{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CB7HE4FICTFX5EUJOXMR7IXZ6Z","short_pith_number":"pith:CB7HE4FI","schema_version":"1.0","canonical_sha256":"107e7270a814cb7e928975d91fa2f9f65f4ed6680d694417ee14396084a05556","source":{"kind":"arxiv","id":"1211.0945","version":1},"attestation_state":"computed","paper":{"title":"Dualities in Koszul graded AS Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Roberto Martinez-Villa","submitted_at":"2012-11-05T17:45:03Z","abstract_excerpt":"The paper is dedicated to the study of certain non commutative graded AS Gorenstein algebras $\\Lambda $.\n  The main result of the paper is that for Koszul algebras $\\Lambda $ with Yoneda algebra $\\Gamma $, such that both $\\Lambda $ and $\\Gamma $ are graded AS Gorenstein noetherian of finite local cohomology dimension on both sides, there are dualities of triangulated categories:\n\\underline{$gr$}$_{\\Lambda}[\\Omega ^{-1}]$ $\\cong D^{b}(Qgr_{\\Gamma})$ and \\underline{$gr$}$_{\\Gamma}[\\Omega ^{-1}]$ $\\cong D^{b}(Qgr_{\\Lambda})$\nwhere, and $Qgr_{\\Gamma}$ is the category of tails, this is: the categor"},"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":"1211.0945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2012-11-05T17:45:03Z","cross_cats_sorted":[],"title_canon_sha256":"a6564347122cf1c85a5e7940b3bbe259d137076ada1027a9c4670b348e608546","abstract_canon_sha256":"82a8a2711ba3fc8e92b14a475c188758a63eb5e49d24c798c7ef448793f88b04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:31.217642Z","signature_b64":"k2P2cmySEKWvQg3A1VLPmXnF96VEaOB2uaBo/iZ9g6gOVLe0kz37kkGY/Vj6LltaDCcrKBBwAJB+VRMUkhY9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"107e7270a814cb7e928975d91fa2f9f65f4ed6680d694417ee14396084a05556","last_reissued_at":"2026-05-18T03:41:31.217032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:31.217032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dualities in Koszul graded AS Gorenstein algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Roberto Martinez-Villa","submitted_at":"2012-11-05T17:45:03Z","abstract_excerpt":"The paper is dedicated to the study of certain non commutative graded AS Gorenstein algebras $\\Lambda $.\n  The main result of the paper is that for Koszul algebras $\\Lambda $ with Yoneda algebra $\\Gamma $, such that both $\\Lambda $ and $\\Gamma $ are graded AS Gorenstein noetherian of finite local cohomology dimension on both sides, there are dualities of triangulated categories:\n\\underline{$gr$}$_{\\Lambda}[\\Omega ^{-1}]$ $\\cong D^{b}(Qgr_{\\Gamma})$ and \\underline{$gr$}$_{\\Gamma}[\\Omega ^{-1}]$ $\\cong D^{b}(Qgr_{\\Lambda})$\nwhere, and $Qgr_{\\Gamma}$ is the category of tails, this is: the categor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0945","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":"1211.0945","created_at":"2026-05-18T03:41:31.217125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.0945v1","created_at":"2026-05-18T03:41:31.217125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0945","created_at":"2026-05-18T03:41:31.217125+00:00"},{"alias_kind":"pith_short_12","alias_value":"CB7HE4FICTFX","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CB7HE4FICTFX5EUJ","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CB7HE4FI","created_at":"2026-05-18T12:27:01.376967+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/CB7HE4FICTFX5EUJOXMR7IXZ6Z","json":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z.json","graph_json":"https://pith.science/api/pith-number/CB7HE4FICTFX5EUJOXMR7IXZ6Z/graph.json","events_json":"https://pith.science/api/pith-number/CB7HE4FICTFX5EUJOXMR7IXZ6Z/events.json","paper":"https://pith.science/paper/CB7HE4FI"},"agent_actions":{"view_html":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z","download_json":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z.json","view_paper":"https://pith.science/paper/CB7HE4FI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.0945&json=true","fetch_graph":"https://pith.science/api/pith-number/CB7HE4FICTFX5EUJOXMR7IXZ6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/CB7HE4FICTFX5EUJOXMR7IXZ6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z/action/storage_attestation","attest_author":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z/action/author_attestation","sign_citation":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z/action/citation_signature","submit_replication":"https://pith.science/pith/CB7HE4FICTFX5EUJOXMR7IXZ6Z/action/replication_record"}},"created_at":"2026-05-18T03:41:31.217125+00:00","updated_at":"2026-05-18T03:41:31.217125+00:00"}