{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OKHUQXWGNRN57PVSB5UYPX6SA5","short_pith_number":"pith:OKHUQXWG","schema_version":"1.0","canonical_sha256":"728f485ec66c5bdfbeb20f6987dfd2074b7fa633163113756b89d78d9db6338e","source":{"kind":"arxiv","id":"1204.5419","version":2},"attestation_state":"computed","paper":{"title":"On J. C. C. Nitsche type inequality for annuli on Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"David Kalaj","submitted_at":"2012-04-24T16:08:53Z","abstract_excerpt":"Assume that $(\\mathcal{N},\\hbar)$ and $(\\mathcal{M},\\wp)$ are two Riemann surfaces with conformal metrics $\\hbar$ and $\\wp$. We prove that if there is a harmonic homeomorphism between an annulus $\\mathcal{A}\\subset \\mathcal{N}$ with a conformal modulus $\\mathrm{Mod}(\\mathcal{A})$ and a geodesic annulus $A_\\wp(p,\\rho_1,\\rho_2)\\subset \\mathcal{M}$, then we have ${\\rho_2}/{\\rho_1}\\ge \\Psi_\\wp\\mathrm{Mod}(\\mathcal{A})^2+1,$ where $\\Psi_\\wp$ is a certain positive constant depending on the upper bound of Gaussian curvature of the metric $\\wp$. An application for the minimal surfaces is given."},"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":"1204.5419","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-24T16:08:53Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"e486916a195349b19eee75df1ec015b71cf325887c393c0f0b3a6609f4bd9ebb","abstract_canon_sha256":"90d17adba6cc5b833be9ee8178eb3933e9f1e05b51bfae2fe6876681a2714e1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:47.254805Z","signature_b64":"07k8AFcs7cFvXaJFH97hRbwhsRP1trRJbzKedfOkR3b6ZEROtH7BEiJBsrCTy7hhBH/Dt3qeOgm5vljSCBt/Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"728f485ec66c5bdfbeb20f6987dfd2074b7fa633163113756b89d78d9db6338e","last_reissued_at":"2026-05-18T03:56:47.254068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:47.254068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On J. C. C. Nitsche type inequality for annuli on Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"David Kalaj","submitted_at":"2012-04-24T16:08:53Z","abstract_excerpt":"Assume that $(\\mathcal{N},\\hbar)$ and $(\\mathcal{M},\\wp)$ are two Riemann surfaces with conformal metrics $\\hbar$ and $\\wp$. We prove that if there is a harmonic homeomorphism between an annulus $\\mathcal{A}\\subset \\mathcal{N}$ with a conformal modulus $\\mathrm{Mod}(\\mathcal{A})$ and a geodesic annulus $A_\\wp(p,\\rho_1,\\rho_2)\\subset \\mathcal{M}$, then we have ${\\rho_2}/{\\rho_1}\\ge \\Psi_\\wp\\mathrm{Mod}(\\mathcal{A})^2+1,$ where $\\Psi_\\wp$ is a certain positive constant depending on the upper bound of Gaussian curvature of the metric $\\wp$. An application for the minimal surfaces is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5419","kind":"arxiv","version":2},"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":"1204.5419","created_at":"2026-05-18T03:56:47.254186+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5419v2","created_at":"2026-05-18T03:56:47.254186+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5419","created_at":"2026-05-18T03:56:47.254186+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKHUQXWGNRN5","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKHUQXWGNRN57PVS","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKHUQXWG","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/OKHUQXWGNRN57PVSB5UYPX6SA5","json":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5.json","graph_json":"https://pith.science/api/pith-number/OKHUQXWGNRN57PVSB5UYPX6SA5/graph.json","events_json":"https://pith.science/api/pith-number/OKHUQXWGNRN57PVSB5UYPX6SA5/events.json","paper":"https://pith.science/paper/OKHUQXWG"},"agent_actions":{"view_html":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5","download_json":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5.json","view_paper":"https://pith.science/paper/OKHUQXWG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5419&json=true","fetch_graph":"https://pith.science/api/pith-number/OKHUQXWGNRN57PVSB5UYPX6SA5/graph.json","fetch_events":"https://pith.science/api/pith-number/OKHUQXWGNRN57PVSB5UYPX6SA5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5/action/storage_attestation","attest_author":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5/action/author_attestation","sign_citation":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5/action/citation_signature","submit_replication":"https://pith.science/pith/OKHUQXWGNRN57PVSB5UYPX6SA5/action/replication_record"}},"created_at":"2026-05-18T03:56:47.254186+00:00","updated_at":"2026-05-18T03:56:47.254186+00:00"}