{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EJVHWVMW2MTSSZIJNNBJCODLVL","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":"0e2eeeb939f598fafe7f5e953112a9e0ca0028a7868725830ac1ea1fd0bd16e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-26T19:57:46Z","title_canon_sha256":"c2732a7bafd958aa57083fd8069fab4502527326fa299b4ec5a57efe21a2940d"},"schema_version":"1.0","source":{"id":"2404.17680","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.17680","created_at":"2026-06-03T01:05:42Z"},{"alias_kind":"arxiv_version","alias_value":"2404.17680v2","created_at":"2026-06-03T01:05:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.17680","created_at":"2026-06-03T01:05:42Z"},{"alias_kind":"pith_short_12","alias_value":"EJVHWVMW2MTS","created_at":"2026-06-03T01:05:42Z"},{"alias_kind":"pith_short_16","alias_value":"EJVHWVMW2MTSSZIJ","created_at":"2026-06-03T01:05:42Z"},{"alias_kind":"pith_short_8","alias_value":"EJVHWVMW","created_at":"2026-06-03T01:05:42Z"}],"graph_snapshots":[{"event_id":"sha256:d28158050d935c2bd3ffc3c3564c16583ff9151132f79f1aa9052b5d8149cfd6","target":"graph","created_at":"2026-06-03T01:05:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.17680/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be a commutative noetherian local ring, and let $M$ be a finitely generated $R$-module. Inspired by works of Vasconcelos and Briggs on characterization of complete intersection local rings through the homological properties of the conormal module, in this paper, we define the characteristic module T$_M$ and the cocharacteristic module E$_M$ of $M$, and investigate their properties. Our main results include characterizations of Cohen--Macaulay and Gorenstein local rings. Also, we show that if the injective dimension of the conormal module over an almost complete intersection ring is fin","authors_text":"Mohsen Gheibi, Ryo Takahashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-26T19:57:46Z","title":"Characteristic modules over a local ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.17680","kind":"arxiv","version":2},"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:fd7e698e52387d1262b44df0fbf9da0c5c124b8bdf10bd920be0ba394f35a9a8","target":"record","created_at":"2026-06-03T01:05:42Z","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":"0e2eeeb939f598fafe7f5e953112a9e0ca0028a7868725830ac1ea1fd0bd16e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2024-04-26T19:57:46Z","title_canon_sha256":"c2732a7bafd958aa57083fd8069fab4502527326fa299b4ec5a57efe21a2940d"},"schema_version":"1.0","source":{"id":"2404.17680","kind":"arxiv","version":2}},"canonical_sha256":"226a7b5596d3272965096b4291386baad9ebf71019cbe3c280139675701aafd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"226a7b5596d3272965096b4291386baad9ebf71019cbe3c280139675701aafd2","first_computed_at":"2026-06-03T01:05:42.666076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:42.666076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8r/4wnYdunFPH8Sm2n3KByzF31JA3M2Zs3qNL9zjMUU9lHtKyZ3wNm8Thu3MKGh5b0dIxegg9iapa/JRwoimAw==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:42.666616Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.17680","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd7e698e52387d1262b44df0fbf9da0c5c124b8bdf10bd920be0ba394f35a9a8","sha256:d28158050d935c2bd3ffc3c3564c16583ff9151132f79f1aa9052b5d8149cfd6"],"state_sha256":"1add7ca371addc5aca1f964220b2409674e3d809f9e29c218c317a31aa354af4"}