{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HLPVE5TMQQNRXYRW4MBBVLBAPK","short_pith_number":"pith:HLPVE5TM","schema_version":"1.0","canonical_sha256":"3adf52766c841b1be236e3021aac207abcbd29bfb3158b9808ea538cd5b1561c","source":{"kind":"arxiv","id":"1603.03843","version":1},"attestation_state":"computed","paper":{"title":"Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Kleshchev, Anton Evseev","submitted_at":"2016-03-12T01:56:44Z","abstract_excerpt":"We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like `local' objects, which replace wreath products of Brauer tree algebras in the context of the Brou\\'e abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath products of zigzag algebras and imaginary semicuspidal quotients of affine KLR algebras."},"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":"1603.03843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-12T01:56:44Z","cross_cats_sorted":[],"title_canon_sha256":"88e9aa435e1a86d686ac0c01fb1a2e693ee5b88041322b7ef67099bd82ffadcc","abstract_canon_sha256":"9634bc7f9726c50bf8bd80e2dff0a2f8efc20a060aa2835ac6d4354ee2ce4ef6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:10.352488Z","signature_b64":"hK2gKp5v6600SfT2spA6ASeYFp+ECFvNYY86VWQYA78KiEZqVeP7hnBIFM5FOCvK0M5lpfMY2F+aQTuKdHtWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3adf52766c841b1be236e3021aac207abcbd29bfb3158b9808ea538cd5b1561c","last_reissued_at":"2026-05-18T01:19:10.351718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:10.351718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Kleshchev, Anton Evseev","submitted_at":"2016-03-12T01:56:44Z","abstract_excerpt":"We prove Turner's conjecture, which describes the blocks of the Hecke algebras of the symmetric groups up to derived equivalence as certain explicit Turner double algebras. Turner doubles are Schur-algebra-like `local' objects, which replace wreath products of Brauer tree algebras in the context of the Brou\\'e abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups. The main tools used in the proof are generalized Schur algebras corresponding to wreath products of zigzag algebras and imaginary semicuspidal quotients of affine KLR algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03843","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":"1603.03843","created_at":"2026-05-18T01:19:10.351848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.03843v1","created_at":"2026-05-18T01:19:10.351848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03843","created_at":"2026-05-18T01:19:10.351848+00:00"},{"alias_kind":"pith_short_12","alias_value":"HLPVE5TMQQNR","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HLPVE5TMQQNRXYRW","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HLPVE5TM","created_at":"2026-05-18T12:30:19.053100+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/HLPVE5TMQQNRXYRW4MBBVLBAPK","json":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK.json","graph_json":"https://pith.science/api/pith-number/HLPVE5TMQQNRXYRW4MBBVLBAPK/graph.json","events_json":"https://pith.science/api/pith-number/HLPVE5TMQQNRXYRW4MBBVLBAPK/events.json","paper":"https://pith.science/paper/HLPVE5TM"},"agent_actions":{"view_html":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK","download_json":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK.json","view_paper":"https://pith.science/paper/HLPVE5TM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.03843&json=true","fetch_graph":"https://pith.science/api/pith-number/HLPVE5TMQQNRXYRW4MBBVLBAPK/graph.json","fetch_events":"https://pith.science/api/pith-number/HLPVE5TMQQNRXYRW4MBBVLBAPK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK/action/storage_attestation","attest_author":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK/action/author_attestation","sign_citation":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK/action/citation_signature","submit_replication":"https://pith.science/pith/HLPVE5TMQQNRXYRW4MBBVLBAPK/action/replication_record"}},"created_at":"2026-05-18T01:19:10.351848+00:00","updated_at":"2026-05-18T01:19:10.351848+00:00"}