{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FMF3NRJEO2U2IRWWNXJSIQP5PK","short_pith_number":"pith:FMF3NRJE","canonical_record":{"source":{"id":"1307.5505","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2013-07-21T09:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"8b9bdb422f0b766cbac86b89413b1c540816672b9406d04bc217979fe88dd72b","abstract_canon_sha256":"363327dd170f1b41abd7fe9d076ab157f10ea6bf03ababc003aba4e196ef8b18"},"schema_version":"1.0"},"canonical_sha256":"2b0bb6c52476a9a446d66dd32441fd7ab7c42807d053e32f6e7bc4bd9c773fa6","source":{"kind":"arxiv","id":"1307.5505","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5505","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5505v4","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5505","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"FMF3NRJEO2U2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FMF3NRJEO2U2IRWW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FMF3NRJE","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FMF3NRJEO2U2IRWWNXJSIQP5PK","target":"record","payload":{"canonical_record":{"source":{"id":"1307.5505","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2013-07-21T09:01:39Z","cross_cats_sorted":[],"title_canon_sha256":"8b9bdb422f0b766cbac86b89413b1c540816672b9406d04bc217979fe88dd72b","abstract_canon_sha256":"363327dd170f1b41abd7fe9d076ab157f10ea6bf03ababc003aba4e196ef8b18"},"schema_version":"1.0"},"canonical_sha256":"2b0bb6c52476a9a446d66dd32441fd7ab7c42807d053e32f6e7bc4bd9c773fa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:44.216696Z","signature_b64":"g+AgSrbqEnox5oUNdDobEAXwlwImW3xZOh01gBjEw5M4fIll/WuoGGYllR1UIlGuK+pDWWfq3LtjdbCVEGIeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b0bb6c52476a9a446d66dd32441fd7ab7c42807d053e32f6e7bc4bd9c773fa6","last_reissued_at":"2026-05-18T03:05:44.216071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:44.216071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.5505","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rwSMKE75dEstZoZ7sc+GWf8a2HnZwEH5zIXgaalI5FxxE35lJHy6HteO2c7AYGcYUtAwp8OplpxyRUgL0U5DDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T17:21:11.101354Z"},"content_sha256":"1a18156767d1cb01b11ef40fc5f0c535b7451a5dff6ce142550caa725aebea22","schema_version":"1.0","event_id":"sha256:1a18156767d1cb01b11ef40fc5f0c535b7451a5dff6ce142550caa725aebea22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FMF3NRJEO2U2IRWWNXJSIQP5PK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flat quasi-coherent sheaves of finite cotorsion dimension","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Esmaeil Hosseini","submitted_at":"2013-07-21T09:01:39Z","abstract_excerpt":"Let X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent and n-perfect(not necessarily of finite krull dimension), we prove that every at quasi-coherent sheaf has finite pure injective dimension. Also, we show that there is an equivalence K(PinfX)---> D(FlatX) of homotopy categories, whenever K(PinfX) is the homotopy category of pure injective at quasi-coherent sheaves and D(FlatX) is the pure derived category of at quasi-coherent sheaves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5505","kind":"arxiv","version":4},"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":"2026-05-18T03:05:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SHDOifBD4OqAeC13LCBaX6w9hNWqwhpB9ZLUSjjIH6mkps5zRrk+rGGN5umVuDNqQUJMN2NQ7Jq/zct0k/P3Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T17:21:11.101704Z"},"content_sha256":"047d386ac2ea4b513889e23c223e1014a53cf4e6b7ca69da4c1c82f70a846818","schema_version":"1.0","event_id":"sha256:047d386ac2ea4b513889e23c223e1014a53cf4e6b7ca69da4c1c82f70a846818"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK/bundle.json","state_url":"https://pith.science/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK/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":"2026-07-01T17:21:11Z","links":{"resolver":"https://pith.science/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK","bundle":"https://pith.science/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK/bundle.json","state":"https://pith.science/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMF3NRJEO2U2IRWWNXJSIQP5PK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FMF3NRJEO2U2IRWWNXJSIQP5PK","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":"363327dd170f1b41abd7fe9d076ab157f10ea6bf03ababc003aba4e196ef8b18","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2013-07-21T09:01:39Z","title_canon_sha256":"8b9bdb422f0b766cbac86b89413b1c540816672b9406d04bc217979fe88dd72b"},"schema_version":"1.0","source":{"id":"1307.5505","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5505","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5505v4","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5505","created_at":"2026-05-18T03:05:44Z"},{"alias_kind":"pith_short_12","alias_value":"FMF3NRJEO2U2","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FMF3NRJEO2U2IRWW","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FMF3NRJE","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:047d386ac2ea4b513889e23c223e1014a53cf4e6b7ca69da4c1c82f70a846818","target":"graph","created_at":"2026-05-18T03:05:44Z","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 X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent and n-perfect(not necessarily of finite krull dimension), we prove that every at quasi-coherent sheaf has finite pure injective dimension. Also, we show that there is an equivalence K(PinfX)---> D(FlatX) of homotopy categories, whenever K(PinfX) is the homotopy category of pure injective at quasi-coherent sheaves and D(FlatX) is the pure derived category of at quasi-coherent sheaves.","authors_text":"Esmaeil Hosseini","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2013-07-21T09:01:39Z","title":"Flat quasi-coherent sheaves of finite cotorsion dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5505","kind":"arxiv","version":4},"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":"sha256:1a18156767d1cb01b11ef40fc5f0c535b7451a5dff6ce142550caa725aebea22","target":"record","created_at":"2026-05-18T03:05:44Z","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":"363327dd170f1b41abd7fe9d076ab157f10ea6bf03ababc003aba4e196ef8b18","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.AG","submitted_at":"2013-07-21T09:01:39Z","title_canon_sha256":"8b9bdb422f0b766cbac86b89413b1c540816672b9406d04bc217979fe88dd72b"},"schema_version":"1.0","source":{"id":"1307.5505","kind":"arxiv","version":4}},"canonical_sha256":"2b0bb6c52476a9a446d66dd32441fd7ab7c42807d053e32f6e7bc4bd9c773fa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b0bb6c52476a9a446d66dd32441fd7ab7c42807d053e32f6e7bc4bd9c773fa6","first_computed_at":"2026-05-18T03:05:44.216071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:44.216071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g+AgSrbqEnox5oUNdDobEAXwlwImW3xZOh01gBjEw5M4fIll/WuoGGYllR1UIlGuK+pDWWfq3LtjdbCVEGIeAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:44.216696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5505","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a18156767d1cb01b11ef40fc5f0c535b7451a5dff6ce142550caa725aebea22","sha256:047d386ac2ea4b513889e23c223e1014a53cf4e6b7ca69da4c1c82f70a846818"],"state_sha256":"52bf43f6a376982ca2952808332e301fa6924e0546c53168caab4b3497878080"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3byW6970qNf/vyO/p21I/fSqRNO4Ph7eIBed1vk8bXSFJpUegp5dCytkiBp6DUXN0s/kKTWfyFO5mpJvlgCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T17:21:11.103594Z","bundle_sha256":"1c2baa0a186d1fe3d4bfce3842d7a3929d5796f60d47fc22a89982de72d97847"}}