{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7PIKYABLMXMCGASYYLRU7S7BAY","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":"2c8396ba58d4269ae4f647526f9c8f2c661c8005bd0066ee058a5c611685558c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-13T11:36:39Z","title_canon_sha256":"6bdbecb82029f77bdc8e209d4c845dd7ff5a366ff16bfed46a4c404ac554d96e"},"schema_version":"1.0","source":{"id":"1511.04246","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04246","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04246v2","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04246","created_at":"2026-05-18T01:08:12Z"},{"alias_kind":"pith_short_12","alias_value":"7PIKYABLMXMC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7PIKYABLMXMCGASY","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7PIKYABL","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:5ba66d445c412c12e4290e1b42b4f82f2dce347d0fc18fe966af7dbd113f4315","target":"graph","created_at":"2026-05-18T01:08:12Z","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":"We study necessary and sufficient conditions for a meromorphic quadratic differential with prescribed poles to be the Schwarzian derivative of a rational map. We give geometric interpretations of these conditions. We also study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case, the analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.","authors_text":"Guizhen Cui, Lei Tan (LAREMA), Rugh Hans Henrik, Yan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-13T11:36:39Z","title":"Rational maps as Schwarzian primitives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04246","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":"sha256:84fec148e24e128dbb66a0b492851c41182f3e46931fb878c2f46125783a3ac2","target":"record","created_at":"2026-05-18T01:08:12Z","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":"2c8396ba58d4269ae4f647526f9c8f2c661c8005bd0066ee058a5c611685558c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-11-13T11:36:39Z","title_canon_sha256":"6bdbecb82029f77bdc8e209d4c845dd7ff5a366ff16bfed46a4c404ac554d96e"},"schema_version":"1.0","source":{"id":"1511.04246","kind":"arxiv","version":2}},"canonical_sha256":"fbd0ac002b65d8230258c2e34fcbe106175b7f9d87cf0fdf2fc6f00e3d8ae29f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbd0ac002b65d8230258c2e34fcbe106175b7f9d87cf0fdf2fc6f00e3d8ae29f","first_computed_at":"2026-05-18T01:08:12.741395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:12.741395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s+wzrEdwJLMA3r970PlcKzgRyvq1pie6i+ooekF5OfmbVRwp/B1YSmTfU/X4zBmIG+mcm+x3DCyv5hp+MVwFAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:12.741834Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04246","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84fec148e24e128dbb66a0b492851c41182f3e46931fb878c2f46125783a3ac2","sha256:5ba66d445c412c12e4290e1b42b4f82f2dce347d0fc18fe966af7dbd113f4315"],"state_sha256":"321e8a9bfd1b9b6d8a9ce2bc20bc5b276f278158a2e3672b797439944c3824eb"}