{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DJ3YCQFXP7AOHWWQKS3YFEXZD2","short_pith_number":"pith:DJ3YCQFX","schema_version":"1.0","canonical_sha256":"1a778140b77fc0e3dad054b78292f91e9834df3187e819d97f03779e4737e1a2","source":{"kind":"arxiv","id":"1506.07842","version":4},"attestation_state":"computed","paper":{"title":"The $\\bar{\\partial}$-equation, duality, and holomorphic forms on a reduced complex space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"H{\\aa}kan Samuelsson Kalm","submitted_at":"2015-06-25T18:30:36Z","abstract_excerpt":"We solve the $\\bar{\\partial}$-equation for $(p,q)$-forms locally on any reduced pure-dimensional complex space and we prove an explicit version of Serre duality by introducing suitable concrete fine sheaves of certain $(p,q)$-currents. In particular this gives a precise condition for the $\\bar{\\partial}$-equation to be globally solvable. Our results extend results for $(0,q)$-forms and give information about holomorphic $p$-forms on singular spaces."},"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":"1506.07842","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-06-25T18:30:36Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ed66be46b920d169a9f3c35dd21baf4ec4e3294174576b207a951be3ed06ceca","abstract_canon_sha256":"dccbc025975586789f44256eb524345b34517fbc9dcb31b0c8c748179fb04039"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:53.534875Z","signature_b64":"Om4DrSJOMI07jSjjZdeVh2HCQyyL0TsgIxTrqFfREh4rC6uXpgQOtMZJq6UOSf3kgttXvqw9QhPZ0mwlMlhsCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a778140b77fc0e3dad054b78292f91e9834df3187e819d97f03779e4737e1a2","last_reissued_at":"2026-05-18T00:24:53.534082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:53.534082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $\\bar{\\partial}$-equation, duality, and holomorphic forms on a reduced complex space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"H{\\aa}kan Samuelsson Kalm","submitted_at":"2015-06-25T18:30:36Z","abstract_excerpt":"We solve the $\\bar{\\partial}$-equation for $(p,q)$-forms locally on any reduced pure-dimensional complex space and we prove an explicit version of Serre duality by introducing suitable concrete fine sheaves of certain $(p,q)$-currents. In particular this gives a precise condition for the $\\bar{\\partial}$-equation to be globally solvable. Our results extend results for $(0,q)$-forms and give information about holomorphic $p$-forms on singular spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07842","kind":"arxiv","version":4},"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":"1506.07842","created_at":"2026-05-18T00:24:53.534216+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.07842v4","created_at":"2026-05-18T00:24:53.534216+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07842","created_at":"2026-05-18T00:24:53.534216+00:00"},{"alias_kind":"pith_short_12","alias_value":"DJ3YCQFXP7AO","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DJ3YCQFXP7AOHWWQ","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DJ3YCQFX","created_at":"2026-05-18T12:29:17.054201+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/DJ3YCQFXP7AOHWWQKS3YFEXZD2","json":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2.json","graph_json":"https://pith.science/api/pith-number/DJ3YCQFXP7AOHWWQKS3YFEXZD2/graph.json","events_json":"https://pith.science/api/pith-number/DJ3YCQFXP7AOHWWQKS3YFEXZD2/events.json","paper":"https://pith.science/paper/DJ3YCQFX"},"agent_actions":{"view_html":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2","download_json":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2.json","view_paper":"https://pith.science/paper/DJ3YCQFX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.07842&json=true","fetch_graph":"https://pith.science/api/pith-number/DJ3YCQFXP7AOHWWQKS3YFEXZD2/graph.json","fetch_events":"https://pith.science/api/pith-number/DJ3YCQFXP7AOHWWQKS3YFEXZD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2/action/storage_attestation","attest_author":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2/action/author_attestation","sign_citation":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2/action/citation_signature","submit_replication":"https://pith.science/pith/DJ3YCQFXP7AOHWWQKS3YFEXZD2/action/replication_record"}},"created_at":"2026-05-18T00:24:53.534216+00:00","updated_at":"2026-05-18T00:24:53.534216+00:00"}