{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DH4NPAYNKLN2ER3T2J7WQFMZLO","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":"db656126a7051a822ae916be48f288d45043c21171b49e9404291edb5aa2c1cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-11T07:58:33Z","title_canon_sha256":"d2c1c54f52dfa4d65b2698649d6b954a12623611c0e445998bc4f30f20489966"},"schema_version":"1.0","source":{"id":"1711.04093","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04093","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04093v3","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04093","created_at":"2026-05-17T23:51:14Z"},{"alias_kind":"pith_short_12","alias_value":"DH4NPAYNKLN2","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DH4NPAYNKLN2ER3T","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DH4NPAYN","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:58032ab4b3844c268ccbe380dcd4de510804576e23508efb4bc6cd8ea267e3e9","target":"graph","created_at":"2026-05-17T23:51:14Z","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":"In this paper, we obtain some estimations of the saddle order which is the sole topological invariant of the non-integrable resonant saddles of planar polynomial vector fields of arbitrary degree $n$. Firstly, we prove that, for any given resonance $p:-q$, $(p, q)=1$, and sufficiently big integer $n$, the maximal saddle order can grow at least as rapidly as $n^2$. Secondly, we show that there exists an integer $k_0$, which grows at least as rapidly as $3n^2/2$, such that $L_{k_0}$ does not belong to the ideal generated by the first $k_0-1$ saddle values $L_1, L_2, \\cdots, L_{k_0-1}$, where $L_","authors_text":"Changjian Liu, Guangfeng Dong, Jiazhong Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-11T07:58:33Z","title":"On the maximal saddle order of p:-q resonant saddle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04093","kind":"arxiv","version":3},"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":"sha256:682d9c3ba356972203511a929fb47c21dd40700a146445ceb5e664771d1e4d30","target":"record","created_at":"2026-05-17T23:51:14Z","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":"db656126a7051a822ae916be48f288d45043c21171b49e9404291edb5aa2c1cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-11T07:58:33Z","title_canon_sha256":"d2c1c54f52dfa4d65b2698649d6b954a12623611c0e445998bc4f30f20489966"},"schema_version":"1.0","source":{"id":"1711.04093","kind":"arxiv","version":3}},"canonical_sha256":"19f8d7830d52dba24773d27f6815995b93051f1d394d16b01506b1731328dc21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19f8d7830d52dba24773d27f6815995b93051f1d394d16b01506b1731328dc21","first_computed_at":"2026-05-17T23:51:14.780840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:14.780840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p4Y2OW90tMMrJFN68T7S5IwhADoR4qfUwZ/CpOjDlCHeW7VcDK5WIoR55cr0fg7U6xPH3X6IJjLV6tnmsV7rBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:14.781401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04093","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:682d9c3ba356972203511a929fb47c21dd40700a146445ceb5e664771d1e4d30","sha256:58032ab4b3844c268ccbe380dcd4de510804576e23508efb4bc6cd8ea267e3e9"],"state_sha256":"305697823ebe0259206cd3dc6b08bfb7e9311e7cf5975f9b97758ab30d3d806f"}