{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YNSKRR6CEYIPDKOIVMM6EJO7ZO","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":"36681050ea53774744b04783705282b49a464f7d8057918bf71fa570b474e30e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-05T02:30:55Z","title_canon_sha256":"9cfac3bb51ad60f1c9892920ce766999de1b18b50dcd8a6bda87a81fc64eaa78"},"schema_version":"1.0","source":{"id":"1808.01553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01553","created_at":"2026-05-18T00:08:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01553v1","created_at":"2026-05-18T00:08:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01553","created_at":"2026-05-18T00:08:52Z"},{"alias_kind":"pith_short_12","alias_value":"YNSKRR6CEYIP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YNSKRR6CEYIPDKOI","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YNSKRR6C","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:9dbfdb4ed037ca9b77ac897968a8a11740a947a5901514947ff6e6777a05c8c4","target":"graph","created_at":"2026-05-18T00:08:52Z","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":"This paper investigates the exact number of limit cycles given by the averaging theory of first order for the piecewise smooth integrable non-Hamiltonian system \\begin{eqnarray*} (\\dot{x},\\ \\dot{y})=\\begin{cases} (-y(x+a)^2+\\varepsilon f^+(x,y),\\ x(x+a)^2+\\varepsilon g^+(x,y)),\\ \\ x\\geq0,\\\\ (-y(x+b)^2+\\varepsilon f^-(x,y),\\ x(x+b)^2+\\varepsilon g^-(x,y)),\\ ~ \\, x<0,\\\\ \\end{cases}\\end{eqnarray*} where $ab\\neq 0$, $0<|\\varepsilon|\\ll 1$, and $f^\\pm(x,y)$ and $g^\\pm(x,y)$ are polynomials of degree $n$. It is proved that the exact number of limit cycles emerging from the period annulus surrounding","authors_text":"Jihua Yang, Liqin Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-05T02:30:55Z","title":"Limit cycles appearing from perturbations of cubic piecewise smooth center with double invariant real straight lines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01553","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":"sha256:4a608991ed02cd411077ebf282423f2f3a38f57a47e4735addded2dc80f449c0","target":"record","created_at":"2026-05-18T00:08:52Z","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":"36681050ea53774744b04783705282b49a464f7d8057918bf71fa570b474e30e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-05T02:30:55Z","title_canon_sha256":"9cfac3bb51ad60f1c9892920ce766999de1b18b50dcd8a6bda87a81fc64eaa78"},"schema_version":"1.0","source":{"id":"1808.01553","kind":"arxiv","version":1}},"canonical_sha256":"c364a8c7c22610f1a9c8ab19e225dfcbbad1f876e3025f25e53f065e49b1f34b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c364a8c7c22610f1a9c8ab19e225dfcbbad1f876e3025f25e53f065e49b1f34b","first_computed_at":"2026-05-18T00:08:52.616674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:52.616674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aU3VA4jAB93PfVEFIdfW+rjMKibqw/nRgshO3rHObNLU3xL6fU/qtiw2ulsw6fnUMMQBqVd/CffSNsvMC5lxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:52.617451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a608991ed02cd411077ebf282423f2f3a38f57a47e4735addded2dc80f449c0","sha256:9dbfdb4ed037ca9b77ac897968a8a11740a947a5901514947ff6e6777a05c8c4"],"state_sha256":"6cef43d9da8c5d7bcedc4b17ce9c0f6576e7e9b138a89beb96023f33bc899c9c"}