{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VCGNIP3BZ6FBGPD6J35S5VIDPP","short_pith_number":"pith:VCGNIP3B","schema_version":"1.0","canonical_sha256":"a88cd43f61cf8a133c7e4efb2ed5037bd42a44c9a529d9fed691b10f0ddf8170","source":{"kind":"arxiv","id":"1407.6457","version":3},"attestation_state":"computed","paper":{"title":"A categorification of $\\mathfrak{q}(2)$-crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Dimitar Grantcharov, Ji Hye Jung, MyungHo Kim, Seok-Jin Kang","submitted_at":"2014-07-24T05:32:45Z","abstract_excerpt":"We provide a categorification of $\\mathfrak{q}(2)$-crystals on the singular $\\mathfrak{gl}_{n}$-category ${\\mathcal O}_{n}$. Our result extends the $\\mathfrak{gl}_{2}$-crystal structure on ${\\rm Irr} ({\\mathcal O}_{n})$ defined by Bernstein-Frenkel-Khovanov. Further properties of the ${\\mathfrak q}(2)$-crystal ${\\rm Irr}({\\mathcal O}_{n})$ are also discussed."},"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":"1407.6457","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-07-24T05:32:45Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"6fbf07f3c310926903329aac64190638c22ffd1b0f7237fcb2cab2270f666f8d","abstract_canon_sha256":"0b9d2232b7c3570dfa0b90055938f5fdf72f8b4b5d92fc00363b7c29f27b3305"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:34.766397Z","signature_b64":"nflGYi6orahxxSh9YHCQp8iRgdLMste0GoGacbdSIuURxNGIx/hjn6mqiFRWFmSUzuJ+/h0PYJlxdctthuMxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a88cd43f61cf8a133c7e4efb2ed5037bd42a44c9a529d9fed691b10f0ddf8170","last_reissued_at":"2026-05-18T01:01:34.765884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:34.765884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A categorification of $\\mathfrak{q}(2)$-crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Dimitar Grantcharov, Ji Hye Jung, MyungHo Kim, Seok-Jin Kang","submitted_at":"2014-07-24T05:32:45Z","abstract_excerpt":"We provide a categorification of $\\mathfrak{q}(2)$-crystals on the singular $\\mathfrak{gl}_{n}$-category ${\\mathcal O}_{n}$. Our result extends the $\\mathfrak{gl}_{2}$-crystal structure on ${\\rm Irr} ({\\mathcal O}_{n})$ defined by Bernstein-Frenkel-Khovanov. Further properties of the ${\\mathfrak q}(2)$-crystal ${\\rm Irr}({\\mathcal O}_{n})$ are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6457","kind":"arxiv","version":3},"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":"1407.6457","created_at":"2026-05-18T01:01:34.765969+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.6457v3","created_at":"2026-05-18T01:01:34.765969+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6457","created_at":"2026-05-18T01:01:34.765969+00:00"},{"alias_kind":"pith_short_12","alias_value":"VCGNIP3BZ6FB","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"VCGNIP3BZ6FBGPD6","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"VCGNIP3B","created_at":"2026-05-18T12:28:52.271510+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP","json":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP.json","graph_json":"https://pith.science/api/pith-number/VCGNIP3BZ6FBGPD6J35S5VIDPP/graph.json","events_json":"https://pith.science/api/pith-number/VCGNIP3BZ6FBGPD6J35S5VIDPP/events.json","paper":"https://pith.science/paper/VCGNIP3B"},"agent_actions":{"view_html":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP","download_json":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP.json","view_paper":"https://pith.science/paper/VCGNIP3B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.6457&json=true","fetch_graph":"https://pith.science/api/pith-number/VCGNIP3BZ6FBGPD6J35S5VIDPP/graph.json","fetch_events":"https://pith.science/api/pith-number/VCGNIP3BZ6FBGPD6J35S5VIDPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP/action/storage_attestation","attest_author":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP/action/author_attestation","sign_citation":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP/action/citation_signature","submit_replication":"https://pith.science/pith/VCGNIP3BZ6FBGPD6J35S5VIDPP/action/replication_record"}},"created_at":"2026-05-18T01:01:34.765969+00:00","updated_at":"2026-05-18T01:01:34.765969+00:00"}