{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6JWRUNI2BLJ4CHID7KLUI5I6QQ","short_pith_number":"pith:6JWRUNI2","canonical_record":{"source":{"id":"1110.5672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-25T21:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"8f9b5e163d3c2881ba1a1a2ba3396ffef6dd55b7ace537ed6c1570f797f64ecb","abstract_canon_sha256":"d44a3ff7e495aa8b35b8b8239fb8d7b127e6fac5732b0402226925f57e47043a"},"schema_version":"1.0"},"canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","source":{"kind":"arxiv","id":"1110.5672","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5672","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5672v2","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5672","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"6JWRUNI2BLJ4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6JWRUNI2BLJ4CHID","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6JWRUNI2","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6JWRUNI2BLJ4CHID7KLUI5I6QQ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5672","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-25T21:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"8f9b5e163d3c2881ba1a1a2ba3396ffef6dd55b7ace537ed6c1570f797f64ecb","abstract_canon_sha256":"d44a3ff7e495aa8b35b8b8239fb8d7b127e6fac5732b0402226925f57e47043a"},"schema_version":"1.0"},"canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:07.512079Z","signature_b64":"fUSXV92woZo+cgMfyR9LUJnOJ+KCwDWFLDsA1ZqbrB3Okx/goAPlnBMwGap516s426HNCAw2Cu7ZX6rV42qMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","last_reissued_at":"2026-05-18T04:06:07.511586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:07.511586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5672","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":"2026-05-18T04:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yp0Dbnpntw49e87WyiXr71rD9XyB9DXHn3bG/d1h34o8kN/kCFR+aqbuIU8BfCX7np7C+1V7Dx3nip+RjKD2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:32:28.921544Z"},"content_sha256":"d247ef93c432018c48051cfbfb3ec5dbcc03285bc6e267e73d80bb2ecefb31dd","schema_version":"1.0","event_id":"sha256:d247ef93c432018c48051cfbfb3ec5dbcc03285bc6e267e73d80bb2ecefb31dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6JWRUNI2BLJ4CHID7KLUI5I6QQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kazhdan--Lusztig cells and the Frobenius--Schur indicator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Meinolf Geck","submitted_at":"2011-10-25T21:47:00Z","abstract_excerpt":"Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of $W$ into Kazhdan--Lusztig cells. The proof uses a generalisation of the Frobenius--Schur indicator to symmetric algebras, which may be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5672","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":"2026-05-18T04:06:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbszQ/c0kxv+36KHelUxWb5ArO4NDODb0tiEB0akI3L26Yfigd5jXA2y96Xk8g+Qt0/de6Mox9LaTuiRmHa1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T14:32:28.921891Z"},"content_sha256":"4f01fe6dcb38cb6c6e6d8f8ec4155b17331f43d138bca42a23a996297da67020","schema_version":"1.0","event_id":"sha256:4f01fe6dcb38cb6c6e6d8f8ec4155b17331f43d138bca42a23a996297da67020"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/bundle.json","state_url":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/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":"2026-05-28T14:32:28Z","links":{"resolver":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ","bundle":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/bundle.json","state":"https://pith.science/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6JWRUNI2BLJ4CHID7KLUI5I6QQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6JWRUNI2BLJ4CHID7KLUI5I6QQ","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":"d44a3ff7e495aa8b35b8b8239fb8d7b127e6fac5732b0402226925f57e47043a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-25T21:47:00Z","title_canon_sha256":"8f9b5e163d3c2881ba1a1a2ba3396ffef6dd55b7ace537ed6c1570f797f64ecb"},"schema_version":"1.0","source":{"id":"1110.5672","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5672","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5672v2","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5672","created_at":"2026-05-18T04:06:07Z"},{"alias_kind":"pith_short_12","alias_value":"6JWRUNI2BLJ4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6JWRUNI2BLJ4CHID","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6JWRUNI2","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:4f01fe6dcb38cb6c6e6d8f8ec4155b17331f43d138bca42a23a996297da67020","target":"graph","created_at":"2026-05-18T04:06:07Z","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":"Let $W$ be a finite Coxeter group. It is well-known that the number of involutions in $W$ is equal to the sum of the degrees of the irreducible characters of $W$. Following a suggestion of Lusztig, we show that this equality is compatible with the decomposition of $W$ into Kazhdan--Lusztig cells. The proof uses a generalisation of the Frobenius--Schur indicator to symmetric algebras, which may be of independent interest.","authors_text":"Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-25T21:47:00Z","title":"Kazhdan--Lusztig cells and the Frobenius--Schur indicator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5672","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:d247ef93c432018c48051cfbfb3ec5dbcc03285bc6e267e73d80bb2ecefb31dd","target":"record","created_at":"2026-05-18T04:06:07Z","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":"d44a3ff7e495aa8b35b8b8239fb8d7b127e6fac5732b0402226925f57e47043a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-10-25T21:47:00Z","title_canon_sha256":"8f9b5e163d3c2881ba1a1a2ba3396ffef6dd55b7ace537ed6c1570f797f64ecb"},"schema_version":"1.0","source":{"id":"1110.5672","kind":"arxiv","version":2}},"canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f26d1a351a0ad3c11d03fa9744751e840846346bb94da5f1e01081984adec8a8","first_computed_at":"2026-05-18T04:06:07.511586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:07.511586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fUSXV92woZo+cgMfyR9LUJnOJ+KCwDWFLDsA1ZqbrB3Okx/goAPlnBMwGap516s426HNCAw2Cu7ZX6rV42qMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:07.512079Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5672","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d247ef93c432018c48051cfbfb3ec5dbcc03285bc6e267e73d80bb2ecefb31dd","sha256:4f01fe6dcb38cb6c6e6d8f8ec4155b17331f43d138bca42a23a996297da67020"],"state_sha256":"be0f7c6e519349591b240bafe07484594a83b2789abff1310ec15223835c1d15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmL4g6d6RYM0lHjseijNrbjS/hhlFNMVG1U3jMLporHu/hNcFOzFqP9De6khMnvu/hB22vPkXz64q3yo4hMbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T14:32:28.923787Z","bundle_sha256":"c2f18da109e1069c41efc22156b0d9e513cb397db1cf74b997b9d483cc901a54"}}