTe9YOrNMNV9yVfpZPP5IVPdOcnNjKOr9PHBBSVqYloyTwS/R4/CZils0VeMmboHI/nuGOF1+TAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:36:59.038185Z"},"content_sha256":"16f15433c4c45b4e9d01754fe6f922b8d5974e433e43a58aac6342681eb3f456","schema_version":"1.0","event_id":"sha256:16f15433c4c45b4e9d01754fe6f922b8d5974e433e43a58aac6342681eb3f456"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JAG6IWQPNKMC6IKRWUGASL4HVD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit cycles bifurcating from a period annulus in continuous piecewise differential systems with three zones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Claudio Pessoa, Maur\\'icio F. S. Lima, Weber F. Pereira","submitted_at":"2015-11-23T12:44:51Z","abstract_excerpt":"We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincar\\'e map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits at least two limit cycles that appear by perturbations of a period annulus. Moreover, we describe the bifurcation of the limit cycles for this class through two examples of two-parameter families of piecewise linear vector fields with three zones."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07200","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QhffKrYhDF0T9RuZTVgywYBS01twO/z693MDUGmxgfiSwJ05Y5G2wFkIzPQrbKb2NHBTRQVQVhGB0JoKA0xOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:36:59.038550Z"},"content_sha256":"c8bf7d28f67b8582d73fde4e3ee01180775f687f23b4f4717045ff57c8e460e6","schema_version":"1.0","event_id":"sha256:c8bf7d28f67b8582d73fde4e3ee01180775f687f23b4f4717045ff57c8e460e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAG6IWQPNKMC6IKRWUGASL4HVD/bundle.json","state_url":"https://pith.science/pith/JAG6IWQPNKMC6IKRWUGASL4HVD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAG6IWQPNKMC6IKRWUGASL4HVD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T02:36:59Z","links":{"resolver":"https://pith.science/pith/JAG6IWQPNKMC6IKRWUGASL4HVD","bundle":"https://pith.science/pith/JAG6IWQPNKMC6IKRWUGASL4HVD/bundle.json","state":"https://pith.science/pith/JAG6IWQPNKMC6IKRWUGASL4HVD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAG6IWQPNKMC6IKRWUGASL4HVD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JAG6IWQPNKMC6IKRWUGASL4HVD","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":"0e4f5822569b7de64c82f8d8cd8ed467afe13573af97b0a1e6cdeba991671855","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-23T12:44:51Z","title_canon_sha256":"8449e34819a340a852c6bac1aa14ff413353b2ed8732df2656d0dfeec0c3c6a7"},"schema_version":"1.0","source":{"id":"1511.07200","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.07200","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"arxiv_version","alias_value":"1511.07200v1","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.07200","created_at":"2026-05-18T01:26:11Z"},{"alias_kind":"pith_short_12","alias_value":"JAG6IWQPNKMC","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAG6IWQPNKMC6IKR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAG6IWQP","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:c8bf7d28f67b8582d73fde4e3ee01180775f687f23b4f4717045ff57c8e460e6","target":"graph","created_at":"2026-05-18T01:26:11Z","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 study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincar\\'e map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that this class admits at least two limit cycles that appear by perturbations of a period annulus. Moreover, we describe the bifurcation of the limit cycles for this class through two examples of two-parameter families of piecewise linear vector fields with three zones.","authors_text":"Claudio Pessoa, Maur\\'icio F. S. Lima, Weber F. Pereira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-23T12:44:51Z","title":"Limit cycles bifurcating from a period annulus in continuous piecewise differential systems with three zones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07200","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":"sha256:16f15433c4c45b4e9d01754fe6f922b8d5974e433e43a58aac6342681eb3f456","target":"record","created_at":"2026-05-18T01:26:11Z","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":"0e4f5822569b7de64c82f8d8cd8ed467afe13573af97b0a1e6cdeba991671855","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-11-23T12:44:51Z","title_canon_sha256":"8449e34819a340a852c6bac1aa14ff413353b2ed8732df2656d0dfeec0c3c6a7"},"schema_version":"1.0","source":{"id":"1511.07200","kind":"arxiv","version":1}},"canonical_sha256":"480de45a0f6a982f2151b50c092f87a8d49d72c094698d7bdccceeb6d6d17b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480de45a0f6a982f2151b50c092f87a8d49d72c094698d7bdccceeb6d6d17b3c","first_computed_at":"2026-05-18T01:26:11.976653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:11.976653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oqGb3ydUAL8edJBttfrZrZlHfUXa1jww0vOE6/eFQTnvBxCamCSl2ycKH+t8JpWHeSmovl7R5Delv1NokBdjAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:11.977122Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.07200","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16f15433c4c45b4e9d01754fe6f922b8d5974e433e43a58aac6342681eb3f456","sha256:c8bf7d28f67b8582d73fde4e3ee01180775f687f23b4f4717045ff57c8e460e6"],"state_sha256":"f03cc0ba37829fff43e9ec7464c410fefd5da4e43c3dbd6d9a4b4001bb9f752e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5ZH3yL5dd85C5qEBcAsKgpW7sgA/2DTm22fdkQMHthlznRiiqdD2puMFRtInex7KcL0dX5tUZiJc3K61YhSAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:36:59.040518Z","bundle_sha256":"188240fbb3eadf5f9c77bca6e9505f768ce8c4b05bd24af1409165f04a9cc025"}}