{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YPHYUXW5E4E4MD4DSYJZFHKFRX","short_pith_number":"pith:YPHYUXW5","schema_version":"1.0","canonical_sha256":"c3cf8a5edd2709c60f839613929d458de0ba564959846bd954e1330bb8e7cfb9","source":{"kind":"arxiv","id":"1502.01548","version":2},"attestation_state":"computed","paper":{"title":"A Scalar Associated with the Inverse of Some Abelian Integrals and a Ramified Riemann Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Junjiro Noguchi","submitted_at":"2015-02-05T13:50:29Z","abstract_excerpt":"We introduce a positive scalar function $\\rho(a, \\Omega)$ for a domain $\\Omega$ of a complex manifold $X$ with a global holomorphic frame of the cotangent bundle by closed Abelian differentials, which heuristically measure the distance from $a \\in \\Omega$ to the boundary $\\del\\Omega$. We prove an {\\em estimate of Cartan--Thullen type with $\\rho(a, \\Omega)$} for holomorphically convex hulls of compact subsets. In one dimensional case, we apply the obtained estimate of $\\rho(a, \\Omega)$ to give a new proof of Behnke-Stein's Theorem for the Steiness of open Riemann surfaces. We then use the same "},"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":"1502.01548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-02-05T13:50:29Z","cross_cats_sorted":[],"title_canon_sha256":"56f8c59dea2e37583009c6d13443f4f9511c45f8e7398f6be4562b56a6e5519d","abstract_canon_sha256":"d51ea801095cb738ddb655a0fdc484d40e4ab760f89aa17748fc831b3f9a6850"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:53.010725Z","signature_b64":"85rfb4ph5TpWYGtxbTwsR+mSTnVrcOrkoeeu5Rjlgqe67rqruXHO6DYaY4eSMTJYrwOe6pom8DFQJlZUiRqDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3cf8a5edd2709c60f839613929d458de0ba564959846bd954e1330bb8e7cfb9","last_reissued_at":"2026-05-18T02:17:53.010103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:53.010103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Scalar Associated with the Inverse of Some Abelian Integrals and a Ramified Riemann Domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Junjiro Noguchi","submitted_at":"2015-02-05T13:50:29Z","abstract_excerpt":"We introduce a positive scalar function $\\rho(a, \\Omega)$ for a domain $\\Omega$ of a complex manifold $X$ with a global holomorphic frame of the cotangent bundle by closed Abelian differentials, which heuristically measure the distance from $a \\in \\Omega$ to the boundary $\\del\\Omega$. We prove an {\\em estimate of Cartan--Thullen type with $\\rho(a, \\Omega)$} for holomorphically convex hulls of compact subsets. In one dimensional case, we apply the obtained estimate of $\\rho(a, \\Omega)$ to give a new proof of Behnke-Stein's Theorem for the Steiness of open Riemann surfaces. We then use the same "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01548","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":"1502.01548","created_at":"2026-05-18T02:17:53.010213+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.01548v2","created_at":"2026-05-18T02:17:53.010213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01548","created_at":"2026-05-18T02:17:53.010213+00:00"},{"alias_kind":"pith_short_12","alias_value":"YPHYUXW5E4E4","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_16","alias_value":"YPHYUXW5E4E4MD4D","created_at":"2026-05-18T12:29:50.041715+00:00"},{"alias_kind":"pith_short_8","alias_value":"YPHYUXW5","created_at":"2026-05-18T12:29:50.041715+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/YPHYUXW5E4E4MD4DSYJZFHKFRX","json":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX.json","graph_json":"https://pith.science/api/pith-number/YPHYUXW5E4E4MD4DSYJZFHKFRX/graph.json","events_json":"https://pith.science/api/pith-number/YPHYUXW5E4E4MD4DSYJZFHKFRX/events.json","paper":"https://pith.science/paper/YPHYUXW5"},"agent_actions":{"view_html":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX","download_json":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX.json","view_paper":"https://pith.science/paper/YPHYUXW5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.01548&json=true","fetch_graph":"https://pith.science/api/pith-number/YPHYUXW5E4E4MD4DSYJZFHKFRX/graph.json","fetch_events":"https://pith.science/api/pith-number/YPHYUXW5E4E4MD4DSYJZFHKFRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX/action/storage_attestation","attest_author":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX/action/author_attestation","sign_citation":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX/action/citation_signature","submit_replication":"https://pith.science/pith/YPHYUXW5E4E4MD4DSYJZFHKFRX/action/replication_record"}},"created_at":"2026-05-18T02:17:53.010213+00:00","updated_at":"2026-05-18T02:17:53.010213+00:00"}