{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SG6W435JLDMLHONWG2A5CANQAR","short_pith_number":"pith:SG6W435J","schema_version":"1.0","canonical_sha256":"91bd6e6fa958d8b3b9b63681d101b004783be4e24c7f8dce3f8b64e5114e658d","source":{"kind":"arxiv","id":"1110.2918","version":2},"attestation_state":"computed","paper":{"title":"Matrix factorizations over projective schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jesse Burke, Mark E. Walker","submitted_at":"2011-10-13T12:44:52Z","abstract_excerpt":"We study matrix factorizations of locally free coherent sheaves on a scheme. For a scheme that is projective over an affine scheme, we show that homomorphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we give another proof of Orlov's theorem that there is a fully faithful embedding of the homotopy category of matrix factorizations into the singularity category of the corresponding zero subscheme. We also give a complete description of the image of this functor."},"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":"1110.2918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-13T12:44:52Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"21b975ec669e1db098add3055cdbf914cb5610cac099c38e7a410bbf8e52ba4c","abstract_canon_sha256":"31b8f09ef4912d7bb1fd4747db6ed6984a2a2b62d300a8fcca14b479f1b27cc9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:56.047404Z","signature_b64":"W9j7n5QApDfnX90YCffD4AkarhEQOu+b0uVQPba2YdlwprSvJ6ui+jXRfu1AupIprBZ+v2I40Gv4Q9TumhjIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91bd6e6fa958d8b3b9b63681d101b004783be4e24c7f8dce3f8b64e5114e658d","last_reissued_at":"2026-05-18T03:55:56.046687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:56.046687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix factorizations over projective schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Jesse Burke, Mark E. Walker","submitted_at":"2011-10-13T12:44:52Z","abstract_excerpt":"We study matrix factorizations of locally free coherent sheaves on a scheme. For a scheme that is projective over an affine scheme, we show that homomorphisms in the homotopy category of matrix factorizations may be computed as the hypercohomology of a certain mapping complex. Using this explicit description, we give another proof of Orlov's theorem that there is a fully faithful embedding of the homotopy category of matrix factorizations into the singularity category of the corresponding zero subscheme. We also give a complete description of the image of this functor."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2918","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":"1110.2918","created_at":"2026-05-18T03:55:56.046795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.2918v2","created_at":"2026-05-18T03:55:56.046795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2918","created_at":"2026-05-18T03:55:56.046795+00:00"},{"alias_kind":"pith_short_12","alias_value":"SG6W435JLDML","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SG6W435JLDMLHONW","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SG6W435J","created_at":"2026-05-18T12:26:41.206345+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/SG6W435JLDMLHONWG2A5CANQAR","json":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR.json","graph_json":"https://pith.science/api/pith-number/SG6W435JLDMLHONWG2A5CANQAR/graph.json","events_json":"https://pith.science/api/pith-number/SG6W435JLDMLHONWG2A5CANQAR/events.json","paper":"https://pith.science/paper/SG6W435J"},"agent_actions":{"view_html":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR","download_json":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR.json","view_paper":"https://pith.science/paper/SG6W435J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.2918&json=true","fetch_graph":"https://pith.science/api/pith-number/SG6W435JLDMLHONWG2A5CANQAR/graph.json","fetch_events":"https://pith.science/api/pith-number/SG6W435JLDMLHONWG2A5CANQAR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR/action/storage_attestation","attest_author":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR/action/author_attestation","sign_citation":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR/action/citation_signature","submit_replication":"https://pith.science/pith/SG6W435JLDMLHONWG2A5CANQAR/action/replication_record"}},"created_at":"2026-05-18T03:55:56.046795+00:00","updated_at":"2026-05-18T03:55:56.046795+00:00"}