{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:5PMKCCTA6ECT5YTJYOXHA6GH6A","short_pith_number":"pith:5PMKCCTA","canonical_record":{"source":{"id":"1901.09461","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-27T23:22:21Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"1ace3b90d4b5e8ac44e0283779a30ce944626cf896c782b6b854516054b7463a","abstract_canon_sha256":"0831538127ba2311dac038de0932ac9f2bcb9a107bcf79948bd1184fff0ee51f"},"schema_version":"1.0"},"canonical_sha256":"ebd8a10a60f1053ee269c3ae7078c7f02fa5df428148fd94a3443f3b1325f18c","source":{"kind":"arxiv","id":"1901.09461","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09461","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09461v2","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09461","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"5PMKCCTA6ECT","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"pith_short_16","alias_value":"5PMKCCTA6ECT5YTJ","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"pith_short_8","alias_value":"5PMKCCTA","created_at":"2026-07-05T00:54:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:5PMKCCTA6ECT5YTJYOXHA6GH6A","target":"record","payload":{"canonical_record":{"source":{"id":"1901.09461","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-27T23:22:21Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"1ace3b90d4b5e8ac44e0283779a30ce944626cf896c782b6b854516054b7463a","abstract_canon_sha256":"0831538127ba2311dac038de0932ac9f2bcb9a107bcf79948bd1184fff0ee51f"},"schema_version":"1.0"},"canonical_sha256":"ebd8a10a60f1053ee269c3ae7078c7f02fa5df428148fd94a3443f3b1325f18c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:22.251512Z","signature_b64":"BkOtV0P1sMffn3+5IEK5YO1DxBeKKEXC0AWABcGrDADpL0Kf8Q4ZRn4hYX6APuXioZIrSXtyrqihDoaX1WhjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebd8a10a60f1053ee269c3ae7078c7f02fa5df428148fd94a3443f3b1325f18c","last_reissued_at":"2026-07-05T00:54:22.251093Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:22.251093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.09461","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:54:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//YXU5nNEw7strMkxmP4xsEwCTX/p11RBrtA3g6HT4V9k5rNotYkISwvKTab5WCXBAaDh2MUkn9VGfl8eoFsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T12:33:51.173641Z"},"content_sha256":"e1d1d65889fbbb2bc36d758fb006a1f94be23e87d3e367c85bf44a7dcf3a15b4","schema_version":"1.0","event_id":"sha256:e1d1d65889fbbb2bc36d758fb006a1f94be23e87d3e367c85bf44a7dcf3a15b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:5PMKCCTA6ECT5YTJYOXHA6GH6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three notions of dimension for triangulated categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AG","authors_text":"Alexey Elagin, Valery A. Lunts","submitted_at":"2019-01-27T23:22:21Z","abstract_excerpt":"In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09461","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/1901.09461/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":"2026-07-05T00:54:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tiUaaq2xFBqOJ+PdrKv4lxVShFyA3XOlF8LzxqXrXTsxFk/sQjNkauhklUG/noU3D3p0okA/U6HQd9Wrf0M6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T12:33:51.174287Z"},"content_sha256":"a22a3ab9be3bb19e5f04684dd6f2679d0d216a0095ae0da52ed7118b8e233a34","schema_version":"1.0","event_id":"sha256:a22a3ab9be3bb19e5f04684dd6f2679d0d216a0095ae0da52ed7118b8e233a34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A/bundle.json","state_url":"https://pith.science/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A/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":"2026-08-15T12:33:51Z","links":{"resolver":"https://pith.science/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A","bundle":"https://pith.science/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A/bundle.json","state":"https://pith.science/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PMKCCTA6ECT5YTJYOXHA6GH6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:5PMKCCTA6ECT5YTJYOXHA6GH6A","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":"0831538127ba2311dac038de0932ac9f2bcb9a107bcf79948bd1184fff0ee51f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-27T23:22:21Z","title_canon_sha256":"1ace3b90d4b5e8ac44e0283779a30ce944626cf896c782b6b854516054b7463a"},"schema_version":"1.0","source":{"id":"1901.09461","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.09461","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1901.09461v2","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.09461","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"5PMKCCTA6ECT","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"pith_short_16","alias_value":"5PMKCCTA6ECT5YTJ","created_at":"2026-07-05T00:54:22Z"},{"alias_kind":"pith_short_8","alias_value":"5PMKCCTA","created_at":"2026-07-05T00:54:22Z"}],"graph_snapshots":[{"event_id":"sha256:a22a3ab9be3bb19e5f04684dd6f2679d0d216a0095ae0da52ed7118b8e233a34","target":"graph","created_at":"2026-07-05T00:54:22Z","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/1901.09461/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems.","authors_text":"Alexey Elagin, Valery A. Lunts","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-27T23:22:21Z","title":"Three notions of dimension for triangulated categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09461","kind":"arxiv","version":2},"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:e1d1d65889fbbb2bc36d758fb006a1f94be23e87d3e367c85bf44a7dcf3a15b4","target":"record","created_at":"2026-07-05T00:54:22Z","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":"0831538127ba2311dac038de0932ac9f2bcb9a107bcf79948bd1184fff0ee51f","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-01-27T23:22:21Z","title_canon_sha256":"1ace3b90d4b5e8ac44e0283779a30ce944626cf896c782b6b854516054b7463a"},"schema_version":"1.0","source":{"id":"1901.09461","kind":"arxiv","version":2}},"canonical_sha256":"ebd8a10a60f1053ee269c3ae7078c7f02fa5df428148fd94a3443f3b1325f18c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebd8a10a60f1053ee269c3ae7078c7f02fa5df428148fd94a3443f3b1325f18c","first_computed_at":"2026-07-05T00:54:22.251093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:22.251093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BkOtV0P1sMffn3+5IEK5YO1DxBeKKEXC0AWABcGrDADpL0Kf8Q4ZRn4hYX6APuXioZIrSXtyrqihDoaX1WhjCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:22.251512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.09461","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1d1d65889fbbb2bc36d758fb006a1f94be23e87d3e367c85bf44a7dcf3a15b4","sha256:a22a3ab9be3bb19e5f04684dd6f2679d0d216a0095ae0da52ed7118b8e233a34"],"state_sha256":"708e4a904f3b0a353d4650d183cb6c29cd89a039340423830bf1a9211eb404c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4fFwrwAEJNDSqx1O5T+8BAQ7xvWIW7TTuPsqFdUOyJP8tQsarlYnMmHQaOv9m4rFwRIx6YnBBFk0CKCbmldCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T12:33:51.181621Z","bundle_sha256":"b83fbd9d1b6c0bc1baaa0f96d1737cab300752ecdc50b1bf0b1d0d620a1140d3"}}