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Every meromorphic mapping $f:H_n^q(r)\\to Y$, where $Y$ is a $q$ - -complete complex space, extends to a meromorphic mapping from $\\Delta^{n+q}$ to $Y$. Here $H_n^q(r):=\\Delta^n\\times (\\Delta^q\\setminus \\bar\\Delta_r^q)\\cup \\Delta_r^n\\times \\Delta^q$ is a \"q-concave\" Hartogs figure in $C^{n+q}$.\n Remark that in the case $q=1$, i.e. when $Y$ is Stein, the statement of the Theorem is exactly the Theorem"},"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":"math/9810159","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"1998-10-28T10:30:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0b61ff383a6a281080d181e9ac6ce999b5d0fcae10a074767cf8207f0c0617fb","abstract_canon_sha256":"d5fcb61b30c32813ce3542b49567d4e8b6a142a95419542013a15d9042e7fb77"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:33.628854Z","signature_b64":"YVruP9KOaXfYnSGct7wdB0zCcG9Sk+5ZRonKOxvfxZscYEppFvY8Y3rFy5z6jy44Glo9ad4DFNmZ5s1R2Q+4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6683c9eb958a0bcd583d191e8c9b98c1bb069120775de2d9e45769ef431c4c0a","last_reissued_at":"2026-05-18T01:05:33.628269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:33.628269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Hartpgs-type extension theorem for meromorphic mappings into q-complete complex spaces","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Alessandro Silva, Sergei Ivashkovich","submitted_at":"1998-10-28T10:30:11Z","abstract_excerpt":"We prove in this note a result on extension of meromorphic mappings, which can be considered as a direct generalisation of the Hartogs extension theorem for holomorphic functions. 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Here $H_n^q(r):=\\Delta^n\\times (\\Delta^q\\setminus \\bar\\Delta_r^q)\\cup \\Delta_r^n\\times \\Delta^q$ is a \"q-concave\" Hartogs figure in $C^{n+q}$.\n Remark that in the case $q=1$, i.e. when $Y$ is Stein, the statement of the Theorem is exactly the Theorem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9810159","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":"math/9810159","created_at":"2026-05-18T01:05:33.628368+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9810159v1","created_at":"2026-05-18T01:05:33.628368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9810159","created_at":"2026-05-18T01:05:33.628368+00:00"},{"alias_kind":"pith_short_12","alias_value":"M2B4T24VRIF4","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"M2B4T24VRIF42WB5","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"M2B4T24V","created_at":"2026-05-18T12:25:49.038998+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/M2B4T24VRIF42WB5DEPIZG4YYG","json":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG.json","graph_json":"https://pith.science/api/pith-number/M2B4T24VRIF42WB5DEPIZG4YYG/graph.json","events_json":"https://pith.science/api/pith-number/M2B4T24VRIF42WB5DEPIZG4YYG/events.json","paper":"https://pith.science/paper/M2B4T24V"},"agent_actions":{"view_html":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG","download_json":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG.json","view_paper":"https://pith.science/paper/M2B4T24V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9810159&json=true","fetch_graph":"https://pith.science/api/pith-number/M2B4T24VRIF42WB5DEPIZG4YYG/graph.json","fetch_events":"https://pith.science/api/pith-number/M2B4T24VRIF42WB5DEPIZG4YYG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG/action/storage_attestation","attest_author":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG/action/author_attestation","sign_citation":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG/action/citation_signature","submit_replication":"https://pith.science/pith/M2B4T24VRIF42WB5DEPIZG4YYG/action/replication_record"}},"created_at":"2026-05-18T01:05:33.628368+00:00","updated_at":"2026-05-18T01:05:33.628368+00:00"}