{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TG24ABO7OH4SNH37QQJ7M3AYS6","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":"f9a5f9d71c8fe5915c8bb4291ee7a8be8ebb41f56ac9e7e9c4eff0bb43944aba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-03T13:36:05Z","title_canon_sha256":"117c3c4cdad6003ae64da37417b3520fec5af195e19a205af3e064b097b750b5"},"schema_version":"1.0","source":{"id":"1206.0443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.0443","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"arxiv_version","alias_value":"1206.0443v1","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0443","created_at":"2026-05-18T03:54:17Z"},{"alias_kind":"pith_short_12","alias_value":"TG24ABO7OH4S","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TG24ABO7OH4SNH37","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TG24ABO7","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:1c8ced35c313f9b36cd72629dfeee4adebd68f4093c595ee05d08909371bc080","target":"graph","created_at":"2026-05-18T03:54:17Z","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":"Kottwitz' conjecture is concerned with the intersections of Kazhdan--Lusztig cells with conjugacy classes of involutions in finite Coxeter groups. In joint work with Bonnaf\\'e, we have recently found a way to prove this conjecture for groups of type $B_n$ and $D_n$. The argument for type $D_n$ relies on two ingredients which were used there without proof: (1) a strengthened version of the \"branching rule\" and (2) the consideration of \"$\\diamond$-twisted\" involutions where $\\diamond$ is a graph automorphism. In this paper we deal with (1), (2) and complete the argument for type $D_n$; moreover,","authors_text":"Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-03T13:36:05Z","title":"On Kottwitz' conjecture for twisted involutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0443","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":"sha256:966a97f72afb698d7001fa147ef4777095b648d39e65411a70addcd0ef327c61","target":"record","created_at":"2026-05-18T03:54:17Z","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":"f9a5f9d71c8fe5915c8bb4291ee7a8be8ebb41f56ac9e7e9c4eff0bb43944aba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-06-03T13:36:05Z","title_canon_sha256":"117c3c4cdad6003ae64da37417b3520fec5af195e19a205af3e064b097b750b5"},"schema_version":"1.0","source":{"id":"1206.0443","kind":"arxiv","version":1}},"canonical_sha256":"99b5c005df71f9269f7f8413f66c1897a1962707afc5bc52ad664d9216a55afa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99b5c005df71f9269f7f8413f66c1897a1962707afc5bc52ad664d9216a55afa","first_computed_at":"2026-05-18T03:54:17.666115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:17.666115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ly+I0svmd126i+kuiFS4EDBoDXNkxdWDorVVk0rAT7gj/0Q93TNtBWn1jcZlZrHgL9y7UFDZfZiC8BHH7QjeDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:17.666758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.0443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:966a97f72afb698d7001fa147ef4777095b648d39e65411a70addcd0ef327c61","sha256:1c8ced35c313f9b36cd72629dfeee4adebd68f4093c595ee05d08909371bc080"],"state_sha256":"08b3242fe3cb96662a31b164b1ceb65cc17a349f9cdf4af5112f6623d5b49836"}