{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KL2N7XOREN2766BO5ZVFKFHQ5X","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":"7e288e657462728a02e84590cefcd5202f32ef5f5beb7d1a694b86c9563a861d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-21T11:52:57Z","title_canon_sha256":"ab6352825e5c4f868dabb71c712afc4dc8d3b2d0519e29f5b3b383ea09c9a1a3"},"schema_version":"1.0","source":{"id":"1104.4242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4242","created_at":"2026-05-18T04:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4242v1","created_at":"2026-05-18T04:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4242","created_at":"2026-05-18T04:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"KL2N7XOREN27","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KL2N7XOREN2766BO","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KL2N7XOR","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:dccd475b039e9cc33992f636ceb4873067ec765e72a9043fa606784b672da632","target":"graph","created_at":"2026-05-18T04:23:44Z","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":"The main objective of this paper is to generalize a notion of Koszul resolutions and charcterizing modules which admits such a resolution. We turn out that for a noetherian ring $A$ and a coherent $A$ module $M$, $M$ has a two dimensional generalized Koszul resolution if and only if $M$ is a pure weight two module in the sense of \\cite{HM09}.","authors_text":"Akiyoshi Sannai, Satoshi Mochizuki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-21T11:52:57Z","title":"Generalized Koszul resolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4242","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":"sha256:23966698c82b86c4071c5b0b2aa053d2fb2dc1fa2f22d705b604f2c334eaa6ea","target":"record","created_at":"2026-05-18T04:23:44Z","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":"7e288e657462728a02e84590cefcd5202f32ef5f5beb7d1a694b86c9563a861d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-04-21T11:52:57Z","title_canon_sha256":"ab6352825e5c4f868dabb71c712afc4dc8d3b2d0519e29f5b3b383ea09c9a1a3"},"schema_version":"1.0","source":{"id":"1104.4242","kind":"arxiv","version":1}},"canonical_sha256":"52f4dfddd12375ff782eee6a5514f0edc0482f8e8b4d2b9e6f5782331de3ed9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52f4dfddd12375ff782eee6a5514f0edc0482f8e8b4d2b9e6f5782331de3ed9b","first_computed_at":"2026-05-18T04:23:44.755067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:44.755067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6UXEcxKhdsayYTkipFVaE1VyoJywvt2EbLJc4i5Pm1LG+5KpFVpaiIeL0iIJwx6e2ht7lLCFC/XReE68eZEsCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:44.755783Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23966698c82b86c4071c5b0b2aa053d2fb2dc1fa2f22d705b604f2c334eaa6ea","sha256:dccd475b039e9cc33992f636ceb4873067ec765e72a9043fa606784b672da632"],"state_sha256":"0debd9c809006fe11e14c93bf1bb1fa2654f9623f1374a4d690566b17a893b78"}