{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WREG2VOXLDXR2LVO5UULEN4NE6","short_pith_number":"pith:WREG2VOX","schema_version":"1.0","canonical_sha256":"b4486d55d758ef1d2eaeed28b2378d2781bd18436e2f7d461a3773656d03cbce","source":{"kind":"arxiv","id":"1303.5220","version":1},"attestation_state":"computed","paper":{"title":"Integrating holomorphic $L^1$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A.-K. Herbig","submitted_at":"2013-03-21T10:33:51Z","abstract_excerpt":"Let $\\Omega\\Subset\\mathbb{C}^{n}$ be a domain with smooth boundary, $k\\in\\mathbb{N}$. It is shown that the integral of a holomorphic function in $L^1(\\Omega)$ may be represented as the integral of this function against a smooth function vanishing to order $k-1$ on $b\\Omega$. An application for a smoothing property of the Bergman projection for conjugate holomorphic functions 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":"1303.5220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-03-21T10:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"c8e1392dba17f571bc922c07733f19e35d583e52d75bce977d3bef3e3d32e1e4","abstract_canon_sha256":"a14bf6b33d3b340a50d46ad8fcde5abefc9961c815ad75b4d8131638044b2b58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:13.578633Z","signature_b64":"aa4NrCJo8mqUthZSqR9pFpZdLl16gslWTRojxDduYnhjlSwUXgIJH2dRO9bvV5++D0bvKuLyp08yx6ltmthWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4486d55d758ef1d2eaeed28b2378d2781bd18436e2f7d461a3773656d03cbce","last_reissued_at":"2026-05-18T03:30:13.577362Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:13.577362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrating holomorphic $L^1$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A.-K. Herbig","submitted_at":"2013-03-21T10:33:51Z","abstract_excerpt":"Let $\\Omega\\Subset\\mathbb{C}^{n}$ be a domain with smooth boundary, $k\\in\\mathbb{N}$. It is shown that the integral of a holomorphic function in $L^1(\\Omega)$ may be represented as the integral of this function against a smooth function vanishing to order $k-1$ on $b\\Omega$. An application for a smoothing property of the Bergman projection for conjugate holomorphic functions is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5220","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":"1303.5220","created_at":"2026-05-18T03:30:13.577549+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5220v1","created_at":"2026-05-18T03:30:13.577549+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5220","created_at":"2026-05-18T03:30:13.577549+00:00"},{"alias_kind":"pith_short_12","alias_value":"WREG2VOXLDXR","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WREG2VOXLDXR2LVO","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WREG2VOX","created_at":"2026-05-18T12:28:04.890932+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/WREG2VOXLDXR2LVO5UULEN4NE6","json":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6.json","graph_json":"https://pith.science/api/pith-number/WREG2VOXLDXR2LVO5UULEN4NE6/graph.json","events_json":"https://pith.science/api/pith-number/WREG2VOXLDXR2LVO5UULEN4NE6/events.json","paper":"https://pith.science/paper/WREG2VOX"},"agent_actions":{"view_html":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6","download_json":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6.json","view_paper":"https://pith.science/paper/WREG2VOX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5220&json=true","fetch_graph":"https://pith.science/api/pith-number/WREG2VOXLDXR2LVO5UULEN4NE6/graph.json","fetch_events":"https://pith.science/api/pith-number/WREG2VOXLDXR2LVO5UULEN4NE6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6/action/storage_attestation","attest_author":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6/action/author_attestation","sign_citation":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6/action/citation_signature","submit_replication":"https://pith.science/pith/WREG2VOXLDXR2LVO5UULEN4NE6/action/replication_record"}},"created_at":"2026-05-18T03:30:13.577549+00:00","updated_at":"2026-05-18T03:30:13.577549+00:00"}