{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:EHBLXB4HFOQGVMNXPEJ63MAISV","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":"18ce40c88a2c430f0c1e248e7f9ce062113eea593463a890681e785f76b2b21c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T10:50:03Z","title_canon_sha256":"1fb15dd09d093a0d35568b1bb4f4073072a2d0d92a7d7d5ab18a60f4ee517158"},"schema_version":"1.0","source":{"id":"1109.6470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6470","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6470v1","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6470","created_at":"2026-05-18T04:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"EHBLXB4HFOQG","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"EHBLXB4HFOQGVMNX","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"EHBLXB4H","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:ef514300dee78f802799d8f4a3040383de0ac48e1bf0231dec06fb67e32e277e","target":"graph","created_at":"2026-05-18T04:12:01Z","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":"Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a lower bound of the maximal number of limit cycles. Using the method and basing on some known results for lower degree we obtain new estimations of the number of limit cycles in the systems which greatly improve existing results.","authors_text":"Maoan Han, Valery G. Romanovski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T10:50:03Z","title":"On the number of limit cycles of polynomial Lienard systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6470","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":"sha256:80d1b53e5ebbf67601f540ffddff7a4adb472c08514f2387306ba4fd170f87ea","target":"record","created_at":"2026-05-18T04:12:01Z","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":"18ce40c88a2c430f0c1e248e7f9ce062113eea593463a890681e785f76b2b21c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-29T10:50:03Z","title_canon_sha256":"1fb15dd09d093a0d35568b1bb4f4073072a2d0d92a7d7d5ab18a60f4ee517158"},"schema_version":"1.0","source":{"id":"1109.6470","kind":"arxiv","version":1}},"canonical_sha256":"21c2bb87872ba06ab1b77913edb0089566e6f3585efaab9246e34daf1a010f9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21c2bb87872ba06ab1b77913edb0089566e6f3585efaab9246e34daf1a010f9d","first_computed_at":"2026-05-18T04:12:01.505756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:01.505756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sl5uceZnWCXlc6XI/z0g4GE+YSSEwZ2peGi5s0Ervt0nzeTwxa70CX7Xc+BfGeAI6MK9YOb4q982V1AtjhZWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:01.506254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80d1b53e5ebbf67601f540ffddff7a4adb472c08514f2387306ba4fd170f87ea","sha256:ef514300dee78f802799d8f4a3040383de0ac48e1bf0231dec06fb67e32e277e"],"state_sha256":"9181636830d2bffaff4cdf603141fd01ab149f8f4454d9f77eb59e0aabf63174"}