{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:5OV4PRSDY5FY7OO3MF3MONXVYS","short_pith_number":"pith:5OV4PRSD","schema_version":"1.0","canonical_sha256":"ebabc7c643c74b8fb9db6176c736f5c48a990b2eeba591df9b115b85cc6c0ae6","source":{"kind":"arxiv","id":"2201.05542","version":2},"attestation_state":"computed","paper":{"title":"The homotopy category of acyclic complexes of pure-projective modules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.AT","authors_text":"James Gillespie","submitted_at":"2022-01-14T16:27:40Z","abstract_excerpt":"Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put this homotopy category into a recollement with two other compactly generated triangulated categories: The usual derived category of $R$ and the pure derived category of $R$. This also gives a new model for the derived category."},"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":"2201.05542","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2022-01-14T16:27:40Z","cross_cats_sorted":["math.CT","math.RA"],"title_canon_sha256":"e0d764e9d4797cae883139c0d7e405978fd8261c5ec9b46c01c556fdfec6ad2b","abstract_canon_sha256":"a4b7117ecc0cacaaa09fd49908feba0e84237ed8809401bb763c17ba4282a810"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:50:04.587346Z","signature_b64":"8GXXiVyVTUvkviK9cmiOe/EaFCUwD2yOFPz/leUsIXoBamoFdeGfAiCsj5X0XGnl8SPNvI7aq3xMAgaqP9xoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebabc7c643c74b8fb9db6176c736f5c48a990b2eeba591df9b115b85cc6c0ae6","last_reissued_at":"2026-07-05T03:50:04.586961Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:50:04.586961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The homotopy category of acyclic complexes of pure-projective modules","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.AT","authors_text":"James Gillespie","submitted_at":"2022-01-14T16:27:40Z","abstract_excerpt":"Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put this homotopy category into a recollement with two other compactly generated triangulated categories: The usual derived category of $R$ and the pure derived category of $R$. This also gives a new model for the derived category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05542","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.05542/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":"2201.05542","created_at":"2026-07-05T03:50:04.587017+00:00"},{"alias_kind":"arxiv_version","alias_value":"2201.05542v2","created_at":"2026-07-05T03:50:04.587017+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05542","created_at":"2026-07-05T03:50:04.587017+00:00"},{"alias_kind":"pith_short_12","alias_value":"5OV4PRSDY5FY","created_at":"2026-07-05T03:50:04.587017+00:00"},{"alias_kind":"pith_short_16","alias_value":"5OV4PRSDY5FY7OO3","created_at":"2026-07-05T03:50:04.587017+00:00"},{"alias_kind":"pith_short_8","alias_value":"5OV4PRSD","created_at":"2026-07-05T03:50:04.587017+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/5OV4PRSDY5FY7OO3MF3MONXVYS","json":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS.json","graph_json":"https://pith.science/api/pith-number/5OV4PRSDY5FY7OO3MF3MONXVYS/graph.json","events_json":"https://pith.science/api/pith-number/5OV4PRSDY5FY7OO3MF3MONXVYS/events.json","paper":"https://pith.science/paper/5OV4PRSD"},"agent_actions":{"view_html":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS","download_json":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS.json","view_paper":"https://pith.science/paper/5OV4PRSD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2201.05542&json=true","fetch_graph":"https://pith.science/api/pith-number/5OV4PRSDY5FY7OO3MF3MONXVYS/graph.json","fetch_events":"https://pith.science/api/pith-number/5OV4PRSDY5FY7OO3MF3MONXVYS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS/action/storage_attestation","attest_author":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS/action/author_attestation","sign_citation":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS/action/citation_signature","submit_replication":"https://pith.science/pith/5OV4PRSDY5FY7OO3MF3MONXVYS/action/replication_record"}},"created_at":"2026-07-05T03:50:04.587017+00:00","updated_at":"2026-07-05T03:50:04.587017+00:00"}