{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CHOSGKC2I573VOJCSKG33BFSWO","short_pith_number":"pith:CHOSGKC2","canonical_record":{"source":{"id":"1112.3064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-13T22:42:37Z","cross_cats_sorted":[],"title_canon_sha256":"20dc3e40b8b75c02a60ec811d1761253b8f697048074d03f2982a5e08e60b44e","abstract_canon_sha256":"52a3eb7d57ca77b3f096ff69b69bba7790e51101a0c8c2b2fe8f0b2590dfed65"},"schema_version":"1.0"},"canonical_sha256":"11dd23285a477fbab922928dbd84b2b3b0fe6b5651bac7fbbdb8f01d39e7cc7f","source":{"kind":"arxiv","id":"1112.3064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3064","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3064v1","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3064","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"CHOSGKC2I573","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CHOSGKC2I573VOJC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CHOSGKC2","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CHOSGKC2I573VOJCSKG33BFSWO","target":"record","payload":{"canonical_record":{"source":{"id":"1112.3064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-13T22:42:37Z","cross_cats_sorted":[],"title_canon_sha256":"20dc3e40b8b75c02a60ec811d1761253b8f697048074d03f2982a5e08e60b44e","abstract_canon_sha256":"52a3eb7d57ca77b3f096ff69b69bba7790e51101a0c8c2b2fe8f0b2590dfed65"},"schema_version":"1.0"},"canonical_sha256":"11dd23285a477fbab922928dbd84b2b3b0fe6b5651bac7fbbdb8f01d39e7cc7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:20.293468Z","signature_b64":"NsIva48g0+1q94D/4tj1Cq4MWBgcbZ/2TETsY+IoXy68cDGLUDFWQknyh9jca+P7Zk78b4Uwca97JifEoNSXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11dd23285a477fbab922928dbd84b2b3b0fe6b5651bac7fbbdb8f01d39e7cc7f","last_reissued_at":"2026-05-18T04:06:20.292761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:20.292761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.3064","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+VJUgmdEfDZ+9ezSm8n3jHWVv77KoZhuKkEt+9TruLhhSo5PKZoFTqi+ZPhEW1x+lKVscoNsZusYOfSxViYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:03:08.496010Z"},"content_sha256":"c448b51e05b0b3137445eadda63e4967c63b5189876c0da88844655bae4396d2","schema_version":"1.0","event_id":"sha256:c448b51e05b0b3137445eadda63e4967c63b5189876c0da88844655bae4396d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CHOSGKC2I573VOJCSKG33BFSWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Duality for Koszul Homology over Gorenstein Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Claudia Miller, Hamidreza Rahmati, Janet Striuli","submitted_at":"2011-12-13T22:42:37Z","abstract_excerpt":"We study Koszul homology over Gorenstein rings. If an ideal is strongly Cohen-Macaulay, the Koszul homology algebra satisfies Poincar\\'e duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3064","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sIgUgH1CjoALFyqGjpkYLCp+JrW4FMKa9VO1yn/lFm2Sx9Zly4mvanveZIlvF0LE8925ndodSSWb7DE0EgdBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T07:03:08.496366Z"},"content_sha256":"da8a3e5491e32d9ecd634c8f8589965f338b39909b4fa5ca1d808567567311a6","schema_version":"1.0","event_id":"sha256:da8a3e5491e32d9ecd634c8f8589965f338b39909b4fa5ca1d808567567311a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CHOSGKC2I573VOJCSKG33BFSWO/bundle.json","state_url":"https://pith.science/pith/CHOSGKC2I573VOJCSKG33BFSWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CHOSGKC2I573VOJCSKG33BFSWO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T07:03:08Z","links":{"resolver":"https://pith.science/pith/CHOSGKC2I573VOJCSKG33BFSWO","bundle":"https://pith.science/pith/CHOSGKC2I573VOJCSKG33BFSWO/bundle.json","state":"https://pith.science/pith/CHOSGKC2I573VOJCSKG33BFSWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CHOSGKC2I573VOJCSKG33BFSWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CHOSGKC2I573VOJCSKG33BFSWO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"52a3eb7d57ca77b3f096ff69b69bba7790e51101a0c8c2b2fe8f0b2590dfed65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-13T22:42:37Z","title_canon_sha256":"20dc3e40b8b75c02a60ec811d1761253b8f697048074d03f2982a5e08e60b44e"},"schema_version":"1.0","source":{"id":"1112.3064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3064","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3064v1","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3064","created_at":"2026-05-18T04:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"CHOSGKC2I573","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CHOSGKC2I573VOJC","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CHOSGKC2","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:da8a3e5491e32d9ecd634c8f8589965f338b39909b4fa5ca1d808567567311a6","target":"graph","created_at":"2026-05-18T04:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study Koszul homology over Gorenstein rings. If an ideal is strongly Cohen-Macaulay, the Koszul homology algebra satisfies Poincar\\'e duality. We prove a version of this duality which holds for all ideals and allows us to give two criteria for an ideal to be strongly Cohen-Macaulay. The first can be compared to a result of Hartshorne and Ogus; the second is a generalization of a result of Herzog, Simis, and Vasconcelos using sliding depth.","authors_text":"Claudia Miller, Hamidreza Rahmati, Janet Striuli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-13T22:42:37Z","title":"Duality for Koszul Homology over Gorenstein Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3064","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c448b51e05b0b3137445eadda63e4967c63b5189876c0da88844655bae4396d2","target":"record","created_at":"2026-05-18T04:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"52a3eb7d57ca77b3f096ff69b69bba7790e51101a0c8c2b2fe8f0b2590dfed65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-13T22:42:37Z","title_canon_sha256":"20dc3e40b8b75c02a60ec811d1761253b8f697048074d03f2982a5e08e60b44e"},"schema_version":"1.0","source":{"id":"1112.3064","kind":"arxiv","version":1}},"canonical_sha256":"11dd23285a477fbab922928dbd84b2b3b0fe6b5651bac7fbbdb8f01d39e7cc7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"11dd23285a477fbab922928dbd84b2b3b0fe6b5651bac7fbbdb8f01d39e7cc7f","first_computed_at":"2026-05-18T04:06:20.292761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:20.292761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NsIva48g0+1q94D/4tj1Cq4MWBgcbZ/2TETsY+IoXy68cDGLUDFWQknyh9jca+P7Zk78b4Uwca97JifEoNSXCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:20.293468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c448b51e05b0b3137445eadda63e4967c63b5189876c0da88844655bae4396d2","sha256:da8a3e5491e32d9ecd634c8f8589965f338b39909b4fa5ca1d808567567311a6"],"state_sha256":"4b5c314bdc821e6381907a799abb6189d324bacabafb44135a1a9852cb834381"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slR5dDw4o3O0LHBlPRucoqzJ58BZamvtmfbLGG0WdluhRVbqQUjrTW738XVaGd1Ma+hiGCF9FBFPyZACJJHLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T07:03:08.498360Z","bundle_sha256":"830f1864fcfcd3c52b3bf56bd3580dd012aadb649ea780f10453e93fb89945a4"}}