{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DQS5THQTVQT2OCTV6Y6JCQGUEM","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":"5410ef90872c1a69faa18b9e0d4555c67900240c8d94495eadb86c6922d77ec4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-26T20:53:43Z","title_canon_sha256":"6256e6ce33c99962a971df564ed58256ed6e0cd1bafe8b04abd0491ee085decd"},"schema_version":"1.0","source":{"id":"1302.6457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6457","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6457v2","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6457","created_at":"2026-05-18T01:22:25Z"},{"alias_kind":"pith_short_12","alias_value":"DQS5THQTVQT2","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DQS5THQTVQT2OCTV","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DQS5THQT","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:0e1109a35448ed1798f2cf8ea54e5f3ac0254685847625fad06395b2edc0d732","target":"graph","created_at":"2026-05-18T01:22:25Z","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":"A conformal metric $g$ with constant curvature one and finite conical singularities on a compact Riemann surface $\\Sigma$ can be thought of as the pullback of the standard metric on the 2-sphere by a multi-valued locally univalent meromorphic function $f$ on $\\Sigma\\backslash \\{{\\rm singularities}\\}$, called the {\\it developing map} of the metric $g$. When the developing map $f$ of such a metric $g$ on the compact Riemann surface $\\Sigma$ has reducible monodromy, we show that, up to some M{\\\" o}bius transformation on $f$, the logarithmic differential $d\\,(\\log\\, f)$ of $f$ turns out to be an a","authors_text":"Bin Xu, Qing Chen, Wei Wang, Yingyi Wu","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-26T20:53:43Z","title":"Conformal metrics with constant curvature one and finite conical singularities on compact Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6457","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:cc648e8502c261cf49d150be4a3c37824ef6d3078b88d30210439e2bda803090","target":"record","created_at":"2026-05-18T01:22:25Z","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":"5410ef90872c1a69faa18b9e0d4555c67900240c8d94495eadb86c6922d77ec4","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-26T20:53:43Z","title_canon_sha256":"6256e6ce33c99962a971df564ed58256ed6e0cd1bafe8b04abd0491ee085decd"},"schema_version":"1.0","source":{"id":"1302.6457","kind":"arxiv","version":2}},"canonical_sha256":"1c25d99e13ac27a70a75f63c9140d42337b2feee512045cc3e1eda9883f43d6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c25d99e13ac27a70a75f63c9140d42337b2feee512045cc3e1eda9883f43d6d","first_computed_at":"2026-05-18T01:22:25.663283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:25.663283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1pMoSHGJh52ujkuCs4S80FsoBS1Gd9jbJ3Q2KWNuVuQnuCvHx0UhNuV55HMNVOpZXI7JgjZquH0EiKa2yrjWCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:25.664335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc648e8502c261cf49d150be4a3c37824ef6d3078b88d30210439e2bda803090","sha256:0e1109a35448ed1798f2cf8ea54e5f3ac0254685847625fad06395b2edc0d732"],"state_sha256":"0953d02849bf74a93affb47339a7bd0e112deda94c0c60fa1f6d919f51e01073"}