{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LM3YHJLJ3TWKIK5T75E2N6OYJN","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":"39b777ff6e3820b98e666f1ab89bd2ebfe5ec5ceb45d0cb04ed9c4c206f77d53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-18T07:52:20Z","title_canon_sha256":"a851863d9b0d1b1ec9eaf2f14ab958f55f7bdc7090641e98e0f33b127b30df1d"},"schema_version":"1.0","source":{"id":"1906.07425","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.07425","created_at":"2026-05-17T23:42:41Z"},{"alias_kind":"arxiv_version","alias_value":"1906.07425v3","created_at":"2026-05-17T23:42:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.07425","created_at":"2026-05-17T23:42:41Z"},{"alias_kind":"pith_short_12","alias_value":"LM3YHJLJ3TWK","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LM3YHJLJ3TWKIK5T","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LM3YHJLJ","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:d6c00b00464f13920aa167902cbe66752d57bd184549c0f5349a23f0adb5cb6d","target":"graph","created_at":"2026-05-17T23:42:41Z","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 study the transformations linearizing isochronous centers of planar Hamiltonian differential systems with polynomial Hamiltonian functions $H(x,y)$ having only isolated singularities. Assuming the origin is an isochronous center lying on the level curve $L_0$ defined by $H(x,y)=0$, we prove that, there exists a canonical linearizing transformation analytic on a simply-connected open set $\\Omega$ with closure $\\overline{\\Omega}=\\mathbb{R}^2$, if and only if,\n  $L_0$ consists of only isolated points; furthermore, if the origin is the unique center, then the condition that $L_0$ ","authors_text":"Guangfeng Dong, Yuyi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-18T07:52:20Z","title":"On the transformations linearizing isochronous centers of Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07425","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:cd4d37108c57d085f35635ccb0ebb13550b54ee39b955501da2756bdb7cabe0e","target":"record","created_at":"2026-05-17T23:42:41Z","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":"39b777ff6e3820b98e666f1ab89bd2ebfe5ec5ceb45d0cb04ed9c4c206f77d53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2019-06-18T07:52:20Z","title_canon_sha256":"a851863d9b0d1b1ec9eaf2f14ab958f55f7bdc7090641e98e0f33b127b30df1d"},"schema_version":"1.0","source":{"id":"1906.07425","kind":"arxiv","version":3}},"canonical_sha256":"5b3783a569dceca42bb3ff49a6f9d84b61af65dc7f99cf078c1aa28629c00d1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b3783a569dceca42bb3ff49a6f9d84b61af65dc7f99cf078c1aa28629c00d1d","first_computed_at":"2026-05-17T23:42:41.282990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:41.282990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g81QSOBrNFiby0qWOsOhTOonrRAdECvqeWZVuzNoCJaf4Yz3btlmEzuJU4h8qYyNCqVh8Wp5P/G2ekFD+rIjAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:41.283682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.07425","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd4d37108c57d085f35635ccb0ebb13550b54ee39b955501da2756bdb7cabe0e","sha256:d6c00b00464f13920aa167902cbe66752d57bd184549c0f5349a23f0adb5cb6d"],"state_sha256":"52c4b8a60c52f727378a935b9ea3eba7169c052f7ebf39e7678f64f5805e9302"}