{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2PZEPXPOIZSSDVED5KYG5QDHEI","short_pith_number":"pith:2PZEPXPO","canonical_record":{"source":{"id":"1708.07168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-23T19:57:19Z","cross_cats_sorted":[],"title_canon_sha256":"b715e7a4cf6e1200e414f3a9bb58677b40407d008222396ddaf917b745a75891","abstract_canon_sha256":"bd0787d7f7ad3cfa575b1d2d6b597321fd2b7c1d67c78444932dc909d689d28d"},"schema_version":"1.0"},"canonical_sha256":"d3f247ddee466521d483eab06ec0672223666f5902e709ef4243e591fd292bdd","source":{"kind":"arxiv","id":"1708.07168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07168","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07168v1","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07168","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"2PZEPXPOIZSS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PZEPXPOIZSSDVED","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PZEPXPO","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2PZEPXPOIZSSDVED5KYG5QDHEI","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-23T19:57:19Z","cross_cats_sorted":[],"title_canon_sha256":"b715e7a4cf6e1200e414f3a9bb58677b40407d008222396ddaf917b745a75891","abstract_canon_sha256":"bd0787d7f7ad3cfa575b1d2d6b597321fd2b7c1d67c78444932dc909d689d28d"},"schema_version":"1.0"},"canonical_sha256":"d3f247ddee466521d483eab06ec0672223666f5902e709ef4243e591fd292bdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:47.035612Z","signature_b64":"h5rrO3zUmmIhhIRmi1VOaeLAyYMRcAcrT2cn3/LBVeZotZDEtSZNjttTs+B92NCwvYRIzWSiv6TYYy2U9b3+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d3f247ddee466521d483eab06ec0672223666f5902e709ef4243e591fd292bdd","last_reissued_at":"2026-05-18T00:36:47.035008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:47.035008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07168","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":"2026-05-18T00:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5Ep8+ZIPyLuymqoGMarpOP3IA8RmrNPepAqcN7ckaDEemmWlgpR0vyioT70rTl6g7cEv+EDKSf+8cvX6E6yAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T04:47:54.628684Z"},"content_sha256":"1a3ec8fcab868b4fd8905c0c74c164f2d5aba9374cc48b32d2dffa879ef059a3","schema_version":"1.0","event_id":"sha256:1a3ec8fcab868b4fd8905c0c74c164f2d5aba9374cc48b32d2dffa879ef059a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2PZEPXPOIZSSDVED5KYG5QDHEI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of limit cycles and invariant surfaces of sewing piecewise linear differential systems on $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bruno Rodrigues de Freitas, Jo\\~ao Carlos Medrado","submitted_at":"2017-08-23T19:57:19Z","abstract_excerpt":"We consider a class of discontinuous piecewise linear differential systems in $\\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique one-parameter family of periodic orbits, scrolls, invariant cylinders foliated by orbits which can be periodic or no."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07168","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":"2026-05-18T00:36:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tF4Aqok2VUbGpibVhReRAb8yAleJ8Tl3AJcEpK/MOh+ThjEfcxm6c92HnclYgTl+4IdzdRxxjIBjXuklTpRZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T04:47:54.629023Z"},"content_sha256":"830ffb9af912cc36db8f3c09d3533d3c195c5680b5ab434eb8334e085c5862fc","schema_version":"1.0","event_id":"sha256:830ffb9af912cc36db8f3c09d3533d3c195c5680b5ab434eb8334e085c5862fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2PZEPXPOIZSSDVED5KYG5QDHEI/bundle.json","state_url":"https://pith.science/pith/2PZEPXPOIZSSDVED5KYG5QDHEI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2PZEPXPOIZSSDVED5KYG5QDHEI/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":"2026-07-03T04:47:54Z","links":{"resolver":"https://pith.science/pith/2PZEPXPOIZSSDVED5KYG5QDHEI","bundle":"https://pith.science/pith/2PZEPXPOIZSSDVED5KYG5QDHEI/bundle.json","state":"https://pith.science/pith/2PZEPXPOIZSSDVED5KYG5QDHEI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2PZEPXPOIZSSDVED5KYG5QDHEI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2PZEPXPOIZSSDVED5KYG5QDHEI","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":"bd0787d7f7ad3cfa575b1d2d6b597321fd2b7c1d67c78444932dc909d689d28d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-23T19:57:19Z","title_canon_sha256":"b715e7a4cf6e1200e414f3a9bb58677b40407d008222396ddaf917b745a75891"},"schema_version":"1.0","source":{"id":"1708.07168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07168","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07168v1","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07168","created_at":"2026-05-18T00:36:47Z"},{"alias_kind":"pith_short_12","alias_value":"2PZEPXPOIZSS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2PZEPXPOIZSSDVED","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2PZEPXPO","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:830ffb9af912cc36db8f3c09d3533d3c195c5680b5ab434eb8334e085c5862fc","target":"graph","created_at":"2026-05-18T00:36:47Z","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 a class of discontinuous piecewise linear differential systems in $\\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique one-parameter family of periodic orbits, scrolls, invariant cylinders foliated by orbits which can be periodic or no.","authors_text":"Bruno Rodrigues de Freitas, Jo\\~ao Carlos Medrado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-23T19:57:19Z","title":"On the existence of limit cycles and invariant surfaces of sewing piecewise linear differential systems on $\\mathbb{R}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07168","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":"sha256:1a3ec8fcab868b4fd8905c0c74c164f2d5aba9374cc48b32d2dffa879ef059a3","target":"record","created_at":"2026-05-18T00:36:47Z","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":"bd0787d7f7ad3cfa575b1d2d6b597321fd2b7c1d67c78444932dc909d689d28d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-08-23T19:57:19Z","title_canon_sha256":"b715e7a4cf6e1200e414f3a9bb58677b40407d008222396ddaf917b745a75891"},"schema_version":"1.0","source":{"id":"1708.07168","kind":"arxiv","version":1}},"canonical_sha256":"d3f247ddee466521d483eab06ec0672223666f5902e709ef4243e591fd292bdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3f247ddee466521d483eab06ec0672223666f5902e709ef4243e591fd292bdd","first_computed_at":"2026-05-18T00:36:47.035008Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:47.035008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h5rrO3zUmmIhhIRmi1VOaeLAyYMRcAcrT2cn3/LBVeZotZDEtSZNjttTs+B92NCwvYRIzWSiv6TYYy2U9b3+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:47.035612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a3ec8fcab868b4fd8905c0c74c164f2d5aba9374cc48b32d2dffa879ef059a3","sha256:830ffb9af912cc36db8f3c09d3533d3c195c5680b5ab434eb8334e085c5862fc"],"state_sha256":"29a3a4577d50d77cf0fc924a2b8ff7f3673673f74f1aafdd133cc99cc82616f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DChluB9oZ0CiuMIrChwQOBejuOyPbdsFvhEvz0H1dJ0psPmQx95EeTyCWaGF0wzTHVYWrQ+QEdv6oyXhd6hNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T04:47:54.630883Z","bundle_sha256":"d6019fe7af9447a587829c202787c939949cb0b20e87ea4257de5241f09665b0"}}