{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:Y2P5RMG76YKKYULVO2D66EP3GO","short_pith_number":"pith:Y2P5RMG7","schema_version":"1.0","canonical_sha256":"c69fd8b0dff614ac51757687ef11fb33bbd6fdbe61be6f07aa038142d8bc9771","source":{"kind":"arxiv","id":"0802.2772","version":3},"attestation_state":"computed","paper":{"title":"The Auslander-Reiten translate on monomial quotient rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Gunnar Floystad, Morten Brun","submitted_at":"2008-02-20T15:38:27Z","abstract_excerpt":"For a multidegree t in N^n, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Na_t, on the (derived) category of such modules. A monomial ideal I is positively t-determined if every generator x^a has a \\leq t. We compute the multigraded cohomology- and betti spaces of Na_t^k(S/I) for every iterate k, and also the S-module structure of these cohomology modules. This comprehensively generalizes results of Hochster and Gr\\\"abe on local cohomology of Stanley-Reisner rings."},"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":"0802.2772","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-02-20T15:38:27Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"cc59bd071064b780dee88106eb5e0ba313e9d7a47f77ae14e3986e8da9796f2a","abstract_canon_sha256":"d815987d66aa0ab75343f5e7c3f8b087842c39961e6600cc8a8b7b5c466fc077"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:33.536596Z","signature_b64":"wEbulCS9TnZZAbLGBfZ2Xwjkqm8Xqf3OPecvhOq9YVBfaEs2hlGt33xLoDTUgV4co5j3woqYjAasZP3HqWe+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c69fd8b0dff614ac51757687ef11fb33bbd6fdbe61be6f07aa038142d8bc9771","last_reissued_at":"2026-05-18T04:06:33.535735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:33.535735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Auslander-Reiten translate on monomial quotient rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Gunnar Floystad, Morten Brun","submitted_at":"2008-02-20T15:38:27Z","abstract_excerpt":"For a multidegree t in N^n, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the Auslander-Reiten translate, Na_t, on the (derived) category of such modules. A monomial ideal I is positively t-determined if every generator x^a has a \\leq t. We compute the multigraded cohomology- and betti spaces of Na_t^k(S/I) for every iterate k, and also the S-module structure of these cohomology modules. This comprehensively generalizes results of Hochster and Gr\\\"abe on local cohomology of Stanley-Reisner rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2772","kind":"arxiv","version":3},"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":"0802.2772","created_at":"2026-05-18T04:06:33.535882+00:00"},{"alias_kind":"arxiv_version","alias_value":"0802.2772v3","created_at":"2026-05-18T04:06:33.535882+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2772","created_at":"2026-05-18T04:06:33.535882+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2P5RMG76YKK","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2P5RMG76YKKYULV","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2P5RMG7","created_at":"2026-05-18T12:25:58.018023+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/Y2P5RMG76YKKYULVO2D66EP3GO","json":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO.json","graph_json":"https://pith.science/api/pith-number/Y2P5RMG76YKKYULVO2D66EP3GO/graph.json","events_json":"https://pith.science/api/pith-number/Y2P5RMG76YKKYULVO2D66EP3GO/events.json","paper":"https://pith.science/paper/Y2P5RMG7"},"agent_actions":{"view_html":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO","download_json":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO.json","view_paper":"https://pith.science/paper/Y2P5RMG7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0802.2772&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2P5RMG76YKKYULVO2D66EP3GO/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2P5RMG76YKKYULVO2D66EP3GO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO/action/storage_attestation","attest_author":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO/action/author_attestation","sign_citation":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO/action/citation_signature","submit_replication":"https://pith.science/pith/Y2P5RMG76YKKYULVO2D66EP3GO/action/replication_record"}},"created_at":"2026-05-18T04:06:33.535882+00:00","updated_at":"2026-05-18T04:06:33.535882+00:00"}