{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:LVXI7BOM5X4LVPRO3PAGN3C2YX","short_pith_number":"pith:LVXI7BOM","schema_version":"1.0","canonical_sha256":"5d6e8f85ccedf8babe2edbc066ec5ac5fcf7fd4d49f1a5defd48599eab26d1e6","source":{"kind":"arxiv","id":"1407.8464","version":1},"attestation_state":"computed","paper":{"title":"Horrocks Correspondence on ACM Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A.P. Rao, F. Malaspina","submitted_at":"2014-07-31T15:51:10Z","abstract_excerpt":"We describe a vector bundle $\\sE$ on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants $H^i_*(\\sE)$, $1\\leq i \\leq n-1$, and certain graded modules of \"socle elements\" built from $\\sE$. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\\mathbb P^{n+1}$ and the Veronese surface in $\\mathbb P^5$ are considered in more detail."},"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":"1407.8464","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-31T15:51:10Z","cross_cats_sorted":[],"title_canon_sha256":"69acd4deb5b4bdb6c7aa37d857ab60ddd56fc0ea21469da17822f374670f451a","abstract_canon_sha256":"30577591ddc98df9ad6e2fe5aa59a3c117289bc2a4fb98cce3a4cd4bbe7c301c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:21.933819Z","signature_b64":"Je8WsNV6D5zYzOBN2AMJHvdh8V/CJGLDVKQyjqtqTV6r82uU0v53pCPU1vJzbKai+ufAhHk3xlwUgKQWrYTYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d6e8f85ccedf8babe2edbc066ec5ac5fcf7fd4d49f1a5defd48599eab26d1e6","last_reissued_at":"2026-05-18T01:22:21.933099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:21.933099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Horrocks Correspondence on ACM Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A.P. Rao, F. Malaspina","submitted_at":"2014-07-31T15:51:10Z","abstract_excerpt":"We describe a vector bundle $\\sE$ on a smooth $n$-dimensional ACM variety in terms of its cohomological invariants $H^i_*(\\sE)$, $1\\leq i \\leq n-1$, and certain graded modules of \"socle elements\" built from $\\sE$. In this way we give a generalization of the Horrocks correspondence. We prove existence theorems where we construct vector bundles from these invariants and uniqueness theorems where we show that these data determine a bundle up to isomorphisms. The cases of the quadric hypersurface in $\\mathbb P^{n+1}$ and the Veronese surface in $\\mathbb P^5$ are considered in more detail."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8464","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":"1407.8464","created_at":"2026-05-18T01:22:21.933202+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.8464v1","created_at":"2026-05-18T01:22:21.933202+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8464","created_at":"2026-05-18T01:22:21.933202+00:00"},{"alias_kind":"pith_short_12","alias_value":"LVXI7BOM5X4L","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"LVXI7BOM5X4LVPRO","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"LVXI7BOM","created_at":"2026-05-18T12:28:38.356838+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/LVXI7BOM5X4LVPRO3PAGN3C2YX","json":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX.json","graph_json":"https://pith.science/api/pith-number/LVXI7BOM5X4LVPRO3PAGN3C2YX/graph.json","events_json":"https://pith.science/api/pith-number/LVXI7BOM5X4LVPRO3PAGN3C2YX/events.json","paper":"https://pith.science/paper/LVXI7BOM"},"agent_actions":{"view_html":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX","download_json":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX.json","view_paper":"https://pith.science/paper/LVXI7BOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.8464&json=true","fetch_graph":"https://pith.science/api/pith-number/LVXI7BOM5X4LVPRO3PAGN3C2YX/graph.json","fetch_events":"https://pith.science/api/pith-number/LVXI7BOM5X4LVPRO3PAGN3C2YX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX/action/storage_attestation","attest_author":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX/action/author_attestation","sign_citation":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX/action/citation_signature","submit_replication":"https://pith.science/pith/LVXI7BOM5X4LVPRO3PAGN3C2YX/action/replication_record"}},"created_at":"2026-05-18T01:22:21.933202+00:00","updated_at":"2026-05-18T01:22:21.933202+00:00"}