{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:QMWCMK2MKICGRNRDAOEGU5HSXP","short_pith_number":"pith:QMWCMK2M","canonical_record":{"source":{"id":"math/0608228","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2006-08-09T16:51:06Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"95bf972f7ba4029c92adb334724703a3dca6d9c5cd33c76884602439e289352a","abstract_canon_sha256":"ea76302e1d6cdf89931bcc3259ea6b72a26d5ce24f25bd40e6fd83ec4d78b778"},"schema_version":"1.0"},"canonical_sha256":"832c262b4c520468b62303886a74f2bbd0994d4ea2ca5853893696842b8c32fa","source":{"kind":"arxiv","id":"math/0608228","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608228","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608228v5","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608228","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"QMWCMK2MKICG","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"pith_short_16","alias_value":"QMWCMK2MKICGRNRD","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"pith_short_8","alias_value":"QMWCMK2M","created_at":"2026-07-04T15:42:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:QMWCMK2MKICGRNRDAOEGU5HSXP","target":"record","payload":{"canonical_record":{"source":{"id":"math/0608228","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2006-08-09T16:51:06Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"95bf972f7ba4029c92adb334724703a3dca6d9c5cd33c76884602439e289352a","abstract_canon_sha256":"ea76302e1d6cdf89931bcc3259ea6b72a26d5ce24f25bd40e6fd83ec4d78b778"},"schema_version":"1.0"},"canonical_sha256":"832c262b4c520468b62303886a74f2bbd0994d4ea2ca5853893696842b8c32fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:42:16.388284Z","signature_b64":"iAUx+0tnsIIjVG1+pemAQTtqnS54F7c9OpLoqsa8WAO/YZhOc8cJ7VkrWjbpMCaVITidzvPL6+5XJhtSWDJdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"832c262b4c520468b62303886a74f2bbd0994d4ea2ca5853893696842b8c32fa","last_reissued_at":"2026-07-04T15:42:16.387908Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:42:16.387908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0608228","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:42:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SGYy/TRLSNYmuIX2j3RZQhPTeURtSsD//lM2VtV6bbCo5qQs85Y8SsIxfwlvGtCAf/mtro8/PzYw72gTJ8cxCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T15:41:02.503869Z"},"content_sha256":"0f105fbb12a35c6f309f0f8d6566244c128fb8e1a2152bebf871a8cb694b4c9f","schema_version":"1.0","event_id":"sha256:0f105fbb12a35c6f309f0f8d6566244c128fb8e1a2152bebf871a8cb694b4c9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:QMWCMK2MKICGRNRDAOEGU5HSXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stable Infinity Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"Jacob Lurie","submitted_at":"2006-08-09T16:51:06Z","abstract_excerpt":"This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a variety of constructions. We also explain how to construct the derived category of an abelian category (with enough projective objects) as the homotopy category of a suitable stable infinity category; moreover, we characterize this stable infinity category by a universal mapping property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608228","kind":"arxiv","version":5},"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/math/0608228/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":"2026-07-04T15:42:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cw3flxMsIrlCFPJWtCxJXzNcgYhi72lSLRmMRsmO+4W+zd2dUU9y56O+tOIgIFE07hHKQpgt3lMy9khhKUX+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T15:41:02.504446Z"},"content_sha256":"85dc452c660ae22494c7bcacaa6731c63f883630cb53c34701b91b248af09c5e","schema_version":"1.0","event_id":"sha256:85dc452c660ae22494c7bcacaa6731c63f883630cb53c34701b91b248af09c5e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QMWCMK2MKICGRNRDAOEGU5HSXP/bundle.json","state_url":"https://pith.science/pith/QMWCMK2MKICGRNRDAOEGU5HSXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QMWCMK2MKICGRNRDAOEGU5HSXP/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":"2026-08-13T15:41:02Z","links":{"resolver":"https://pith.science/pith/QMWCMK2MKICGRNRDAOEGU5HSXP","bundle":"https://pith.science/pith/QMWCMK2MKICGRNRDAOEGU5HSXP/bundle.json","state":"https://pith.science/pith/QMWCMK2MKICGRNRDAOEGU5HSXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QMWCMK2MKICGRNRDAOEGU5HSXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:QMWCMK2MKICGRNRDAOEGU5HSXP","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":"ea76302e1d6cdf89931bcc3259ea6b72a26d5ce24f25bd40e6fd83ec4d78b778","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2006-08-09T16:51:06Z","title_canon_sha256":"95bf972f7ba4029c92adb334724703a3dca6d9c5cd33c76884602439e289352a"},"schema_version":"1.0","source":{"id":"math/0608228","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0608228","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"math/0608228v5","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0608228","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"QMWCMK2MKICG","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"pith_short_16","alias_value":"QMWCMK2MKICGRNRD","created_at":"2026-07-04T15:42:16Z"},{"alias_kind":"pith_short_8","alias_value":"QMWCMK2M","created_at":"2026-07-04T15:42:16Z"}],"graph_snapshots":[{"event_id":"sha256:85dc452c660ae22494c7bcacaa6731c63f883630cb53c34701b91b248af09c5e","target":"graph","created_at":"2026-07-04T15:42:16Z","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/math/0608228/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is an expository account of the theory of stable infinity categories. We prove that the homotopy category of a stable infinity category is triangulated, and that the collection of stable infinity categories is closed under a variety of constructions. We also explain how to construct the derived category of an abelian category (with enough projective objects) as the homotopy category of a suitable stable infinity category; moreover, we characterize this stable infinity category by a universal mapping property.","authors_text":"Jacob Lurie","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2006-08-09T16:51:06Z","title":"Stable Infinity Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608228","kind":"arxiv","version":5},"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":"sha256:0f105fbb12a35c6f309f0f8d6566244c128fb8e1a2152bebf871a8cb694b4c9f","target":"record","created_at":"2026-07-04T15:42:16Z","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":"ea76302e1d6cdf89931bcc3259ea6b72a26d5ce24f25bd40e6fd83ec4d78b778","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2006-08-09T16:51:06Z","title_canon_sha256":"95bf972f7ba4029c92adb334724703a3dca6d9c5cd33c76884602439e289352a"},"schema_version":"1.0","source":{"id":"math/0608228","kind":"arxiv","version":5}},"canonical_sha256":"832c262b4c520468b62303886a74f2bbd0994d4ea2ca5853893696842b8c32fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"832c262b4c520468b62303886a74f2bbd0994d4ea2ca5853893696842b8c32fa","first_computed_at":"2026-07-04T15:42:16.387908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:42:16.387908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iAUx+0tnsIIjVG1+pemAQTtqnS54F7c9OpLoqsa8WAO/YZhOc8cJ7VkrWjbpMCaVITidzvPL6+5XJhtSWDJdDg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:42:16.388284Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0608228","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f105fbb12a35c6f309f0f8d6566244c128fb8e1a2152bebf871a8cb694b4c9f","sha256:85dc452c660ae22494c7bcacaa6731c63f883630cb53c34701b91b248af09c5e"],"state_sha256":"84b7b223d18c5fa6e2837244fa1247d1df4b7037fca50b03cd0124b31bb800fc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpOSMEfBsmxcFmCwcRcCdk/kVs19igWLyRdv+cqHgdqfSnwUv6ffBQ7OsLeLYs9uiGisxagGVe1wprLk3l4NBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T15:41:02.509444Z","bundle_sha256":"4e25c47d79fd0723b68514b023e06c0c6ced9b5d361972e321a52b5c9bb337e5"}}