{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PEYJ7RZXH55ZBE4W2FQI2CM66N","short_pith_number":"pith:PEYJ7RZX","canonical_record":{"source":{"id":"1412.4085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-12T18:57:16Z","cross_cats_sorted":[],"title_canon_sha256":"d9fa7deb69891fea43f33fb99791084e71000577b3eacb9e2d5bce84c12fd052","abstract_canon_sha256":"d27c13d56cc1bf58cbb94b8b1f72f93125a48ee8159ef7108372df6791adeda5"},"schema_version":"1.0"},"canonical_sha256":"79309fc7373f7b909396d1608d099ef37075352b359d5f5f000e9a09209012ff","source":{"kind":"arxiv","id":"1412.4085","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4085","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4085v2","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4085","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"PEYJ7RZXH55Z","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEYJ7RZXH55ZBE4W","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEYJ7RZX","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PEYJ7RZXH55ZBE4W2FQI2CM66N","target":"record","payload":{"canonical_record":{"source":{"id":"1412.4085","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-12T18:57:16Z","cross_cats_sorted":[],"title_canon_sha256":"d9fa7deb69891fea43f33fb99791084e71000577b3eacb9e2d5bce84c12fd052","abstract_canon_sha256":"d27c13d56cc1bf58cbb94b8b1f72f93125a48ee8159ef7108372df6791adeda5"},"schema_version":"1.0"},"canonical_sha256":"79309fc7373f7b909396d1608d099ef37075352b359d5f5f000e9a09209012ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:30.390003Z","signature_b64":"3LI/uwCPTQW1ikQrmuLBrqJHwjAdzLvG6Cs/Pdf5WerCwupMyJzNsoMD7bIYFRHG9PGFKPqfxQCHgtIJ62rTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79309fc7373f7b909396d1608d099ef37075352b359d5f5f000e9a09209012ff","last_reissued_at":"2026-05-18T01:04:30.389428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:30.389428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.4085","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ANyrlL73hzncmzgfSMEKjQ5aHCDeUSpBgJzaoaoAaWb9oGB/p3tNUSuPQ20bhVvt9fdWebfENcNzPQ9eSFj0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T12:24:46.727509Z"},"content_sha256":"65dd4786811d4bd45f66fc5a7c9f6f555ca249f9d802f1f0e6e6810056c730c8","schema_version":"1.0","event_id":"sha256:65dd4786811d4bd45f66fc5a7c9f6f555ca249f9d802f1f0e6e6810056c730c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PEYJ7RZXH55ZBE4W2FQI2CM66N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The flat stable module category of a coherent ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"James Gillespie","submitted_at":"2014-12-12T18:57:16Z","abstract_excerpt":"Let $R$ by a right coherent ring and $R$-Mod denote the category of left $R$-modules. We show that there is an abelian model structure on $R$-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for constructing model structures, the key step is to show that a module is flat and cotorsion if and only if it is Gorenstein flat and Gorenstein cotorsion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4085","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iluY1XeusCbH8sd2fuSYGAVgamTGOtMLiucB3VkGPLqmH8nv0VQA1kre/SeheTFA9R96Wvrq+QvJy60gu4U+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T12:24:46.727844Z"},"content_sha256":"46e93813995ba7faa75d234fc5b6bf2d08bf8d0d284369ff6425184bdc8234e2","schema_version":"1.0","event_id":"sha256:46e93813995ba7faa75d234fc5b6bf2d08bf8d0d284369ff6425184bdc8234e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N/bundle.json","state_url":"https://pith.science/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N/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":"2026-07-06T12:24:46Z","links":{"resolver":"https://pith.science/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N","bundle":"https://pith.science/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N/bundle.json","state":"https://pith.science/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PEYJ7RZXH55ZBE4W2FQI2CM66N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PEYJ7RZXH55ZBE4W2FQI2CM66N","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":"d27c13d56cc1bf58cbb94b8b1f72f93125a48ee8159ef7108372df6791adeda5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-12T18:57:16Z","title_canon_sha256":"d9fa7deb69891fea43f33fb99791084e71000577b3eacb9e2d5bce84c12fd052"},"schema_version":"1.0","source":{"id":"1412.4085","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4085","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4085v2","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4085","created_at":"2026-05-18T01:04:30Z"},{"alias_kind":"pith_short_12","alias_value":"PEYJ7RZXH55Z","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEYJ7RZXH55ZBE4W","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEYJ7RZX","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:46e93813995ba7faa75d234fc5b6bf2d08bf8d0d284369ff6425184bdc8234e2","target":"graph","created_at":"2026-05-18T01:04:30Z","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 $R$ by a right coherent ring and $R$-Mod denote the category of left $R$-modules. We show that there is an abelian model structure on $R$-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for constructing model structures, the key step is to show that a module is flat and cotorsion if and only if it is Gorenstein flat and Gorenstein cotorsion.","authors_text":"James Gillespie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-12T18:57:16Z","title":"The flat stable module category of a coherent ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4085","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":"sha256:65dd4786811d4bd45f66fc5a7c9f6f555ca249f9d802f1f0e6e6810056c730c8","target":"record","created_at":"2026-05-18T01:04:30Z","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":"d27c13d56cc1bf58cbb94b8b1f72f93125a48ee8159ef7108372df6791adeda5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-12-12T18:57:16Z","title_canon_sha256":"d9fa7deb69891fea43f33fb99791084e71000577b3eacb9e2d5bce84c12fd052"},"schema_version":"1.0","source":{"id":"1412.4085","kind":"arxiv","version":2}},"canonical_sha256":"79309fc7373f7b909396d1608d099ef37075352b359d5f5f000e9a09209012ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79309fc7373f7b909396d1608d099ef37075352b359d5f5f000e9a09209012ff","first_computed_at":"2026-05-18T01:04:30.389428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:30.389428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3LI/uwCPTQW1ikQrmuLBrqJHwjAdzLvG6Cs/Pdf5WerCwupMyJzNsoMD7bIYFRHG9PGFKPqfxQCHgtIJ62rTDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:30.390003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4085","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65dd4786811d4bd45f66fc5a7c9f6f555ca249f9d802f1f0e6e6810056c730c8","sha256:46e93813995ba7faa75d234fc5b6bf2d08bf8d0d284369ff6425184bdc8234e2"],"state_sha256":"fad0568159e940559f75d0061315c1e8f58429ea2355a95aef6036ba7984ebd2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slJ4gzQBixCjdkHeyOL4DMJuWJ9Voa5/dAXy8TELVP7mJOxRLTuhZuDN5Bd1HA5SqWJFPic9WT2B3e0/IAt9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T12:24:46.729690Z","bundle_sha256":"717a60ac4142dcbf687fc5b9089812c61cba8b11d915fcd54fc663f1ea8ca19a"}}