{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MOY2W5VM6FTDM434YDJS6DT7B7","short_pith_number":"pith:MOY2W5VM","schema_version":"1.0","canonical_sha256":"63b1ab76acf16636737cc0d32f0e7f0ffcf790737b42533c0cd360eaeecd0fb2","source":{"kind":"arxiv","id":"1512.04458","version":3},"attestation_state":"computed","paper":{"title":"Face Functors for KLR Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Peter J. McNamara, Peter Tingley","submitted_at":"2015-12-14T18:49:26Z","abstract_excerpt":"Simple representations of KLR algebras can be used to realize the infinity crystal for the corresponding symmetrizable Kac-Moody algebra. It was recently shown that, in finite and affine types, certain sub-categories of cuspidal representations realize crystals for sub Kac-Moody algebras. Here we put that observation an a firmer categorical footing by exhibiting a functor between the category of representations of the KLR algebra for the sub Kac-Moody algebra and the category of cuspidal representations of the original KLR algebra."},"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":"1512.04458","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-14T18:49:26Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"6ad4ed623aed29a38f1d5583053854fa9fd86053a0fe644397fe9078bf848e74","abstract_canon_sha256":"816ee96e3c56a661e7c45c6f47400fed17cde05d4c83356cd1698f5ab35d526b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:43.036285Z","signature_b64":"10Yy317XfQZ87PY2dv7T9DRnvt94i86BIYJ22v66keYvjSNZeY7Z5GDhcjA+Ue2JvA9KYN21smWeAMkvmQtRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63b1ab76acf16636737cc0d32f0e7f0ffcf790737b42533c0cd360eaeecd0fb2","last_reissued_at":"2026-05-18T00:48:43.035700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:43.035700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Face Functors for KLR Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Peter J. McNamara, Peter Tingley","submitted_at":"2015-12-14T18:49:26Z","abstract_excerpt":"Simple representations of KLR algebras can be used to realize the infinity crystal for the corresponding symmetrizable Kac-Moody algebra. It was recently shown that, in finite and affine types, certain sub-categories of cuspidal representations realize crystals for sub Kac-Moody algebras. Here we put that observation an a firmer categorical footing by exhibiting a functor between the category of representations of the KLR algebra for the sub Kac-Moody algebra and the category of cuspidal representations of the original KLR algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04458","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":"1512.04458","created_at":"2026-05-18T00:48:43.035799+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04458v3","created_at":"2026-05-18T00:48:43.035799+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04458","created_at":"2026-05-18T00:48:43.035799+00:00"},{"alias_kind":"pith_short_12","alias_value":"MOY2W5VM6FTD","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MOY2W5VM6FTDM434","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MOY2W5VM","created_at":"2026-05-18T12:29:32.376354+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/MOY2W5VM6FTDM434YDJS6DT7B7","json":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7.json","graph_json":"https://pith.science/api/pith-number/MOY2W5VM6FTDM434YDJS6DT7B7/graph.json","events_json":"https://pith.science/api/pith-number/MOY2W5VM6FTDM434YDJS6DT7B7/events.json","paper":"https://pith.science/paper/MOY2W5VM"},"agent_actions":{"view_html":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7","download_json":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7.json","view_paper":"https://pith.science/paper/MOY2W5VM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04458&json=true","fetch_graph":"https://pith.science/api/pith-number/MOY2W5VM6FTDM434YDJS6DT7B7/graph.json","fetch_events":"https://pith.science/api/pith-number/MOY2W5VM6FTDM434YDJS6DT7B7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7/action/storage_attestation","attest_author":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7/action/author_attestation","sign_citation":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7/action/citation_signature","submit_replication":"https://pith.science/pith/MOY2W5VM6FTDM434YDJS6DT7B7/action/replication_record"}},"created_at":"2026-05-18T00:48:43.035799+00:00","updated_at":"2026-05-18T00:48:43.035799+00:00"}