{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AZY7JJP5KPUAEBIFTYJCQ6G5HP","short_pith_number":"pith:AZY7JJP5","schema_version":"1.0","canonical_sha256":"0671f4a5fd53e80205059e122878dd3bdbef75b262d66f78479e32727375e15d","source":{"kind":"arxiv","id":"1401.7786","version":1},"attestation_state":"computed","paper":{"title":"Uniformisation of a once-punctured annulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tanran Zhang","submitted_at":"2014-01-30T10:31:49Z","abstract_excerpt":"The universal cover or the covering group of a hyperbolic Riemann surface $X$ is important but hard to express explicitly. It can be, however, detected by the uniformisation and a suitable description of $X$. Beardon proposed five different ways to describe twice-punctured disks using fundamental domain, hyperbolic length, collar and extremal length in 2012. We parameterize a once-punctured annulus $A$ in terms of five parameter pairs and give explicit formulas about the hyperbolic structure and the complex structure of $A$. Several degenerating cases are also treated."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1401.7786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-01-30T10:31:49Z","cross_cats_sorted":[],"title_canon_sha256":"3ab020e991782576f017a49e0ada0f96083174c2850181a6c06f59ed174f8f7e","abstract_canon_sha256":"e518082cd7138b9cc56705e75f00aea360f863b4d06cceecdf9d4d4beddab0af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:38.402821Z","signature_b64":"nwRmkVFbaMK5D03NnjrFB+LiiCBjdoa2BCJR1yL66lKwt7JorhTzXxXOwCSEm66OIWlrkA+imnoAdqwe7b5DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0671f4a5fd53e80205059e122878dd3bdbef75b262d66f78479e32727375e15d","last_reissued_at":"2026-05-18T03:00:38.402103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:38.402103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformisation of a once-punctured annulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Tanran Zhang","submitted_at":"2014-01-30T10:31:49Z","abstract_excerpt":"The universal cover or the covering group of a hyperbolic Riemann surface $X$ is important but hard to express explicitly. It can be, however, detected by the uniformisation and a suitable description of $X$. Beardon proposed five different ways to describe twice-punctured disks using fundamental domain, hyperbolic length, collar and extremal length in 2012. We parameterize a once-punctured annulus $A$ in terms of five parameter pairs and give explicit formulas about the hyperbolic structure and the complex structure of $A$. Several degenerating cases are also treated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.7786","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1401.7786","created_at":"2026-05-18T03:00:38.402204+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.7786v1","created_at":"2026-05-18T03:00:38.402204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.7786","created_at":"2026-05-18T03:00:38.402204+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZY7JJP5KPUA","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZY7JJP5KPUAEBIF","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZY7JJP5","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP","json":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP.json","graph_json":"https://pith.science/api/pith-number/AZY7JJP5KPUAEBIFTYJCQ6G5HP/graph.json","events_json":"https://pith.science/api/pith-number/AZY7JJP5KPUAEBIFTYJCQ6G5HP/events.json","paper":"https://pith.science/paper/AZY7JJP5"},"agent_actions":{"view_html":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP","download_json":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP.json","view_paper":"https://pith.science/paper/AZY7JJP5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.7786&json=true","fetch_graph":"https://pith.science/api/pith-number/AZY7JJP5KPUAEBIFTYJCQ6G5HP/graph.json","fetch_events":"https://pith.science/api/pith-number/AZY7JJP5KPUAEBIFTYJCQ6G5HP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP/action/storage_attestation","attest_author":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP/action/author_attestation","sign_citation":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP/action/citation_signature","submit_replication":"https://pith.science/pith/AZY7JJP5KPUAEBIFTYJCQ6G5HP/action/replication_record"}},"created_at":"2026-05-18T03:00:38.402204+00:00","updated_at":"2026-05-18T03:00:38.402204+00:00"}