{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OUAAF6HVNZTV7D7GKUBLLWBHY3","short_pith_number":"pith:OUAAF6HV","schema_version":"1.0","canonical_sha256":"750002f8f56e675f8fe65502b5d827c6c8b5e1e64ced312264758d7592968f6d","source":{"kind":"arxiv","id":"1210.1619","version":1},"attestation_state":"computed","paper":{"title":"The rate of convergence of the hyperbolic density on sequences of domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Greg Markowsky, Nikola Lakic","submitted_at":"2012-10-05T00:37:29Z","abstract_excerpt":"It is known that if a sequence of domains $U_n$ converges to a domain $U$ in the Caratheodory sense then the hyperbolic densities on $U_n$ converge to the hyperbolic density on $U$. In this paper, we study the rate of convergence of the hyperbolic density under a slightly different mode of convergence. In doing so, we are led to consider two other densities on domains, the Teichmueller density and the three-point density. We obtain several results which give rates of convergence in various scenarios."},"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":"1210.1619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-10-05T00:37:29Z","cross_cats_sorted":[],"title_canon_sha256":"021229eb60949deccc731ca166ca1854d0a9934a63687f2c6af23dbdfb2ed78a","abstract_canon_sha256":"25e5639ec5e51eaeb6e11e680806b8c6c71716515f325123d4b0dadf38f967e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:01.826339Z","signature_b64":"E2/jcYSYwVgRcobArvBA/C4X/ysrJKuDubssEzCPKPLBZeQ3jLLfDEBLBkhRlh+S6rz+M6DQFT2PmL65R/mRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"750002f8f56e675f8fe65502b5d827c6c8b5e1e64ced312264758d7592968f6d","last_reissued_at":"2026-05-18T03:44:01.825672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:01.825672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The rate of convergence of the hyperbolic density on sequences of domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Greg Markowsky, Nikola Lakic","submitted_at":"2012-10-05T00:37:29Z","abstract_excerpt":"It is known that if a sequence of domains $U_n$ converges to a domain $U$ in the Caratheodory sense then the hyperbolic densities on $U_n$ converge to the hyperbolic density on $U$. In this paper, we study the rate of convergence of the hyperbolic density under a slightly different mode of convergence. In doing so, we are led to consider two other densities on domains, the Teichmueller density and the three-point density. We obtain several results which give rates of convergence in various scenarios."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.1619","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":"1210.1619","created_at":"2026-05-18T03:44:01.825802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.1619v1","created_at":"2026-05-18T03:44:01.825802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.1619","created_at":"2026-05-18T03:44:01.825802+00:00"},{"alias_kind":"pith_short_12","alias_value":"OUAAF6HVNZTV","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OUAAF6HVNZTV7D7G","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OUAAF6HV","created_at":"2026-05-18T12:27:16.716162+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/OUAAF6HVNZTV7D7GKUBLLWBHY3","json":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3.json","graph_json":"https://pith.science/api/pith-number/OUAAF6HVNZTV7D7GKUBLLWBHY3/graph.json","events_json":"https://pith.science/api/pith-number/OUAAF6HVNZTV7D7GKUBLLWBHY3/events.json","paper":"https://pith.science/paper/OUAAF6HV"},"agent_actions":{"view_html":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3","download_json":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3.json","view_paper":"https://pith.science/paper/OUAAF6HV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.1619&json=true","fetch_graph":"https://pith.science/api/pith-number/OUAAF6HVNZTV7D7GKUBLLWBHY3/graph.json","fetch_events":"https://pith.science/api/pith-number/OUAAF6HVNZTV7D7GKUBLLWBHY3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3/action/storage_attestation","attest_author":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3/action/author_attestation","sign_citation":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3/action/citation_signature","submit_replication":"https://pith.science/pith/OUAAF6HVNZTV7D7GKUBLLWBHY3/action/replication_record"}},"created_at":"2026-05-18T03:44:01.825802+00:00","updated_at":"2026-05-18T03:44:01.825802+00:00"}