{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:L7KF7M5MQR4VEYT7KUY2CFRFAC","short_pith_number":"pith:L7KF7M5M","schema_version":"1.0","canonical_sha256":"5fd45fb3ac847952627f5531a1162500ba81cd188e6883a51c5dac3019b70a73","source":{"kind":"arxiv","id":"1708.04428","version":2},"attestation_state":"computed","paper":{"title":"Monoidal categories associated with strata of flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Euiyong Park, Masaki Kashiwara, MyungHo Kim, Se-Jin Oh","submitted_at":"2017-08-15T08:23:26Z","abstract_excerpt":"We construct a monoidal category $\\mathscr{C}_{w,v}$ which categorifies the doubly-invariant algebra $^{N'(w)}\\mathbb{C}[N]^{N(v)}$ associated with Weyl group elements $w$ and $v$. It gives, after a localization, the coordinate algebra $\\mathbb{C}[\\mathcal{R}_{w,v}]$ of the open Richardson variety associated with $w$ and $v$. The category $\\mathscr{C}_{w,v}$ is realized as a subcategory of the graded module category of a quiver Hecke algebra $R$. When $v= \\mathrm{id}$, $\\mathscr{C}_{w,v}$ is the same as the monoidal category which provides a monoidal categorification of the quantum unipotent c"},"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":"1708.04428","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-15T08:23:26Z","cross_cats_sorted":[],"title_canon_sha256":"9a53fda2c87c56b7666a8b737900e280b76387309804f4ed1554febaf07d770f","abstract_canon_sha256":"183e38dc9d2a9bd525c4e0385d1c8c132340b4a79425fca90d15ee3effeee84c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:23.156958Z","signature_b64":"xlDM5oFVaALh+eREcjr5iWMlZpC1vLbBNY0pLsyhC4WSEO65g6pgf/bj+pHBYsaSwPu9m4VSS2FDWmvc0vFCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fd45fb3ac847952627f5531a1162500ba81cd188e6883a51c5dac3019b70a73","last_reissued_at":"2026-05-18T00:23:23.156248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:23.156248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Monoidal categories associated with strata of flag manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Euiyong Park, Masaki Kashiwara, MyungHo Kim, Se-Jin Oh","submitted_at":"2017-08-15T08:23:26Z","abstract_excerpt":"We construct a monoidal category $\\mathscr{C}_{w,v}$ which categorifies the doubly-invariant algebra $^{N'(w)}\\mathbb{C}[N]^{N(v)}$ associated with Weyl group elements $w$ and $v$. It gives, after a localization, the coordinate algebra $\\mathbb{C}[\\mathcal{R}_{w,v}]$ of the open Richardson variety associated with $w$ and $v$. The category $\\mathscr{C}_{w,v}$ is realized as a subcategory of the graded module category of a quiver Hecke algebra $R$. When $v= \\mathrm{id}$, $\\mathscr{C}_{w,v}$ is the same as the monoidal category which provides a monoidal categorification of the quantum unipotent c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04428","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":""},"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":"1708.04428","created_at":"2026-05-18T00:23:23.156371+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.04428v2","created_at":"2026-05-18T00:23:23.156371+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04428","created_at":"2026-05-18T00:23:23.156371+00:00"},{"alias_kind":"pith_short_12","alias_value":"L7KF7M5MQR4V","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"L7KF7M5MQR4VEYT7","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"L7KF7M5M","created_at":"2026-05-18T12:31:28.150371+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/L7KF7M5MQR4VEYT7KUY2CFRFAC","json":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC.json","graph_json":"https://pith.science/api/pith-number/L7KF7M5MQR4VEYT7KUY2CFRFAC/graph.json","events_json":"https://pith.science/api/pith-number/L7KF7M5MQR4VEYT7KUY2CFRFAC/events.json","paper":"https://pith.science/paper/L7KF7M5M"},"agent_actions":{"view_html":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC","download_json":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC.json","view_paper":"https://pith.science/paper/L7KF7M5M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.04428&json=true","fetch_graph":"https://pith.science/api/pith-number/L7KF7M5MQR4VEYT7KUY2CFRFAC/graph.json","fetch_events":"https://pith.science/api/pith-number/L7KF7M5MQR4VEYT7KUY2CFRFAC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC/action/storage_attestation","attest_author":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC/action/author_attestation","sign_citation":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC/action/citation_signature","submit_replication":"https://pith.science/pith/L7KF7M5MQR4VEYT7KUY2CFRFAC/action/replication_record"}},"created_at":"2026-05-18T00:23:23.156371+00:00","updated_at":"2026-05-18T00:23:23.156371+00:00"}