{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UT6YUKBR6OYD2MPNVJ6FP7COHT","short_pith_number":"pith:UT6YUKBR","schema_version":"1.0","canonical_sha256":"a4fd8a2831f3b03d31edaa7c57fc4e3cee5f36dc9ddc8efb366edc0653699147","source":{"kind":"arxiv","id":"1207.5869","version":2},"attestation_state":"computed","paper":{"title":"Modules that detect finite homological dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Hailong Dao, Olgur Celikbas, Ryo Takahashi","submitted_at":"2012-07-25T02:17:40Z","abstract_excerpt":"We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that, if a commutative Noetherian complete local ring R admits a test module of finite Gorenstein dimension, then R is Gorenstein."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1207.5869","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-07-25T02:17:40Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"c1cc583036ee711544c969f966a3c0bf55a08128f03968e471416efd416f8b1f","abstract_canon_sha256":"3ea8b9f1526390b4c9d9815c7289147cac4e9d39c50167d270355caa44ee70bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:21.649185Z","signature_b64":"JJrHGd86RO0YEXi0pd92FLRCSpw2q4Eyabj8uaG6xNfw50JJQOr52byXlroz5sZNca/V5EHMLIPM+k6+w+zOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4fd8a2831f3b03d31edaa7c57fc4e3cee5f36dc9ddc8efb366edc0653699147","last_reissued_at":"2026-05-18T01:28:21.648673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:21.648673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Modules that detect finite homological dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Hailong Dao, Olgur Celikbas, Ryo Takahashi","submitted_at":"2012-07-25T02:17:40Z","abstract_excerpt":"We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that, if a commutative Noetherian complete local ring R admits a test module of finite Gorenstein dimension, then R is Gorenstein."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5869","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.5869","created_at":"2026-05-18T01:28:21.648765+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.5869v2","created_at":"2026-05-18T01:28:21.648765+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5869","created_at":"2026-05-18T01:28:21.648765+00:00"},{"alias_kind":"pith_short_12","alias_value":"UT6YUKBR6OYD","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"UT6YUKBR6OYD2MPN","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"UT6YUKBR","created_at":"2026-05-18T12:27:25.539911+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT","json":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT.json","graph_json":"https://pith.science/api/pith-number/UT6YUKBR6OYD2MPNVJ6FP7COHT/graph.json","events_json":"https://pith.science/api/pith-number/UT6YUKBR6OYD2MPNVJ6FP7COHT/events.json","paper":"https://pith.science/paper/UT6YUKBR"},"agent_actions":{"view_html":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT","download_json":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT.json","view_paper":"https://pith.science/paper/UT6YUKBR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.5869&json=true","fetch_graph":"https://pith.science/api/pith-number/UT6YUKBR6OYD2MPNVJ6FP7COHT/graph.json","fetch_events":"https://pith.science/api/pith-number/UT6YUKBR6OYD2MPNVJ6FP7COHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT/action/storage_attestation","attest_author":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT/action/author_attestation","sign_citation":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT/action/citation_signature","submit_replication":"https://pith.science/pith/UT6YUKBR6OYD2MPNVJ6FP7COHT/action/replication_record"}},"created_at":"2026-05-18T01:28:21.648765+00:00","updated_at":"2026-05-18T01:28:21.648765+00:00"}