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Namely:\n THEOREM. 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","authors_text":"Alessandro Silva, Sergei Ivashkovich","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"1998-10-28T10:30:11Z","title":"The Hartpgs-type extension theorem for meromorphic mappings into q-complete complex spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9810159","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3fba8c8430a07e365a287a3d2afadb3aa005de4b32cae8f723bb890a6e4ed260","target":"record","created_at":"2026-05-18T01:05:33Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d5fcb61b30c32813ce3542b49567d4e8b6a142a95419542013a15d9042e7fb77","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CV","submitted_at":"1998-10-28T10:30:11Z","title_canon_sha256":"0b61ff383a6a281080d181e9ac6ce999b5d0fcae10a074767cf8207f0c0617fb"},"schema_version":"1.0","source":{"id":"math/9810159","kind":"arxiv","version":1}},"canonical_sha256":"6683c9eb958a0bcd583d191e8c9b98c1bb069120775de2d9e45769ef431c4c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6683c9eb958a0bcd583d191e8c9b98c1bb069120775de2d9e45769ef431c4c0a","first_computed_at":"2026-05-18T01:05:33.628269Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:33.628269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YVruP9KOaXfYnSGct7wdB0zCcG9Sk+5ZRonKOxvfxZscYEppFvY8Y3rFy5z6jy44Glo9ad4DFNmZ5s1R2Q+4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:33.628854Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9810159","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fba8c8430a07e365a287a3d2afadb3aa005de4b32cae8f723bb890a6e4ed260","sha256:bcfc842c9f0114c1b023255a304ab765f04e2eb5fee0d5d8dc9dae2dbce53c35"],"state_sha256":"b4e67281619c4fcd60f183e8d6da9cb796d51929afa9a5c442bc9b10dbd39db1"}