{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:Z6XCAWGSXLTQ3ICIGYVYT2LEQ3","short_pith_number":"pith:Z6XCAWGS","schema_version":"1.0","canonical_sha256":"cfae2058d2bae70da048362b89e96486e53d43c720b355f72a6cf5defa558e23","source":{"kind":"arxiv","id":"1512.08287","version":1},"attestation_state":"computed","paper":{"title":"An alternating matrix and a vector, with application to Aluffi algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2015-12-27T22:56:59Z","abstract_excerpt":"Let $\\mathbf X$ be a generic alternating matrix, $\\mathbf t$ be a generic row vector, and $J$ be the ideal $\\operatorname{Pf}_4({\\mathbf X})+I_1({\\mathbf {t X}})$. We prove that $J$ is a perfect Gorenstein ideal of grade equal to the grade of $\\operatorname{Pf}_4({\\mathbf X})$ plus two. This result is used by Ramos and Simis in their calculation of the Aluffi algebra of the module of derivations of the homogeneous coordinate ring of a smooth projective hypersurface. We also prove that $J$ defines a domain, or a normal ring, or a unique factorization domain if and only if the base ring has 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":"1512.08287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-27T22:56:59Z","cross_cats_sorted":[],"title_canon_sha256":"f3f1e3026ac214582e7bb3952d4c9f7ba226038be6f8d57d92796ae4752cbb88","abstract_canon_sha256":"72654b0bd2ff3cf77937cff4da636b196c71c27749cbf82f83876e49a2435b39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:42.702094Z","signature_b64":"IU6czZPpF8xv0x32ZTRuZxW7HAvwJd/z+XFr2oCi900225NEXRNGo+zTRLAOKzWIWMHFsm6/T5SS/sFpG6CvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfae2058d2bae70da048362b89e96486e53d43c720b355f72a6cf5defa558e23","last_reissued_at":"2026-05-18T01:23:42.701623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:42.701623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An alternating matrix and a vector, with application to Aluffi algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Andrew R. Kustin","submitted_at":"2015-12-27T22:56:59Z","abstract_excerpt":"Let $\\mathbf X$ be a generic alternating matrix, $\\mathbf t$ be a generic row vector, and $J$ be the ideal $\\operatorname{Pf}_4({\\mathbf X})+I_1({\\mathbf {t X}})$. We prove that $J$ is a perfect Gorenstein ideal of grade equal to the grade of $\\operatorname{Pf}_4({\\mathbf X})$ plus two. This result is used by Ramos and Simis in their calculation of the Aluffi algebra of the module of derivations of the homogeneous coordinate ring of a smooth projective hypersurface. We also prove that $J$ defines a domain, or a normal ring, or a unique factorization domain if and only if the base ring has the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08287","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":"1512.08287","created_at":"2026-05-18T01:23:42.701700+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.08287v1","created_at":"2026-05-18T01:23:42.701700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08287","created_at":"2026-05-18T01:23:42.701700+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z6XCAWGSXLTQ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z6XCAWGSXLTQ3ICI","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z6XCAWGS","created_at":"2026-05-18T12:29:52.810259+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/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3","json":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3.json","graph_json":"https://pith.science/api/pith-number/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/graph.json","events_json":"https://pith.science/api/pith-number/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/events.json","paper":"https://pith.science/paper/Z6XCAWGS"},"agent_actions":{"view_html":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3","download_json":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3.json","view_paper":"https://pith.science/paper/Z6XCAWGS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.08287&json=true","fetch_graph":"https://pith.science/api/pith-number/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/graph.json","fetch_events":"https://pith.science/api/pith-number/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/action/storage_attestation","attest_author":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/action/author_attestation","sign_citation":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/action/citation_signature","submit_replication":"https://pith.science/pith/Z6XCAWGSXLTQ3ICIGYVYT2LEQ3/action/replication_record"}},"created_at":"2026-05-18T01:23:42.701700+00:00","updated_at":"2026-05-18T01:23:42.701700+00:00"}