{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:KLG3B6RHL6ST7YUGCA6UEDAQ65","short_pith_number":"pith:KLG3B6RH","schema_version":"1.0","canonical_sha256":"52cdb0fa275fa53fe286103d420c10f77fe05efa18737d9f8737f8a5d26b78b9","source":{"kind":"arxiv","id":"2302.00035","version":1},"attestation_state":"computed","paper":{"title":"On Auslander`s depth formula","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Amit Tripathi, Shashi Ranjan Sinha","submitted_at":"2023-01-31T19:07:54Z","abstract_excerpt":"We show that if Auslander`s depth formula holds for non-zero Tor-independent modules over Cohen-Macaulay local rings of dimension 1, then it holds for such modules over any Cohen-Macaulay local ring. More generally, we show that the depth formula for non-zero Tor-independent modules which have finite Cohen-Macaulay dimension over depth 1 local rings implies the depth formula for such modules over any positive depth local ring."},"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":"2302.00035","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AC","submitted_at":"2023-01-31T19:07:54Z","cross_cats_sorted":[],"title_canon_sha256":"55417b0eba848d5b8c5616b2e29dc30bc3f925d009588f6e0ec478153e3a0815","abstract_canon_sha256":"414a5dc075bed641ba48d3eff431df56aaf7d099a169ac5dbd43cbe8f276a8fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:37:58.683192Z","signature_b64":"5Emk3fEnRXVYbiRnE0FSnWmHLi4P+LPgwTPIysNPz3T7OzYf/HiSNRwl5YbJA9HjtMNUkuhTa2XsJ4F5Nw9TCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52cdb0fa275fa53fe286103d420c10f77fe05efa18737d9f8737f8a5d26b78b9","last_reissued_at":"2026-07-05T05:37:58.682669Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:37:58.682669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Auslander`s depth formula","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Amit Tripathi, Shashi Ranjan Sinha","submitted_at":"2023-01-31T19:07:54Z","abstract_excerpt":"We show that if Auslander`s depth formula holds for non-zero Tor-independent modules over Cohen-Macaulay local rings of dimension 1, then it holds for such modules over any Cohen-Macaulay local ring. More generally, we show that the depth formula for non-zero Tor-independent modules which have finite Cohen-Macaulay dimension over depth 1 local rings implies the depth formula for such modules over any positive depth local ring."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00035","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.00035/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2302.00035","created_at":"2026-07-05T05:37:58.682731+00:00"},{"alias_kind":"arxiv_version","alias_value":"2302.00035v1","created_at":"2026-07-05T05:37:58.682731+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.00035","created_at":"2026-07-05T05:37:58.682731+00:00"},{"alias_kind":"pith_short_12","alias_value":"KLG3B6RHL6ST","created_at":"2026-07-05T05:37:58.682731+00:00"},{"alias_kind":"pith_short_16","alias_value":"KLG3B6RHL6ST7YUG","created_at":"2026-07-05T05:37:58.682731+00:00"},{"alias_kind":"pith_short_8","alias_value":"KLG3B6RH","created_at":"2026-07-05T05:37:58.682731+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/KLG3B6RHL6ST7YUGCA6UEDAQ65","json":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65.json","graph_json":"https://pith.science/api/pith-number/KLG3B6RHL6ST7YUGCA6UEDAQ65/graph.json","events_json":"https://pith.science/api/pith-number/KLG3B6RHL6ST7YUGCA6UEDAQ65/events.json","paper":"https://pith.science/paper/KLG3B6RH"},"agent_actions":{"view_html":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65","download_json":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65.json","view_paper":"https://pith.science/paper/KLG3B6RH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2302.00035&json=true","fetch_graph":"https://pith.science/api/pith-number/KLG3B6RHL6ST7YUGCA6UEDAQ65/graph.json","fetch_events":"https://pith.science/api/pith-number/KLG3B6RHL6ST7YUGCA6UEDAQ65/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65/action/storage_attestation","attest_author":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65/action/author_attestation","sign_citation":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65/action/citation_signature","submit_replication":"https://pith.science/pith/KLG3B6RHL6ST7YUGCA6UEDAQ65/action/replication_record"}},"created_at":"2026-07-05T05:37:58.682731+00:00","updated_at":"2026-07-05T05:37:58.682731+00:00"}