{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DMLOWXAT62ETOQWIXIS5O7JWOX","short_pith_number":"pith:DMLOWXAT","schema_version":"1.0","canonical_sha256":"1b16eb5c13f6893742c8ba25d77d3675fa33270e28488a5f40cbf0a6fb8b7acb","source":{"kind":"arxiv","id":"1212.6076","version":1},"attestation_state":"computed","paper":{"title":"Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.RT"],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, David E. V. Rose, Hoel Queffelec","submitted_at":"2012-12-25T19:15:08Z","abstract_excerpt":"We show that Khovanov homology (and its sl(3) variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of these theories arise as a family of 2-representations of categorified quantum sl(m) via categorical skew Howe duality. Utilizing Cautis-Rozansky categorified clasps we also obtain a unified construction of foam-based categorifications of Jones-Wenzl projectors and their sl(3) analogs purely from the higher representation theory of categorified quantum groups. In the sl(2) case, this work reveals the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.6076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-12-25T19:15:08Z","cross_cats_sorted":["math.GT","math.RT"],"title_canon_sha256":"f98e60b860572ebfd749af432d0fc4f68e8f37153241c493443439a105ef9cc9","abstract_canon_sha256":"c915d56bbc450b121e94c96fb1413cd3c3be4c34be100d27c15b893e89a91d36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:47.890524Z","signature_b64":"HDyKyNLGEhHsWnFgQYylWnk5hy5X2beQYmaiushBhCnrA8w20hmL80Oe4p3hsWi84aNUhqLSSS25QMW7UG0/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b16eb5c13f6893742c8ba25d77d3675fa33270e28488a5f40cbf0a6fb8b7acb","last_reissued_at":"2026-05-18T01:25:47.890068Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:47.890068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.RT"],"primary_cat":"math.QA","authors_text":"Aaron D. Lauda, David E. V. Rose, Hoel Queffelec","submitted_at":"2012-12-25T19:15:08Z","abstract_excerpt":"We show that Khovanov homology (and its sl(3) variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of these theories arise as a family of 2-representations of categorified quantum sl(m) via categorical skew Howe duality. Utilizing Cautis-Rozansky categorified clasps we also obtain a unified construction of foam-based categorifications of Jones-Wenzl projectors and their sl(3) analogs purely from the higher representation theory of categorified quantum groups. In the sl(2) case, this work reveals the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6076","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1212.6076","created_at":"2026-05-18T01:25:47.890131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.6076v1","created_at":"2026-05-18T01:25:47.890131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6076","created_at":"2026-05-18T01:25:47.890131+00:00"},{"alias_kind":"pith_short_12","alias_value":"DMLOWXAT62ET","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"DMLOWXAT62ETOQWI","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"DMLOWXAT","created_at":"2026-05-18T12:27:04.183437+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.01877","citing_title":"Action of the Witt algebra on categorified quantum groups","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX","json":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX.json","graph_json":"https://pith.science/api/pith-number/DMLOWXAT62ETOQWIXIS5O7JWOX/graph.json","events_json":"https://pith.science/api/pith-number/DMLOWXAT62ETOQWIXIS5O7JWOX/events.json","paper":"https://pith.science/paper/DMLOWXAT"},"agent_actions":{"view_html":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX","download_json":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX.json","view_paper":"https://pith.science/paper/DMLOWXAT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.6076&json=true","fetch_graph":"https://pith.science/api/pith-number/DMLOWXAT62ETOQWIXIS5O7JWOX/graph.json","fetch_events":"https://pith.science/api/pith-number/DMLOWXAT62ETOQWIXIS5O7JWOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX/action/storage_attestation","attest_author":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX/action/author_attestation","sign_citation":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX/action/citation_signature","submit_replication":"https://pith.science/pith/DMLOWXAT62ETOQWIXIS5O7JWOX/action/replication_record"}},"created_at":"2026-05-18T01:25:47.890131+00:00","updated_at":"2026-05-18T01:25:47.890131+00:00"}