{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QEM3AUJCAIFP6E47Z55PBP6T7J","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":"03301ab5098c78cdfce3c99be04ef8f0479e36ed1dc321dc8930690a7a9a265d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-17T05:35:07Z","title_canon_sha256":"2b1d7eb1a61806676ec58d6a4d1bd5cb064600f136cc310196df1c058cc1d981"},"schema_version":"1.0","source":{"id":"1408.3796","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.3796","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1408.3796v2","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.3796","created_at":"2026-05-18T01:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"QEM3AUJCAIFP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"QEM3AUJCAIFP6E47","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"QEM3AUJC","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:774920fa295366076dffe5f82bc8bdc263667a20f95732a63531dfed1aa5ce09","target":"graph","created_at":"2026-05-18T01:14:26Z","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":"In this article, we shall characterize torsionfreeness of modules with respect to a semidualizing module in terms of the Serre's condition (S_n). As its applications, we give a characterization of Cohen-Macaulay rings R such that R_p is Gorenstein for all prime ideals p of height less than n, and we will give a partial answer of Tachikawa conjecture and Auslander-Reiten conjecture.","authors_text":"Kei-ichiro Iima, Tokuji Araya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-17T05:35:07Z","title":"Remarks on torsionfreeness and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3796","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":"sha256:351ca103b9fde14e22bcea3a5446231e30e1745f79d2d4f994dfcddea827373d","target":"record","created_at":"2026-05-18T01:14:26Z","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":"03301ab5098c78cdfce3c99be04ef8f0479e36ed1dc321dc8930690a7a9a265d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-08-17T05:35:07Z","title_canon_sha256":"2b1d7eb1a61806676ec58d6a4d1bd5cb064600f136cc310196df1c058cc1d981"},"schema_version":"1.0","source":{"id":"1408.3796","kind":"arxiv","version":2}},"canonical_sha256":"8119b05122020aff139fcf7af0bfd3fa52b5719bb07f7f2689858ddd8cef5a50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8119b05122020aff139fcf7af0bfd3fa52b5719bb07f7f2689858ddd8cef5a50","first_computed_at":"2026-05-18T01:14:26.273058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:26.273058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RxLzvDXK+jhPD2QHkwH/3IueutVrG73vtmlm7zuAdl17fK8Df6vI9ErZUgtgUWxqc6WqbkVgwnnvWIJTxd7jCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:26.273666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.3796","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:351ca103b9fde14e22bcea3a5446231e30e1745f79d2d4f994dfcddea827373d","sha256:774920fa295366076dffe5f82bc8bdc263667a20f95732a63531dfed1aa5ce09"],"state_sha256":"cd6073b983d1d06e9b35afb9302eb1117102e2ba795bc0368b4e7a2a52b07acc"}