{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XZNZLS677FBCMQO67NBGS5GZZY","short_pith_number":"pith:XZNZLS67","canonical_record":{"source":{"id":"1401.6804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-27T11:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"83645ec3f9d0fa66ce6b07a5a40d378322b443ff673087269fbdeb9dae8790f1","abstract_canon_sha256":"9b23a0772e61732160804c5feaaefe614b3b70530efe75d8b280fa518b3596c3"},"schema_version":"1.0"},"canonical_sha256":"be5b95cbdff9422641defb426974d9ce2c9f7c7dc7cc5adc6671925b3a8879b1","source":{"kind":"arxiv","id":"1401.6804","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6804","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6804v3","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6804","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"XZNZLS677FBC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XZNZLS677FBCMQO6","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XZNZLS67","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XZNZLS677FBCMQO67NBGS5GZZY","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-27T11:04:24Z","cross_cats_sorted":[],"title_canon_sha256":"83645ec3f9d0fa66ce6b07a5a40d378322b443ff673087269fbdeb9dae8790f1","abstract_canon_sha256":"9b23a0772e61732160804c5feaaefe614b3b70530efe75d8b280fa518b3596c3"},"schema_version":"1.0"},"canonical_sha256":"be5b95cbdff9422641defb426974d9ce2c9f7c7dc7cc5adc6671925b3a8879b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:00.117375Z","signature_b64":"M1k5f8zwzutbVXoL3adkSc0EiSJGhIssnt5YV9jsqjMxh4QAso1BrVrWQEyKk8K3ab7C8JPQQ0W/P5xN5LEpAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be5b95cbdff9422641defb426974d9ce2c9f7c7dc7cc5adc6671925b3a8879b1","last_reissued_at":"2026-05-18T03:00:00.116664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:00.116664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6804","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:00:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YDwezqnhihKAfzPgcIuKWCeu7upsVSJmaI0SteJFdZzYwctYieuUM9lJZTsPjrGK7g6N9Lxw0IarEjM6xzakCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:32:01.328258Z"},"content_sha256":"00001d097db9b88a6871897cba63127178373549f4a8471e55e7d37aa9c67001","schema_version":"1.0","event_id":"sha256:00001d097db9b88a6871897cba63127178373549f4a8471e55e7d37aa9c67001"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XZNZLS677FBCMQO67NBGS5GZZY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Kazhdan--Lusztig cells in type $E_8$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Abbie Halls, Meinolf Geck","submitted_at":"2014-01-27T11:04:24Z","abstract_excerpt":"In 1979, Kazhdan and Lusztig introduced the notion of \"cells\" (left, right and two-sided) for a Coxeter group $W$, a concept with numerous applications in Lie theory and around. Here, we address algorithmic aspects of this theory for finite $W$ which are important in applications, e.g., run explicitly through all left cells, determine the values of Lusztig's $\\ba$-function, identify the characters of left cell representations. The aim is to show how type $E_8$ (the largest group of exceptional type) can be handled systematically and efficiently, too. This allows us, for the first time, to solv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6804","kind":"arxiv","version":3},"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":"2026-05-18T03:00:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDaHW8qVxfVfpCKod+Q24Xb2phz3RWS4Wi0cNvM96ye0VeH+xPHBNh0LcCUp/eHhLrOsJk7/KB2Ox1PrA7XxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:32:01.328623Z"},"content_sha256":"aef67376a633914f72cb9e82742cdd3395835a9752722bc7687ff883c829c0c8","schema_version":"1.0","event_id":"sha256:aef67376a633914f72cb9e82742cdd3395835a9752722bc7687ff883c829c0c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZNZLS677FBCMQO67NBGS5GZZY/bundle.json","state_url":"https://pith.science/pith/XZNZLS677FBCMQO67NBGS5GZZY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZNZLS677FBCMQO67NBGS5GZZY/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":"2026-05-28T11:32:01Z","links":{"resolver":"https://pith.science/pith/XZNZLS677FBCMQO67NBGS5GZZY","bundle":"https://pith.science/pith/XZNZLS677FBCMQO67NBGS5GZZY/bundle.json","state":"https://pith.science/pith/XZNZLS677FBCMQO67NBGS5GZZY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZNZLS677FBCMQO67NBGS5GZZY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XZNZLS677FBCMQO67NBGS5GZZY","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":"9b23a0772e61732160804c5feaaefe614b3b70530efe75d8b280fa518b3596c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-27T11:04:24Z","title_canon_sha256":"83645ec3f9d0fa66ce6b07a5a40d378322b443ff673087269fbdeb9dae8790f1"},"schema_version":"1.0","source":{"id":"1401.6804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6804","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6804v3","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6804","created_at":"2026-05-18T03:00:00Z"},{"alias_kind":"pith_short_12","alias_value":"XZNZLS677FBC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XZNZLS677FBCMQO6","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XZNZLS67","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:aef67376a633914f72cb9e82742cdd3395835a9752722bc7687ff883c829c0c8","target":"graph","created_at":"2026-05-18T03:00:00Z","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":"In 1979, Kazhdan and Lusztig introduced the notion of \"cells\" (left, right and two-sided) for a Coxeter group $W$, a concept with numerous applications in Lie theory and around. Here, we address algorithmic aspects of this theory for finite $W$ which are important in applications, e.g., run explicitly through all left cells, determine the values of Lusztig's $\\ba$-function, identify the characters of left cell representations. The aim is to show how type $E_8$ (the largest group of exceptional type) can be handled systematically and efficiently, too. This allows us, for the first time, to solv","authors_text":"Abbie Halls, Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-27T11:04:24Z","title":"On the Kazhdan--Lusztig cells in type $E_8$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6804","kind":"arxiv","version":3},"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":"sha256:00001d097db9b88a6871897cba63127178373549f4a8471e55e7d37aa9c67001","target":"record","created_at":"2026-05-18T03:00:00Z","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":"9b23a0772e61732160804c5feaaefe614b3b70530efe75d8b280fa518b3596c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-01-27T11:04:24Z","title_canon_sha256":"83645ec3f9d0fa66ce6b07a5a40d378322b443ff673087269fbdeb9dae8790f1"},"schema_version":"1.0","source":{"id":"1401.6804","kind":"arxiv","version":3}},"canonical_sha256":"be5b95cbdff9422641defb426974d9ce2c9f7c7dc7cc5adc6671925b3a8879b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be5b95cbdff9422641defb426974d9ce2c9f7c7dc7cc5adc6671925b3a8879b1","first_computed_at":"2026-05-18T03:00:00.116664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:00.116664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1k5f8zwzutbVXoL3adkSc0EiSJGhIssnt5YV9jsqjMxh4QAso1BrVrWQEyKk8K3ab7C8JPQQ0W/P5xN5LEpAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:00.117375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00001d097db9b88a6871897cba63127178373549f4a8471e55e7d37aa9c67001","sha256:aef67376a633914f72cb9e82742cdd3395835a9752722bc7687ff883c829c0c8"],"state_sha256":"46b2289146dd6bb35e2bf83639b48b7cd64c1766b55c46600a7dd3d6d068e2f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1pJzDxPsMTCntzZamAJaGtbnVTlEc/9Y+nx3ix1eDvjnaDF5deDkPWeCeODbWGKYFar2CvhuNLezUIyL7UlXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:32:01.330824Z","bundle_sha256":"5c6e97215a720a69c5b3c398b55f71076261a7af0b25bce55cefa67e3d3b0b34"}}