{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HLPVE5TMQQNRXYRW4MBBVLBAPK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9634bc7f9726c50bf8bd80e2dff0a2f8efc20a060aa2835ac6d4354ee2ce4ef6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-12T01:56:44Z","title_canon_sha256":"88e9aa435e1a86d686ac0c01fb1a2e693ee5b88041322b7ef67099bd82ffadcc"},"schema_version":"1.0","source":{"id":"1603.03843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.03843","created_at":"2026-05-18T01:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.03843v1","created_at":"2026-05-18T01:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.03843","created_at":"2026-05-18T01:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"HLPVE5TMQQNR","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HLPVE5TMQQNRXYRW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HLPVE5TM","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:b4ed7de3a28265ee013b7e4580bf46d0d618071658c3be9acdead928f6b6fd5c","target":"graph","created_at":"2026-05-18T01:19:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Alexander Kleshchev, Anton Evseev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-12T01:56:44Z","title":"Blocks of symmetric groups, semicuspidal KLR algebras and zigzag Schur-Weyl duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03843","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:19b7dc61af8575b0566cfb667339b14773c2a78bd46e57531e2289504c5276a8","target":"record","created_at":"2026-05-18T01:19:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9634bc7f9726c50bf8bd80e2dff0a2f8efc20a060aa2835ac6d4354ee2ce4ef6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-03-12T01:56:44Z","title_canon_sha256":"88e9aa435e1a86d686ac0c01fb1a2e693ee5b88041322b7ef67099bd82ffadcc"},"schema_version":"1.0","source":{"id":"1603.03843","kind":"arxiv","version":1}},"canonical_sha256":"3adf52766c841b1be236e3021aac207abcbd29bfb3158b9808ea538cd5b1561c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3adf52766c841b1be236e3021aac207abcbd29bfb3158b9808ea538cd5b1561c","first_computed_at":"2026-05-18T01:19:10.351718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:10.351718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hK2gKp5v6600SfT2spA6ASeYFp+ECFvNYY86VWQYA78KiEZqVeP7hnBIFM5FOCvK0M5lpfMY2F+aQTuKdHtWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:10.352488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.03843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19b7dc61af8575b0566cfb667339b14773c2a78bd46e57531e2289504c5276a8","sha256:b4ed7de3a28265ee013b7e4580bf46d0d618071658c3be9acdead928f6b6fd5c"],"state_sha256":"3881065847d12ac77e0d9f8aaca92ed7abe4b160d46df97d4740955d804333ff"}