{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4EY7G2KX56IPCY4X6GTORF7H3T","short_pith_number":"pith:4EY7G2KX","schema_version":"1.0","canonical_sha256":"e131f36957ef90f16397f1a6e897e7dceea2091f28188544f90b516ed723f1bc","source":{"kind":"arxiv","id":"1703.09091","version":2},"attestation_state":"computed","paper":{"title":"Global Koppelman formulas on (singular) projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mats Andersson","submitted_at":"2017-03-27T14:12:23Z","abstract_excerpt":"Let $i\\colon X\\to \\Pk^N$ be a projective manifold of dimension $n$ embedded in projective space $\\Pk^N$, and let $L$ be the pull-back to $X$ of the line bundle $\\Ok_{\\Pk^N}(1)$. We construct global explicit Koppelman formulas on $X$ for smooth $(0,*)$-forms with values in $L^s$ for any $s$. %The formulas are intrinsic on $X$. The same construction works for singular, even non-reduced, $X$ of pure dimension, if the sheaves of smooth forms are replaced by suitable sheaves $\\A_X^*$ of $(0,*)$-currents with mild singularities at $X_{sing}$. In particular, if $s\\ge \\reg X -1$, where $\\reg X$ is the"},"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":"1703.09091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-03-27T14:12:23Z","cross_cats_sorted":[],"title_canon_sha256":"bffa39f5c367dce2138fdd004df966c6face3a52ef115bcb76afd685933eecfe","abstract_canon_sha256":"756bf80a7b89cd69d2725fead500115a45b1143f031756f9276cce0c918e10c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:07.706352Z","signature_b64":"e+jK8CmJTrFj54xg2SHLrablv0epui15V4YK9UAAStoeRqya0OGWYFjHPan60Orb+wTfERBZ3Bo39oH5yVFOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e131f36957ef90f16397f1a6e897e7dceea2091f28188544f90b516ed723f1bc","last_reissued_at":"2026-05-18T00:13:07.705711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:07.705711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global Koppelman formulas on (singular) projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Mats Andersson","submitted_at":"2017-03-27T14:12:23Z","abstract_excerpt":"Let $i\\colon X\\to \\Pk^N$ be a projective manifold of dimension $n$ embedded in projective space $\\Pk^N$, and let $L$ be the pull-back to $X$ of the line bundle $\\Ok_{\\Pk^N}(1)$. We construct global explicit Koppelman formulas on $X$ for smooth $(0,*)$-forms with values in $L^s$ for any $s$. %The formulas are intrinsic on $X$. The same construction works for singular, even non-reduced, $X$ of pure dimension, if the sheaves of smooth forms are replaced by suitable sheaves $\\A_X^*$ of $(0,*)$-currents with mild singularities at $X_{sing}$. In particular, if $s\\ge \\reg X -1$, where $\\reg X$ is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09091","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":"1703.09091","created_at":"2026-05-18T00:13:07.705818+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.09091v2","created_at":"2026-05-18T00:13:07.705818+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09091","created_at":"2026-05-18T00:13:07.705818+00:00"},{"alias_kind":"pith_short_12","alias_value":"4EY7G2KX56IP","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_16","alias_value":"4EY7G2KX56IPCY4X","created_at":"2026-05-18T12:30:58.224056+00:00"},{"alias_kind":"pith_short_8","alias_value":"4EY7G2KX","created_at":"2026-05-18T12:30:58.224056+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/4EY7G2KX56IPCY4X6GTORF7H3T","json":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T.json","graph_json":"https://pith.science/api/pith-number/4EY7G2KX56IPCY4X6GTORF7H3T/graph.json","events_json":"https://pith.science/api/pith-number/4EY7G2KX56IPCY4X6GTORF7H3T/events.json","paper":"https://pith.science/paper/4EY7G2KX"},"agent_actions":{"view_html":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T","download_json":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T.json","view_paper":"https://pith.science/paper/4EY7G2KX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.09091&json=true","fetch_graph":"https://pith.science/api/pith-number/4EY7G2KX56IPCY4X6GTORF7H3T/graph.json","fetch_events":"https://pith.science/api/pith-number/4EY7G2KX56IPCY4X6GTORF7H3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T/action/storage_attestation","attest_author":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T/action/author_attestation","sign_citation":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T/action/citation_signature","submit_replication":"https://pith.science/pith/4EY7G2KX56IPCY4X6GTORF7H3T/action/replication_record"}},"created_at":"2026-05-18T00:13:07.705818+00:00","updated_at":"2026-05-18T00:13:07.705818+00:00"}