{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GODEUUAM6BVB5MDEIIMBO6W4MI","short_pith_number":"pith:GODEUUAM","canonical_record":{"source":{"id":"1310.7530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-10-28T18:43:10Z","cross_cats_sorted":[],"title_canon_sha256":"c6a8dc54229f7838f02741bb629478c0716fb7424b9ec9ce777722140bfdf6a9","abstract_canon_sha256":"4c9fa303cd86f01e16387692deb4ac60cdaa64d675ed5ab44170ff4dcfdfe9a1"},"schema_version":"1.0"},"canonical_sha256":"33864a500cf06a1eb0644218177adc621141d568a5fc22600bb6d1456b7cfcd8","source":{"kind":"arxiv","id":"1310.7530","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7530","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7530v1","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7530","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"GODEUUAM6BVB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GODEUUAM6BVB5MDE","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GODEUUAM","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GODEUUAM6BVB5MDEIIMBO6W4MI","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7530","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-10-28T18:43:10Z","cross_cats_sorted":[],"title_canon_sha256":"c6a8dc54229f7838f02741bb629478c0716fb7424b9ec9ce777722140bfdf6a9","abstract_canon_sha256":"4c9fa303cd86f01e16387692deb4ac60cdaa64d675ed5ab44170ff4dcfdfe9a1"},"schema_version":"1.0"},"canonical_sha256":"33864a500cf06a1eb0644218177adc621141d568a5fc22600bb6d1456b7cfcd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:38.891067Z","signature_b64":"zrHxbakAPYeTlVxqyIft6v7nS7xn+k72Td8C6nm4qtoR6Sh8vYNprftxcU4pzbuh1IX3lk1w56V29+rYhd0aBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33864a500cf06a1eb0644218177adc621141d568a5fc22600bb6d1456b7cfcd8","last_reissued_at":"2026-05-18T03:08:38.890439Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:38.890439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7530","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4fGDPLbF3sZMamAO+Quc779b+g1mZP7189qGyYl0XDF4E4oYuz4uE5vfXJP0QYwdYga1C2Pl2DihDLcDd99LBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:55:13.793948Z"},"content_sha256":"b32f550f82d6deaef16b9d23c5b98ff038ea8263c86c65fa761adb8acaf72e93","schema_version":"1.0","event_id":"sha256:b32f550f82d6deaef16b9d23c5b98ff038ea8263c86c65fa761adb8acaf72e93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GODEUUAM6BVB5MDEIIMBO6W4MI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact model structures and recollements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"James Gillespie","submitted_at":"2013-10-28T18:43:10Z","abstract_excerpt":"We show how to obtain recollements of triangulated categories using the theory of exact model structures. After noting how the theory relates to well-known notions in the simplest case of Frobenius categories, we apply these ideas to recollements of homotopy categories of chain complexes. In short, we give model categorical explanations for the classical Verdier localization recollement as well as several recollement situations due to Neeman and Murfet."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7530","kind":"arxiv","version":1},"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":"2026-05-18T03:08:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gkJ4+/h3fqhBaj+qJMpEblhdyhrdYrsb2r4rgbWsILQHxq4TDOcoBZZm5tk8XGBz2tA5G77ZcS2WgR4kQnvRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T16:55:13.794290Z"},"content_sha256":"9033bb084d3a283c483ccf824c769768e58713dda6654da037ab4c73a7d8733d","schema_version":"1.0","event_id":"sha256:9033bb084d3a283c483ccf824c769768e58713dda6654da037ab4c73a7d8733d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GODEUUAM6BVB5MDEIIMBO6W4MI/bundle.json","state_url":"https://pith.science/pith/GODEUUAM6BVB5MDEIIMBO6W4MI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GODEUUAM6BVB5MDEIIMBO6W4MI/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":"2026-07-06T16:55:13Z","links":{"resolver":"https://pith.science/pith/GODEUUAM6BVB5MDEIIMBO6W4MI","bundle":"https://pith.science/pith/GODEUUAM6BVB5MDEIIMBO6W4MI/bundle.json","state":"https://pith.science/pith/GODEUUAM6BVB5MDEIIMBO6W4MI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GODEUUAM6BVB5MDEIIMBO6W4MI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GODEUUAM6BVB5MDEIIMBO6W4MI","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":"4c9fa303cd86f01e16387692deb4ac60cdaa64d675ed5ab44170ff4dcfdfe9a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-10-28T18:43:10Z","title_canon_sha256":"c6a8dc54229f7838f02741bb629478c0716fb7424b9ec9ce777722140bfdf6a9"},"schema_version":"1.0","source":{"id":"1310.7530","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7530","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7530v1","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7530","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"GODEUUAM6BVB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GODEUUAM6BVB5MDE","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GODEUUAM","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:9033bb084d3a283c483ccf824c769768e58713dda6654da037ab4c73a7d8733d","target":"graph","created_at":"2026-05-18T03:08:38Z","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":"We show how to obtain recollements of triangulated categories using the theory of exact model structures. After noting how the theory relates to well-known notions in the simplest case of Frobenius categories, we apply these ideas to recollements of homotopy categories of chain complexes. In short, we give model categorical explanations for the classical Verdier localization recollement as well as several recollement situations due to Neeman and Murfet.","authors_text":"James Gillespie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-10-28T18:43:10Z","title":"Exact model structures and recollements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7530","kind":"arxiv","version":1},"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:b32f550f82d6deaef16b9d23c5b98ff038ea8263c86c65fa761adb8acaf72e93","target":"record","created_at":"2026-05-18T03:08:38Z","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":"4c9fa303cd86f01e16387692deb4ac60cdaa64d675ed5ab44170ff4dcfdfe9a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-10-28T18:43:10Z","title_canon_sha256":"c6a8dc54229f7838f02741bb629478c0716fb7424b9ec9ce777722140bfdf6a9"},"schema_version":"1.0","source":{"id":"1310.7530","kind":"arxiv","version":1}},"canonical_sha256":"33864a500cf06a1eb0644218177adc621141d568a5fc22600bb6d1456b7cfcd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33864a500cf06a1eb0644218177adc621141d568a5fc22600bb6d1456b7cfcd8","first_computed_at":"2026-05-18T03:08:38.890439Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:38.890439Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zrHxbakAPYeTlVxqyIft6v7nS7xn+k72Td8C6nm4qtoR6Sh8vYNprftxcU4pzbuh1IX3lk1w56V29+rYhd0aBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:38.891067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7530","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b32f550f82d6deaef16b9d23c5b98ff038ea8263c86c65fa761adb8acaf72e93","sha256:9033bb084d3a283c483ccf824c769768e58713dda6654da037ab4c73a7d8733d"],"state_sha256":"a04cd9b41bb7c2e5a55ea7916ef109451f2eecc83cc29a687f28cb3cea3e4704"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OPAUaN0jUy1hpy7pG2PBf9jx5aEjbg2RBbiVdlkMWMGYTYrc2vL3lALm+TXklhk0Gl6kQP+ykz1mr6ajsNHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T16:55:13.797168Z","bundle_sha256":"c8ad6950d7f6e18cda2a1a92bd8b0f6eede4bdd213fdad58e29d8eca04c93b27"}}