{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:OP6QTUTKJELAOQVU4UJA6OGO4M","short_pith_number":"pith:OP6QTUTK","schema_version":"1.0","canonical_sha256":"73fd09d26a49160742b4e5120f38cee301277ae4ab66cbbc3d5a066dd8d3c246","source":{"kind":"arxiv","id":"math/0608345","version":1},"attestation_state":"computed","paper":{"title":"Divisors over determinantal rings defined by two by two minors","license":"","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2006-08-14T14:10:51Z","abstract_excerpt":"Let E and G be free modules of rank e and g, respectively, over a commutative noetherian ring R. The identity map on E^* tensor G induces the Koszul complex\n ... -> S_mE^* tensor S_nG tensor Wedge^p(E^* tensor G) -> S_{m+1}E^* tensor S_{n+1}G tensor Wedge^{p-1}(E^* tensor G) -> ... and its dual\n ... -> D_{m+1}E tensor D_{n+1}G^* tensor Wedge^{p-1}(E tensor G^*) -> D_mE tensor D_nG^* tensor Wedge^p(E tensor G^*)-> ... Let H_{m,n,p} be the homology of the top complex at S_m tensor S_n tensor Wedge^p and H^{m,n,p} the homology of the bottom complex at D_m tensor D_n tensor Wedge^p. It is known th"},"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/0608345","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2006-08-14T14:10:51Z","cross_cats_sorted":[],"title_canon_sha256":"89529f66900eb9963349ff6d875ed2ba91238b2878cfd4f37d7d8a8433f0d965","abstract_canon_sha256":"23fce330c290032343b4f6521467380307a3ce6e46d80534abb5ca82e9c8e93f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.595031Z","signature_b64":"cacYzHiOCa3vA/qq+ZsUGcLYEfa6WmRjeLqcJx4MVANG3nGyTrTor61T2BDGQvKBJNUFFTmjEy9FtQd8F1ePDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73fd09d26a49160742b4e5120f38cee301277ae4ab66cbbc3d5a066dd8d3c246","last_reissued_at":"2026-05-18T01:05:22.594542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.594542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Divisors over determinantal rings defined by two by two minors","license":"","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2006-08-14T14:10:51Z","abstract_excerpt":"Let E and G be free modules of rank e and g, respectively, over a commutative noetherian ring R. The identity map on E^* tensor G induces the Koszul complex\n ... -> S_mE^* tensor S_nG tensor Wedge^p(E^* tensor G) -> S_{m+1}E^* tensor S_{n+1}G tensor Wedge^{p-1}(E^* tensor G) -> ... and its dual\n ... -> D_{m+1}E tensor D_{n+1}G^* tensor Wedge^{p-1}(E tensor G^*) -> D_mE tensor D_nG^* tensor Wedge^p(E tensor G^*)-> ... Let H_{m,n,p} be the homology of the top complex at S_m tensor S_n tensor Wedge^p and H^{m,n,p} the homology of the bottom complex at D_m tensor D_n tensor Wedge^p. It is known th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608345","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/0608345","created_at":"2026-05-18T01:05:22.594616+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0608345v1","created_at":"2026-05-18T01:05:22.594616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608345","created_at":"2026-05-18T01:05:22.594616+00:00"},{"alias_kind":"pith_short_12","alias_value":"OP6QTUTKJELA","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"OP6QTUTKJELAOQVU","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"OP6QTUTK","created_at":"2026-05-18T12:25:54.717736+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/OP6QTUTKJELAOQVU4UJA6OGO4M","json":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M.json","graph_json":"https://pith.science/api/pith-number/OP6QTUTKJELAOQVU4UJA6OGO4M/graph.json","events_json":"https://pith.science/api/pith-number/OP6QTUTKJELAOQVU4UJA6OGO4M/events.json","paper":"https://pith.science/paper/OP6QTUTK"},"agent_actions":{"view_html":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M","download_json":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M.json","view_paper":"https://pith.science/paper/OP6QTUTK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0608345&json=true","fetch_graph":"https://pith.science/api/pith-number/OP6QTUTKJELAOQVU4UJA6OGO4M/graph.json","fetch_events":"https://pith.science/api/pith-number/OP6QTUTKJELAOQVU4UJA6OGO4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M/action/storage_attestation","attest_author":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M/action/author_attestation","sign_citation":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M/action/citation_signature","submit_replication":"https://pith.science/pith/OP6QTUTKJELAOQVU4UJA6OGO4M/action/replication_record"}},"created_at":"2026-05-18T01:05:22.594616+00:00","updated_at":"2026-05-18T01:05:22.594616+00:00"}