{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ETXWRPDVWRWHQNP6VNZSS3OMQD","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":"9c2ed2bbfe319f96b4639abe9805c8d780741a9ded3342f9250d318d3103fa90","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-06-28T10:59:45Z","title_canon_sha256":"537997931a28bc661c8003821b3c86f41eebdcdb529b5106c33aec8aed4a59cf"},"schema_version":"1.0","source":{"id":"1306.6788","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.6788","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"arxiv_version","alias_value":"1306.6788v2","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.6788","created_at":"2026-05-18T02:48:17Z"},{"alias_kind":"pith_short_12","alias_value":"ETXWRPDVWRWH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"ETXWRPDVWRWHQNP6","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"ETXWRPDV","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:c974b3cafd6106d4592b3e50e4edd2389db120759f50d43f1eaa527857711e83","target":"graph","created_at":"2026-05-18T02:48:17Z","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":"Recently, tilting and cotilting classes over commutative noetherian rings have been classified in arXiv:1203.0907. We proceed and, for each n-cotilting class C, construct an n-cotilting module inducing C by an iteration of injective precovers. A further refinement of the construction yields the unique minimal n-cotilting module inducing C. Finally, we consider localization: a cotilting module is called ample, if all of its localizations are cotilting. We prove that for each 1-cotilting class, there exists an ample cotilting module inducing it, but give an example of a 2-cotilting class which f","authors_text":"Dolors Herbera, Jan Stovicek, Jan Trlifaj","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-06-28T10:59:45Z","title":"Cotilting modules over commutative noetherian rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.6788","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":"sha256:0ed328a0226e90c6f1b5db2c7e2fc9deafbfd8c09093b790cf2d691e43e1f922","target":"record","created_at":"2026-05-18T02:48:17Z","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":"9c2ed2bbfe319f96b4639abe9805c8d780741a9ded3342f9250d318d3103fa90","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-06-28T10:59:45Z","title_canon_sha256":"537997931a28bc661c8003821b3c86f41eebdcdb529b5106c33aec8aed4a59cf"},"schema_version":"1.0","source":{"id":"1306.6788","kind":"arxiv","version":2}},"canonical_sha256":"24ef68bc75b46c7835feab73296dcc80e056a4c844768b6c0a4b8d65141e0082","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24ef68bc75b46c7835feab73296dcc80e056a4c844768b6c0a4b8d65141e0082","first_computed_at":"2026-05-18T02:48:17.721170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:17.721170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c8YsIHjNlceH4/bCqy6HPv9oQMPyVQUS3aBrjK5OvkmtQ7mut/bSM27nNrQga80uab1/wjwVy/sqsdXfcDUjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:17.721693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.6788","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ed328a0226e90c6f1b5db2c7e2fc9deafbfd8c09093b790cf2d691e43e1f922","sha256:c974b3cafd6106d4592b3e50e4edd2389db120759f50d43f1eaa527857711e83"],"state_sha256":"71895a89642d4471fecbd4e9ed4ab5db38993c8e2204f672855f23674bf45ee9"}