{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QZ2Z3E466KFEJOVUBLSGQRJ2GK","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":"9ab311be0728225e4259736c975517d48f67fee20d91a580ca69b9ac02858165","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-08T03:51:35Z","title_canon_sha256":"9d3634cb1d5b78111aa3d338fe1edf2a8785206a8f577eac810024edde477de5"},"schema_version":"1.0","source":{"id":"1311.1877","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1877","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1877v2","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1877","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"QZ2Z3E466KFE","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QZ2Z3E466KFEJOVU","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QZ2Z3E46","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:cac76828a240714d846cb5f65e50bcf65739da3371c3c5188071d1ef31f3aa3a","target":"graph","created_at":"2026-05-18T02:48:17Z","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 first, second and fourth Painlev\\'{e} equations are studied by means of dynamical systems theory and three dimensional weighted projective spaces $\\C P^3(p,q,r,s)$ with suitable weights $(p,q,r,s)$ determined by the Newton diagrams of the equations or the versal deformations of vector fields. Singular normal forms of the equations, a simple proof of the Painlev\\'{e} property and symplectic atlases of the spaces of initial conditions are given with the aid of the orbifold structure of $\\C P^3(p,q,r,s)$. In particular, for the first Painlev\\'{e} equation, a well known Painlev\\'{e}'s transfor","authors_text":"Hayato Chiba","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-08T03:51:35Z","title":"The first, second and fourth Painlev\\'{e} equations on weighted projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1877","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:bd7f665bf0556481953004f755f357c1d1601a958db2a432e39327337a5a400c","target":"record","created_at":"2026-05-18T02:48:17Z","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":"9ab311be0728225e4259736c975517d48f67fee20d91a580ca69b9ac02858165","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-08T03:51:35Z","title_canon_sha256":"9d3634cb1d5b78111aa3d338fe1edf2a8785206a8f577eac810024edde477de5"},"schema_version":"1.0","source":{"id":"1311.1877","kind":"arxiv","version":2}},"canonical_sha256":"86759d939ef28a44bab40ae468453a32ab605c2752e76c29755039283b275bf8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86759d939ef28a44bab40ae468453a32ab605c2752e76c29755039283b275bf8","first_computed_at":"2026-05-18T02:48:17.516021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.516021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qw0jwE7JgRsP+j7zZrxTPiDVY5/36rWT3HXuCAVv3tnJnV602OwvLWP5fvLtEe/2g2nHEmuADlZdz925PfsHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.516574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1877","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd7f665bf0556481953004f755f357c1d1601a958db2a432e39327337a5a400c","sha256:cac76828a240714d846cb5f65e50bcf65739da3371c3c5188071d1ef31f3aa3a"],"state_sha256":"5e1006265167adb5ba3edba677a80a24a97569e65e7a20d39a06f9f977831958"}