{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FCFA4ZH3SHRWP3YBTRN6LEUSJJ","short_pith_number":"pith:FCFA4ZH3","canonical_record":{"source":{"id":"1401.4015","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-16T13:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"b8abd49ff41e60dd4cca038f6f2416332560f7ae0d7be26d74c68c1741bb4db9","abstract_canon_sha256":"26ae181b334f9d96abf2ed2d874aa76b1d6d9503f97ba4b56d096f08e5238a30"},"schema_version":"1.0"},"canonical_sha256":"288a0e64fb91e367ef019c5be592924a68b40505f276ecd2dd582d7071f05958","source":{"kind":"arxiv","id":"1401.4015","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4015","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4015v3","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4015","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"FCFA4ZH3SHRW","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FCFA4ZH3SHRWP3YB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FCFA4ZH3","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FCFA4ZH3SHRWP3YBTRN6LEUSJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1401.4015","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-16T13:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"b8abd49ff41e60dd4cca038f6f2416332560f7ae0d7be26d74c68c1741bb4db9","abstract_canon_sha256":"26ae181b334f9d96abf2ed2d874aa76b1d6d9503f97ba4b56d096f08e5238a30"},"schema_version":"1.0"},"canonical_sha256":"288a0e64fb91e367ef019c5be592924a68b40505f276ecd2dd582d7071f05958","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:33.095155Z","signature_b64":"MszNWb+3sBn+fP4ELoehsbAovXINbgQtORAsqlDk9Me2y7yU49LBRKsOUXhjSzZAGnpRAYD26Oh2WgDbp7HdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"288a0e64fb91e367ef019c5be592924a68b40505f276ecd2dd582d7071f05958","last_reissued_at":"2026-05-18T03:01:33.094427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:33.094427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.4015","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:01:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ibrCkpNkwLwIFd6CGSDuKkAaZ0eLPLfCDEruIfII+XYYHMJCaSBN3asvZPSmoEUiyQLzsvV6WHsYlX0eGTrUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:13:05.039212Z"},"content_sha256":"ec93208d3a23a28991446bd5914ed0343eb9786864f6d0513e4aef20ac8abd71","schema_version":"1.0","event_id":"sha256:ec93208d3a23a28991446bd5914ed0343eb9786864f6d0513e4aef20ac8abd71"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FCFA4ZH3SHRWP3YBTRN6LEUSJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some notes on Gorenstein projective modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jian Wang","submitted_at":"2014-01-16T13:19:21Z","abstract_excerpt":"Let $R$ be a ring. It is proved that $(\\mathcal{GP}(R), \\mathcal{GP}(R)^\\bot)$ is a complete hereditary cotorsion pair, where $\\mathcal{GP}(R)$ denotes the class of the Gorenstein projective left $R$-modules. Then we get that each left $R$-module has a special Gorenstein projective precover. As an application, we prove that all Gorenstein projective left $R$-modules are Gorenstein flat over left noetherian rings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4015","kind":"arxiv","version":3},"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":"2026-05-18T03:01:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dk3/Jy+eVwzjGnDNBStdMxHjh4YoLP03kgwd2KqlAvVfhr5YZwjw7kmHdINwQIWFMTeUkwHnVMX/yGF+Xy5TAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T18:13:05.039964Z"},"content_sha256":"e33dfd434052d16459160e321ac9d95b36a1d8e6587ef6dd8902e4a00c136a7c","schema_version":"1.0","event_id":"sha256:e33dfd434052d16459160e321ac9d95b36a1d8e6587ef6dd8902e4a00c136a7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ/bundle.json","state_url":"https://pith.science/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ/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":"2026-06-09T18:13:05Z","links":{"resolver":"https://pith.science/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ","bundle":"https://pith.science/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ/bundle.json","state":"https://pith.science/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCFA4ZH3SHRWP3YBTRN6LEUSJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FCFA4ZH3SHRWP3YBTRN6LEUSJJ","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":"26ae181b334f9d96abf2ed2d874aa76b1d6d9503f97ba4b56d096f08e5238a30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-16T13:19:21Z","title_canon_sha256":"b8abd49ff41e60dd4cca038f6f2416332560f7ae0d7be26d74c68c1741bb4db9"},"schema_version":"1.0","source":{"id":"1401.4015","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4015","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4015v3","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4015","created_at":"2026-05-18T03:01:33Z"},{"alias_kind":"pith_short_12","alias_value":"FCFA4ZH3SHRW","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FCFA4ZH3SHRWP3YB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FCFA4ZH3","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:e33dfd434052d16459160e321ac9d95b36a1d8e6587ef6dd8902e4a00c136a7c","target":"graph","created_at":"2026-05-18T03:01:33Z","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":"Let $R$ be a ring. It is proved that $(\\mathcal{GP}(R), \\mathcal{GP}(R)^\\bot)$ is a complete hereditary cotorsion pair, where $\\mathcal{GP}(R)$ denotes the class of the Gorenstein projective left $R$-modules. Then we get that each left $R$-module has a special Gorenstein projective precover. As an application, we prove that all Gorenstein projective left $R$-modules are Gorenstein flat over left noetherian rings.","authors_text":"Jian Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-16T13:19:21Z","title":"Some notes on Gorenstein projective modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4015","kind":"arxiv","version":3},"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:ec93208d3a23a28991446bd5914ed0343eb9786864f6d0513e4aef20ac8abd71","target":"record","created_at":"2026-05-18T03:01:33Z","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":"26ae181b334f9d96abf2ed2d874aa76b1d6d9503f97ba4b56d096f08e5238a30","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-01-16T13:19:21Z","title_canon_sha256":"b8abd49ff41e60dd4cca038f6f2416332560f7ae0d7be26d74c68c1741bb4db9"},"schema_version":"1.0","source":{"id":"1401.4015","kind":"arxiv","version":3}},"canonical_sha256":"288a0e64fb91e367ef019c5be592924a68b40505f276ecd2dd582d7071f05958","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"288a0e64fb91e367ef019c5be592924a68b40505f276ecd2dd582d7071f05958","first_computed_at":"2026-05-18T03:01:33.094427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:33.094427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MszNWb+3sBn+fP4ELoehsbAovXINbgQtORAsqlDk9Me2y7yU49LBRKsOUXhjSzZAGnpRAYD26Oh2WgDbp7HdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:33.095155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4015","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec93208d3a23a28991446bd5914ed0343eb9786864f6d0513e4aef20ac8abd71","sha256:e33dfd434052d16459160e321ac9d95b36a1d8e6587ef6dd8902e4a00c136a7c"],"state_sha256":"7c2b5624cfdeee43debaed6c5dc9d339962092f189f046db0eba22af46d036d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"geoQe3968T9cqKujFDrLRGhBDrddT3cYikKQ+EUBBcGiXKFaG0J3NrgzbNNtjXisPjO/pXXPOw6J7++ThYIIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T18:13:05.044157Z","bundle_sha256":"b32ce26afde3d82520b37112a1ea69baad32950be763b0b017356fef8f5d4489"}}