{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PZAFCNAHCNAQGOYDCWWU7PFSKE","short_pith_number":"pith:PZAFCNAH","canonical_record":{"source":{"id":"1205.4092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-18T06:54:50Z","cross_cats_sorted":[],"title_canon_sha256":"9c0d9f15d7dc070c636b04dc04b503b7ef556ae98830808f56a34d2cc07a30ad","abstract_canon_sha256":"3064c398fec95974310c8bdf1f0e5a0cdfb043722b424a63c816fd2988a79f66"},"schema_version":"1.0"},"canonical_sha256":"7e405134071341033b0315ad4fbcb251277f7577956a6a9ac712d20eb6449b7e","source":{"kind":"arxiv","id":"1205.4092","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4092","created_at":"2026-05-18T03:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4092v2","created_at":"2026-05-18T03:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4092","created_at":"2026-05-18T03:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"PZAFCNAHCNAQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PZAFCNAHCNAQGOYD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PZAFCNAH","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PZAFCNAHCNAQGOYDCWWU7PFSKE","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-18T06:54:50Z","cross_cats_sorted":[],"title_canon_sha256":"9c0d9f15d7dc070c636b04dc04b503b7ef556ae98830808f56a34d2cc07a30ad","abstract_canon_sha256":"3064c398fec95974310c8bdf1f0e5a0cdfb043722b424a63c816fd2988a79f66"},"schema_version":"1.0"},"canonical_sha256":"7e405134071341033b0315ad4fbcb251277f7577956a6a9ac712d20eb6449b7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:03.938632Z","signature_b64":"2e0myR3ic7iBfdmWAOgy5a7CCtKSoUsxinSQOigzqvX1wGvsPFW4+AXHQvqhGYYRBfqeTtgWcfXt2Rgjkl6hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e405134071341033b0315ad4fbcb251277f7577956a6a9ac712d20eb6449b7e","last_reissued_at":"2026-05-18T03:54:03.937953Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:03.937953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4092","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpUgGkFowSwKh8IMSp4oJQnGyZlraAYnjKpQdqwti8iXxaGMASJQ0w1c8KqUtEV/fsDQ55DuzGKwh6atXa2DCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:05:32.352669Z"},"content_sha256":"a37fbd92923dcd7800e7f48a63347cdfd9afd17c7e7a6cc86b12a9b7cd8e0cbf","schema_version":"1.0","event_id":"sha256:a37fbd92923dcd7800e7f48a63347cdfd9afd17c7e7a6cc86b12a9b7cd8e0cbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PZAFCNAHCNAQGOYDCWWU7PFSKE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugacy classes of involutions and Kazhdan-Lusztig cells","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e (I3M), Meinolf Geck (ABE)","submitted_at":"2012-05-18T06:54:50Z","abstract_excerpt":"According to an old result of Sch\\\"utzenberger, the involutions in a given two-sided cell of the symmetric group $\\SG_n$ are all conjugate. In this paper, we study possible generalisations of this property to other types of Coxeter groups. We show that Sch\\\"utzenberger's result is a special case of a general result on \"smooth\" two-sided cells. Furthermore, we consider Kottwitz' conjecture concerning the intersections of conjugacy classes of involutions with the left cells in a finite Coxeter group. Our methods lead to a proof of this conjecture for classical types; combined with previous work,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4092","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+icPOblFwovAkcXgDAYId+pZiSTEZrMz3qH+BeiW5R1Ur6VW6pLiaq1zab7ESPp5GvjdQt4noxfrrl3xwWn2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:05:32.353370Z"},"content_sha256":"39a0dec8a89ff23eb6e23986f6fc2e6f4d8ef20ac6fc77c687236281cbefa92f","schema_version":"1.0","event_id":"sha256:39a0dec8a89ff23eb6e23986f6fc2e6f4d8ef20ac6fc77c687236281cbefa92f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE/bundle.json","state_url":"https://pith.science/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T21:05:32Z","links":{"resolver":"https://pith.science/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE","bundle":"https://pith.science/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE/bundle.json","state":"https://pith.science/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZAFCNAHCNAQGOYDCWWU7PFSKE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PZAFCNAHCNAQGOYDCWWU7PFSKE","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":"3064c398fec95974310c8bdf1f0e5a0cdfb043722b424a63c816fd2988a79f66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-18T06:54:50Z","title_canon_sha256":"9c0d9f15d7dc070c636b04dc04b503b7ef556ae98830808f56a34d2cc07a30ad"},"schema_version":"1.0","source":{"id":"1205.4092","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4092","created_at":"2026-05-18T03:54:03Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4092v2","created_at":"2026-05-18T03:54:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4092","created_at":"2026-05-18T03:54:03Z"},{"alias_kind":"pith_short_12","alias_value":"PZAFCNAHCNAQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PZAFCNAHCNAQGOYD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PZAFCNAH","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:39a0dec8a89ff23eb6e23986f6fc2e6f4d8ef20ac6fc77c687236281cbefa92f","target":"graph","created_at":"2026-05-18T03:54:03Z","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":"According to an old result of Sch\\\"utzenberger, the involutions in a given two-sided cell of the symmetric group $\\SG_n$ are all conjugate. In this paper, we study possible generalisations of this property to other types of Coxeter groups. We show that Sch\\\"utzenberger's result is a special case of a general result on \"smooth\" two-sided cells. Furthermore, we consider Kottwitz' conjecture concerning the intersections of conjugacy classes of involutions with the left cells in a finite Coxeter group. Our methods lead to a proof of this conjecture for classical types; combined with previous work,","authors_text":"C\\'edric Bonnaf\\'e (I3M), Meinolf Geck (ABE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-18T06:54:50Z","title":"Conjugacy classes of involutions and Kazhdan-Lusztig cells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4092","kind":"arxiv","version":2},"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:a37fbd92923dcd7800e7f48a63347cdfd9afd17c7e7a6cc86b12a9b7cd8e0cbf","target":"record","created_at":"2026-05-18T03:54:03Z","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":"3064c398fec95974310c8bdf1f0e5a0cdfb043722b424a63c816fd2988a79f66","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-05-18T06:54:50Z","title_canon_sha256":"9c0d9f15d7dc070c636b04dc04b503b7ef556ae98830808f56a34d2cc07a30ad"},"schema_version":"1.0","source":{"id":"1205.4092","kind":"arxiv","version":2}},"canonical_sha256":"7e405134071341033b0315ad4fbcb251277f7577956a6a9ac712d20eb6449b7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e405134071341033b0315ad4fbcb251277f7577956a6a9ac712d20eb6449b7e","first_computed_at":"2026-05-18T03:54:03.937953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:03.937953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2e0myR3ic7iBfdmWAOgy5a7CCtKSoUsxinSQOigzqvX1wGvsPFW4+AXHQvqhGYYRBfqeTtgWcfXt2Rgjkl6hAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:03.938632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4092","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a37fbd92923dcd7800e7f48a63347cdfd9afd17c7e7a6cc86b12a9b7cd8e0cbf","sha256:39a0dec8a89ff23eb6e23986f6fc2e6f4d8ef20ac6fc77c687236281cbefa92f"],"state_sha256":"3911948344e08a94024d3ffc4a9f9b75cfdb3d87dde074fe8a37ddf2535c068f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yyP570tS/eSTkx2tEPvkaPe7aafhGCEpLvF39ozkgTBNGJ84WFPvw5K4EB3oH4yDQ0i3MUg279o/4auimp5BDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:05:32.357112Z","bundle_sha256":"a2481b3504e37545bebba2d65dc19b152217837c705ed9fb046a2bc31656b392"}}