{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:PXENN3EKPBLESBGUTLFREI3XQX","short_pith_number":"pith:PXENN3EK","canonical_record":{"source":{"id":"2208.05684","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-08-11T08:01:11Z","cross_cats_sorted":[],"title_canon_sha256":"bafa46d8ec798882c69a53af61662f24926caa504262348540ebcc34dde5c7e2","abstract_canon_sha256":"b3a78b0c4863bb0034a2bb6e55117f82b3b62ae227781199bc986ee6eaa7957c"},"schema_version":"1.0"},"canonical_sha256":"7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b","source":{"kind":"arxiv","id":"2208.05684","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05684","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05684v3","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05684","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"PXENN3EKPBLE","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"PXENN3EKPBLESBGU","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"PXENN3EK","created_at":"2026-07-05T07:22:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:PXENN3EKPBLESBGUTLFREI3XQX","target":"record","payload":{"canonical_record":{"source":{"id":"2208.05684","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-08-11T08:01:11Z","cross_cats_sorted":[],"title_canon_sha256":"bafa46d8ec798882c69a53af61662f24926caa504262348540ebcc34dde5c7e2","abstract_canon_sha256":"b3a78b0c4863bb0034a2bb6e55117f82b3b62ae227781199bc986ee6eaa7957c"},"schema_version":"1.0"},"canonical_sha256":"7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:22:13.132133Z","signature_b64":"AP/c924bMOfjUFzkylqO8LBfBcnHcQdaUvHjgHdwDW5Oq/JsZ39dpo/TA9BjpRStl4tmnedJOjKnlg4x4Hq7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b","last_reissued_at":"2026-07-05T07:22:13.131646Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:22:13.131646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.05684","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":"2026-07-05T07:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ew3tSR/ajaPJjGVqVovRZ3fIP67Le8IGbx0FaoVJmtIomb+7rtMy+kAJK32TSeP3VLBU2fyHVAkY2tyuT5MYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:08:52.910815Z"},"content_sha256":"9e9dafcdd7bccf1bd14ce3dab6b0d90f7e0a0e3e69180164d8d008ac80874925","schema_version":"1.0","event_id":"sha256:9e9dafcdd7bccf1bd14ce3dab6b0d90f7e0a0e3e69180164d8d008ac80874925"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:PXENN3EKPBLESBGUTLFREI3XQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cotorsion pairs and model structures on Morita rings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jian Cui, Pu Zhang, Shi Rong","submitted_at":"2022-08-11T08:01:11Z","abstract_excerpt":"This paper is to study cotorsion pairs and abelian model structures on some Morita rings \\ $\\Lambda =\\left(\\begin{smallmatrix} A & {}_AN_B\n  {}_BM_A & B\\end{smallmatrix}\\right)$. From cotorsion pairs $(\\mathcal U, \\mathcal X)$ and $(\\mathcal V, \\mathcal Y)$, respectively in $A$-Mod and $B$-Mod, one constructs 4 kinds of cotorsion pairs in $\\Lambda$-Mod. There even exists an algebra $\\Lambda$ such that the four cotorsion pairs above are pairwise different. The heredity and completeness of these cotorsion pairs are studied. The problem of identifications, namely, when the first two cotorsion pai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05684","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.05684/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gjq+LSr3eqM90ewiAq3XFLwJh70BsSARgdO7NwzhC5fKqVhkZdXzQnUYBmG6Dr0uF5UqkZOPRzhsSqGputVoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T02:08:52.911328Z"},"content_sha256":"6f84ae13b854b3e8cbd652861e36782ff653b4b5bc14a03317ff964ec1ef088d","schema_version":"1.0","event_id":"sha256:6f84ae13b854b3e8cbd652861e36782ff653b4b5bc14a03317ff964ec1ef088d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXENN3EKPBLESBGUTLFREI3XQX/bundle.json","state_url":"https://pith.science/pith/PXENN3EKPBLESBGUTLFREI3XQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXENN3EKPBLESBGUTLFREI3XQX/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":"2026-08-06T02:08:52Z","links":{"resolver":"https://pith.science/pith/PXENN3EKPBLESBGUTLFREI3XQX","bundle":"https://pith.science/pith/PXENN3EKPBLESBGUTLFREI3XQX/bundle.json","state":"https://pith.science/pith/PXENN3EKPBLESBGUTLFREI3XQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXENN3EKPBLESBGUTLFREI3XQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PXENN3EKPBLESBGUTLFREI3XQX","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":"b3a78b0c4863bb0034a2bb6e55117f82b3b62ae227781199bc986ee6eaa7957c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-08-11T08:01:11Z","title_canon_sha256":"bafa46d8ec798882c69a53af61662f24926caa504262348540ebcc34dde5c7e2"},"schema_version":"1.0","source":{"id":"2208.05684","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05684","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05684v3","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05684","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"PXENN3EKPBLE","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"pith_short_16","alias_value":"PXENN3EKPBLESBGU","created_at":"2026-07-05T07:22:13Z"},{"alias_kind":"pith_short_8","alias_value":"PXENN3EK","created_at":"2026-07-05T07:22:13Z"}],"graph_snapshots":[{"event_id":"sha256:6f84ae13b854b3e8cbd652861e36782ff653b4b5bc14a03317ff964ec1ef088d","target":"graph","created_at":"2026-07-05T07:22:13Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2208.05684/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is to study cotorsion pairs and abelian model structures on some Morita rings \\ $\\Lambda =\\left(\\begin{smallmatrix} A & {}_AN_B\n  {}_BM_A & B\\end{smallmatrix}\\right)$. From cotorsion pairs $(\\mathcal U, \\mathcal X)$ and $(\\mathcal V, \\mathcal Y)$, respectively in $A$-Mod and $B$-Mod, one constructs 4 kinds of cotorsion pairs in $\\Lambda$-Mod. There even exists an algebra $\\Lambda$ such that the four cotorsion pairs above are pairwise different. The heredity and completeness of these cotorsion pairs are studied. The problem of identifications, namely, when the first two cotorsion pai","authors_text":"Jian Cui, Pu Zhang, Shi Rong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-08-11T08:01:11Z","title":"Cotorsion pairs and model structures on Morita rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05684","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":"sha256:9e9dafcdd7bccf1bd14ce3dab6b0d90f7e0a0e3e69180164d8d008ac80874925","target":"record","created_at":"2026-07-05T07:22:13Z","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":"b3a78b0c4863bb0034a2bb6e55117f82b3b62ae227781199bc986ee6eaa7957c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2022-08-11T08:01:11Z","title_canon_sha256":"bafa46d8ec798882c69a53af61662f24926caa504262348540ebcc34dde5c7e2"},"schema_version":"1.0","source":{"id":"2208.05684","kind":"arxiv","version":3}},"canonical_sha256":"7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dc8d6ec8a78564904d49acb12237785d163f5df6ee9fe4076e75d958db2395b","first_computed_at":"2026-07-05T07:22:13.131646Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:22:13.131646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AP/c924bMOfjUFzkylqO8LBfBcnHcQdaUvHjgHdwDW5Oq/JsZ39dpo/TA9BjpRStl4tmnedJOjKnlg4x4Hq7Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:22:13.132133Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.05684","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e9dafcdd7bccf1bd14ce3dab6b0d90f7e0a0e3e69180164d8d008ac80874925","sha256:6f84ae13b854b3e8cbd652861e36782ff653b4b5bc14a03317ff964ec1ef088d"],"state_sha256":"570782f3af2b05b270306632b5700a5ce173748171da676945a22964be77c3ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2bq06T/H1izzU6NwfkejW3i+auBz4nzQ1gFlAYQPz0dcIRBQPJ+jmIGHDT30Y4MXpMhzI50m5JVJAR6NOG+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T02:08:52.916761Z","bundle_sha256":"eb325223e9c8418442feb4af8ee56e7d79332ee35a22a8aaa7bb764a7945dc92"}}