{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2ZL3TXN2UGJDM2R6PWBXZ63EH4","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":"e5d358df95d946daf5e9221a92ae248c37664dfc71a3a3445b0668120e227770","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-08T21:23:22Z","title_canon_sha256":"286c5c516189c662bf2720566f8c82a09035e070d2fad1b84850593787ab4d0e"},"schema_version":"1.0","source":{"id":"1501.01987","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.01987","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"arxiv_version","alias_value":"1501.01987v2","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.01987","created_at":"2026-05-18T02:29:17Z"},{"alias_kind":"pith_short_12","alias_value":"2ZL3TXN2UGJD","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2ZL3TXN2UGJDM2R6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2ZL3TXN2","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:d4cb6e633cf1663e7d27d04dbff08db134a7f83247dba3a08d7a487e47e4ef39","target":"graph","created_at":"2026-05-18T02:29:17Z","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 orbits of the reversible differential system $\\dot{x}=-y$, $\\dot{y}=x$, $\\dot{z}=0$, with $x,y \\in R$ and $z\\in R^d$, are periodic with the exception of the equilibrium points $(0,0, z)$. We compute the maximum number of limit cycles which bifurcate from the periodic orbits of the system $\\dot{x}=-y$, $\\dot{y}=x$, $\\dot{z}=0$, using the averaging theory of first order, when this system is perturbed, first inside the class of all polynomial differential systems of degree $n$, and second inside the class of all discontinuous piecewise polynomial differential systems of degree $n$ with two pi","authors_text":"I.O. Zeli, J. Llibre, M.A. Teixeira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-08T21:23:22Z","title":"Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+2)-dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.01987","kind":"arxiv","version":2},"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:be14747e5703804ade7ee328204023a634c54304fb0fc03642dcc5b71da913f1","target":"record","created_at":"2026-05-18T02:29:17Z","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":"e5d358df95d946daf5e9221a92ae248c37664dfc71a3a3445b0668120e227770","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-01-08T21:23:22Z","title_canon_sha256":"286c5c516189c662bf2720566f8c82a09035e070d2fad1b84850593787ab4d0e"},"schema_version":"1.0","source":{"id":"1501.01987","kind":"arxiv","version":2}},"canonical_sha256":"d657b9ddbaa192366a3e7d837cfb643f24f4b9a510834a904a443a55c93bd307","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d657b9ddbaa192366a3e7d837cfb643f24f4b9a510834a904a443a55c93bd307","first_computed_at":"2026-05-18T02:29:17.054862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:17.054862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"37txQgWULDOhdlWFzNDqpfLtAdnSd2bTo1jVbpBuLMPoT2uXDJtCQ5dSE6gRJ1xIt7tfAACibqmt3ySnt8dWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:17.055252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.01987","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be14747e5703804ade7ee328204023a634c54304fb0fc03642dcc5b71da913f1","sha256:d4cb6e633cf1663e7d27d04dbff08db134a7f83247dba3a08d7a487e47e4ef39"],"state_sha256":"a7541e59ef66e5782846dd2483525a49d4c7cd8dcc880b4781a836321d035cd7"}