{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:GV4K7GZVWQIRH47FLWYQPL2RBT","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":"7c57cc668243827779410961cc304ade5adc9973c25d048d5b3c8ef3899c70d0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-03-28T14:13:53Z","title_canon_sha256":"f7590818881e0a98d1baa2110381e57b3078a4e7584a5bea4362c10621d5bd67"},"schema_version":"1.0","source":{"id":"0803.4121","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.4121","created_at":"2026-07-05T10:03:36Z"},{"alias_kind":"arxiv_version","alias_value":"0803.4121v2","created_at":"2026-07-05T10:03:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.4121","created_at":"2026-07-05T10:03:36Z"},{"alias_kind":"pith_short_12","alias_value":"GV4K7GZVWQIR","created_at":"2026-07-05T10:03:36Z"},{"alias_kind":"pith_short_16","alias_value":"GV4K7GZVWQIRH47F","created_at":"2026-07-05T10:03:36Z"},{"alias_kind":"pith_short_8","alias_value":"GV4K7GZV","created_at":"2026-07-05T10:03:36Z"}],"graph_snapshots":[{"event_id":"sha256:853f2f04a97ab9bc6742ef79399730fa64d7ec15e059deabc795ef57e6a33755","target":"graph","created_at":"2026-07-05T10:03:36Z","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/0803.4121/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"To each graph without loops and multiple edges we assign a family of rings. Categories of projective modules over these rings categorify $U^-_q(\\mathfrak{g})$, where $\\mathfrak{g}$ is the Kac-Moody Lie algebra associated with the graph.","authors_text":"Aaron D. Lauda, Mikhail Khovanov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-03-28T14:13:53Z","title":"A diagrammatic approach to categorification of quantum groups I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.4121","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":"sha256:4efeaadaf6771953704ec5424f209b202611e9bd77db9788558720f4843371c0","target":"record","created_at":"2026-07-05T10:03:36Z","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":"7c57cc668243827779410961cc304ade5adc9973c25d048d5b3c8ef3899c70d0","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-03-28T14:13:53Z","title_canon_sha256":"f7590818881e0a98d1baa2110381e57b3078a4e7584a5bea4362c10621d5bd67"},"schema_version":"1.0","source":{"id":"0803.4121","kind":"arxiv","version":2}},"canonical_sha256":"3578af9b35b41113f3e55db107af510cf2f71642b3d2fd42627044a1b72c9c5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3578af9b35b41113f3e55db107af510cf2f71642b3d2fd42627044a1b72c9c5c","first_computed_at":"2026-07-05T10:03:36.238477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:03:36.238477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vQY/WIR8nKKI+4wdz33ZL0vERTuZIE8uWjiM0pade4yzIxbeeudwO4PHcRgNwUcPCF+ohLzem659enIj0CdWBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:03:36.238888Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.4121","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4efeaadaf6771953704ec5424f209b202611e9bd77db9788558720f4843371c0","sha256:853f2f04a97ab9bc6742ef79399730fa64d7ec15e059deabc795ef57e6a33755"],"state_sha256":"93250b2864d67d6335d9f73fe2c3d293ebd59ab35cf8fe9a232a643696dae053"}