{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:65AQLTOVI7GMJ3G6A6FHLKMWIU","short_pith_number":"pith:65AQLTOV","schema_version":"1.0","canonical_sha256":"f74105cdd547ccc4ecde078a75a996450ad1fdc3ed57f04fa5c061d7f444cf41","source":{"kind":"arxiv","id":"1905.11435","version":1},"attestation_state":"computed","paper":{"title":"Use DG-methods to build a matrix factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2019-05-27T18:13:27Z","abstract_excerpt":"Let P be a commutative Noetherian ring, K be an ideal of P which is generated by a regular sequence of length four, f be a regular element of P, and Pbar be the hypersurface ring P/(f). Assume that K:f is a grade four Gorenstein ideal of P. We give a resolution N of Pbar/K Pbar by free Pbar-modules.\n  The resolution N is built from a Differential Graded Algebra resolution of P/(K:f) by free P-modules, together with one homotopy map. In particular, we give an explicit form for the matrix factorization which is the infinite tail of the resolution N."},"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":"1905.11435","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2019-05-27T18:13:27Z","cross_cats_sorted":[],"title_canon_sha256":"3b100921997c44165edd9877fb0935d4c88e9e9a5f3a74538198256d8d6849b8","abstract_canon_sha256":"33942fcd229238b7f9cdb09cbd6ded74372fa1918f032a4fc613d8997dff4226"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:53.426899Z","signature_b64":"rh47vMJ4Y7OGtdrE/7Fbcx1PFqZTGV4Tx45V2d5PEPsa5ycSIgKpkp9Fnb8ODGX04F5aoxtzuHV68lEb/8IRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f74105cdd547ccc4ecde078a75a996450ad1fdc3ed57f04fa5c061d7f444cf41","last_reissued_at":"2026-05-17T23:44:53.426406Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:53.426406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Use DG-methods to build a matrix factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2019-05-27T18:13:27Z","abstract_excerpt":"Let P be a commutative Noetherian ring, K be an ideal of P which is generated by a regular sequence of length four, f be a regular element of P, and Pbar be the hypersurface ring P/(f). Assume that K:f is a grade four Gorenstein ideal of P. We give a resolution N of Pbar/K Pbar by free Pbar-modules.\n  The resolution N is built from a Differential Graded Algebra resolution of P/(K:f) by free P-modules, together with one homotopy map. In particular, we give an explicit form for the matrix factorization which is the infinite tail of the resolution N."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11435","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":"1905.11435","created_at":"2026-05-17T23:44:53.426480+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.11435v1","created_at":"2026-05-17T23:44:53.426480+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11435","created_at":"2026-05-17T23:44:53.426480+00:00"},{"alias_kind":"pith_short_12","alias_value":"65AQLTOVI7GM","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"65AQLTOVI7GMJ3G6","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"65AQLTOV","created_at":"2026-05-18T12:33:10.108867+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/65AQLTOVI7GMJ3G6A6FHLKMWIU","json":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU.json","graph_json":"https://pith.science/api/pith-number/65AQLTOVI7GMJ3G6A6FHLKMWIU/graph.json","events_json":"https://pith.science/api/pith-number/65AQLTOVI7GMJ3G6A6FHLKMWIU/events.json","paper":"https://pith.science/paper/65AQLTOV"},"agent_actions":{"view_html":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU","download_json":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU.json","view_paper":"https://pith.science/paper/65AQLTOV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.11435&json=true","fetch_graph":"https://pith.science/api/pith-number/65AQLTOVI7GMJ3G6A6FHLKMWIU/graph.json","fetch_events":"https://pith.science/api/pith-number/65AQLTOVI7GMJ3G6A6FHLKMWIU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU/action/storage_attestation","attest_author":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU/action/author_attestation","sign_citation":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU/action/citation_signature","submit_replication":"https://pith.science/pith/65AQLTOVI7GMJ3G6A6FHLKMWIU/action/replication_record"}},"created_at":"2026-05-17T23:44:53.426480+00:00","updated_at":"2026-05-17T23:44:53.426480+00:00"}