{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YL3CLAPX3YYY6NCTMAS7NL46QD","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":"265baf7fcf3713c92397e2e5fcaa5a3a2583bf43401f5bc83f5862628b069824","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-15T06:39:43Z","title_canon_sha256":"f2ae74d751c613859cb6c2c0b4bbab0f0cb2dcbd4f7948542962ffa920331cdd"},"schema_version":"1.0","source":{"id":"1606.04655","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04655","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04655v2","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04655","created_at":"2026-05-18T00:48:42Z"},{"alias_kind":"pith_short_12","alias_value":"YL3CLAPX3YYY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YL3CLAPX3YYY6NCT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YL3CLAPX","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:63398bb15fdde0f3026ad7826bd038993694917b38ff0d2617838faf831dd352","target":"graph","created_at":"2026-05-18T00:48:42Z","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 celebrated and deep theorem in the theory of Riemann surfaces states the existence and uniqueness of the Jenkins-Strebel differentials on a Riemann surface under some conditions, but the proof is non-constructive and examples are difficult to find. This paper deals with an example of a simple case, namely Jenkins-Strebel differentials on the Riemann sphere with four fixed simple poles. We will give explicit expressions of these Jenkins-Strebel differentials by means of the Weierstrass $\\wp$ function and expose a simple algorithm determining the correspondence between these differentials and ","authors_text":"Bin Xu, Xujia Chen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-15T06:39:43Z","title":"Jenkins-Strebel Differentials on the Riemann Sphere with Four Simple Poles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04655","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":"sha256:0fb935c638da7ee76004c679846a31483016ea784ad7825a2eb68305c778b2a9","target":"record","created_at":"2026-05-18T00:48:42Z","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":"265baf7fcf3713c92397e2e5fcaa5a3a2583bf43401f5bc83f5862628b069824","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-06-15T06:39:43Z","title_canon_sha256":"f2ae74d751c613859cb6c2c0b4bbab0f0cb2dcbd4f7948542962ffa920331cdd"},"schema_version":"1.0","source":{"id":"1606.04655","kind":"arxiv","version":2}},"canonical_sha256":"c2f62581f7de318f34536025f6af9e80e6883f218d6a0f7517619de1b06a7385","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2f62581f7de318f34536025f6af9e80e6883f218d6a0f7517619de1b06a7385","first_computed_at":"2026-05-18T00:48:42.648082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:42.648082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3RBRjZbsD/Hoj2LiVWTUTvgl11yKyN/tJB4z9xLd5WDgQfSwuXTVTw33W4HPSNbclevVBPNAvfuCXHjcJw4FAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:42.648544Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04655","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fb935c638da7ee76004c679846a31483016ea784ad7825a2eb68305c778b2a9","sha256:63398bb15fdde0f3026ad7826bd038993694917b38ff0d2617838faf831dd352"],"state_sha256":"729e4a5ef723539458612b26285fda360eebec265b1190a63ebd1d5f0f2a72bb"}