{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q3ZUZ32HTWQIA4FJBOWGQWNU2Q","short_pith_number":"pith:Q3ZUZ32H","canonical_record":{"source":{"id":"1410.5611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-21T10:33:41Z","cross_cats_sorted":[],"title_canon_sha256":"62fd11988627c452cba664ff58939ad0148cf57003af26e2de458364cb9af30d","abstract_canon_sha256":"39b2189fecdd239d2185853f2db5268e4251424bbaeb5d129fde0856946a1e7b"},"schema_version":"1.0"},"canonical_sha256":"86f34cef479da08070a90bac6859b4d411db268fdf302ccbadeb21abdb725d39","source":{"kind":"arxiv","id":"1410.5611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5611","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5611v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5611","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"Q3ZUZ32HTWQI","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3ZUZ32HTWQIA4FJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3ZUZ32H","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q3ZUZ32HTWQIA4FJBOWGQWNU2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-21T10:33:41Z","cross_cats_sorted":[],"title_canon_sha256":"62fd11988627c452cba664ff58939ad0148cf57003af26e2de458364cb9af30d","abstract_canon_sha256":"39b2189fecdd239d2185853f2db5268e4251424bbaeb5d129fde0856946a1e7b"},"schema_version":"1.0"},"canonical_sha256":"86f34cef479da08070a90bac6859b4d411db268fdf302ccbadeb21abdb725d39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:39.460086Z","signature_b64":"c/X3VsdM7jeQqKOLeCrok5+1snl2LqnUCZ1e7AmkPHYJZitF7IiTLRJvJw4x6w2Yg6/r35wzBNNCLwHZI7L8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86f34cef479da08070a90bac6859b4d411db268fdf302ccbadeb21abdb725d39","last_reissued_at":"2026-05-18T02:39:39.459575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:39.459575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5611","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVuwZ5oZrPGQDkodNDZ3yRxnlIRULJWrKZCJvIyYmZvDM/N8KHy8i8MwwVQY/RvisMkvitGr352SsPjA/MBSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:26:01.799004Z"},"content_sha256":"00e48a0a3c183ef9301ca7d808ea9830d61bcfeaa3d50811e5c781ac8c82b3e5","schema_version":"1.0","event_id":"sha256:00e48a0a3c183ef9301ca7d808ea9830d61bcfeaa3d50811e5c781ac8c82b3e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q3ZUZ32HTWQIA4FJBOWGQWNU2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximations by maximal Cohen-Macaulay modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Henrik Holm","submitted_at":"2014-10-21T10:33:41Z","abstract_excerpt":"Auslander and Buchweitz have proved that every finitely generated module over a Cohen-Macaulay (CM) ring with a dualizing module admits a so-called maximal CM approximation. In terms of relative homological algebra, this means that every finitely generated module has a special maximal CM precover. In this paper, we prove the existence of special maximal CM preenvelopes and, in the case where the ground ring is henselian, of maximal CM envelopes. We also characterize the rings over which every finitely generated module has a maximal CM envelope with the unique lifting property. Finally, we show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5611","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:39:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BzIIdmzCJB8Zm54kCRBWC7jHnTEhk9khnPCoxbakMy05D3xJONKN7UlVdca3BLJxawPZLpKLlgDFEYosUPBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:26:01.799361Z"},"content_sha256":"8bce8a198baf42252242987909d1840da1d53da600b250de080cbc625eee1307","schema_version":"1.0","event_id":"sha256:8bce8a198baf42252242987909d1840da1d53da600b250de080cbc625eee1307"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q/bundle.json","state_url":"https://pith.science/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T18:26:01Z","links":{"resolver":"https://pith.science/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q","bundle":"https://pith.science/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q/bundle.json","state":"https://pith.science/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3ZUZ32HTWQIA4FJBOWGQWNU2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q3ZUZ32HTWQIA4FJBOWGQWNU2Q","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":"39b2189fecdd239d2185853f2db5268e4251424bbaeb5d129fde0856946a1e7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-21T10:33:41Z","title_canon_sha256":"62fd11988627c452cba664ff58939ad0148cf57003af26e2de458364cb9af30d"},"schema_version":"1.0","source":{"id":"1410.5611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5611","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5611v1","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5611","created_at":"2026-05-18T02:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"Q3ZUZ32HTWQI","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q3ZUZ32HTWQIA4FJ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q3ZUZ32H","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:8bce8a198baf42252242987909d1840da1d53da600b250de080cbc625eee1307","target":"graph","created_at":"2026-05-18T02:39:39Z","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":"Auslander and Buchweitz have proved that every finitely generated module over a Cohen-Macaulay (CM) ring with a dualizing module admits a so-called maximal CM approximation. In terms of relative homological algebra, this means that every finitely generated module has a special maximal CM precover. In this paper, we prove the existence of special maximal CM preenvelopes and, in the case where the ground ring is henselian, of maximal CM envelopes. We also characterize the rings over which every finitely generated module has a maximal CM envelope with the unique lifting property. Finally, we show","authors_text":"Henrik Holm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-21T10:33:41Z","title":"Approximations by maximal Cohen-Macaulay modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5611","kind":"arxiv","version":1},"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":"sha256:00e48a0a3c183ef9301ca7d808ea9830d61bcfeaa3d50811e5c781ac8c82b3e5","target":"record","created_at":"2026-05-18T02:39:39Z","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":"39b2189fecdd239d2185853f2db5268e4251424bbaeb5d129fde0856946a1e7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-10-21T10:33:41Z","title_canon_sha256":"62fd11988627c452cba664ff58939ad0148cf57003af26e2de458364cb9af30d"},"schema_version":"1.0","source":{"id":"1410.5611","kind":"arxiv","version":1}},"canonical_sha256":"86f34cef479da08070a90bac6859b4d411db268fdf302ccbadeb21abdb725d39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86f34cef479da08070a90bac6859b4d411db268fdf302ccbadeb21abdb725d39","first_computed_at":"2026-05-18T02:39:39.459575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:39.459575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c/X3VsdM7jeQqKOLeCrok5+1snl2LqnUCZ1e7AmkPHYJZitF7IiTLRJvJw4x6w2Yg6/r35wzBNNCLwHZI7L8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:39.460086Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00e48a0a3c183ef9301ca7d808ea9830d61bcfeaa3d50811e5c781ac8c82b3e5","sha256:8bce8a198baf42252242987909d1840da1d53da600b250de080cbc625eee1307"],"state_sha256":"2a2e58a55f063a265d91d257b7f7921727a969d8ea93cac0d4e88a34796a6e18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f7N9NvOwXMzkgLan6RKt1gyjLkhjcq0Sma6DV9bVxeFcM1gz9JbR3f4b1Lwm3UAyS2p4/Uexovgpzn6pxZtpAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:26:01.801309Z","bundle_sha256":"c073ca9cfe1f5632a482ed80cf294ba07600740d629b3f895bc9119db4c8baeb"}}