{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XXXOGSWDJVGEMMRYWHQH4LHSIU","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":"1910269d56b5d5ed5436ba4946d5dfc60ff3d562458f95f90a5f63827dfed9d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-05T18:04:26Z","title_canon_sha256":"0c38c24f55f93d17a3c7da3ea8275595bf680bba148179bfa987d5f66f5b1353"},"schema_version":"1.0","source":{"id":"1502.01661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01661","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01661v1","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01661","created_at":"2026-05-18T02:27:51Z"},{"alias_kind":"pith_short_12","alias_value":"XXXOGSWDJVGE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XXXOGSWDJVGEMMRY","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XXXOGSWD","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:627d58b1599b7ea47c681bb8cdd2414c4fb8134ae4addb1bb2c2f7ac613c6fde","target":"graph","created_at":"2026-05-18T02:27:51Z","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, Vogan introduced a generalised $\\\\tau$ -invariant for characterising primitive ideals in enveloping algebras. Via a known dictionary this translates to an invariant of left cells in the sense of Kazhdan and Lusztig. Although it is not a complete invariant, it is extremely useful in describing left cells. Here, we propose a general framework for defining such invariants which also applies to Hecke algebras with unequal parameters.","authors_text":"C\\'edric Bonnaf\\'e (I3M), Meinolf Geck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-05T18:04:26Z","title":"Hecke algebras with unequal parameters and Vogan's left cell invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01661","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":"sha256:3856ad3dae544907fc694465534f15f5ffedfcbcb91c2a5f19404c24a2f7eb2e","target":"record","created_at":"2026-05-18T02:27:51Z","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":"1910269d56b5d5ed5436ba4946d5dfc60ff3d562458f95f90a5f63827dfed9d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-02-05T18:04:26Z","title_canon_sha256":"0c38c24f55f93d17a3c7da3ea8275595bf680bba148179bfa987d5f66f5b1353"},"schema_version":"1.0","source":{"id":"1502.01661","kind":"arxiv","version":1}},"canonical_sha256":"bdeee34ac34d4c463238b1e07e2cf24519a658f0ee65d83fa179cdfd6ef6c7e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdeee34ac34d4c463238b1e07e2cf24519a658f0ee65d83fa179cdfd6ef6c7e9","first_computed_at":"2026-05-18T02:27:51.600547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:51.600547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oUbrRUtsguTyxHwDjgSscY3BhFwdAu38JzOXo9WfmKQ+hVDJHDQGjmV29mvdBZ+k8I8fJZr5NIO0iAJkP1Q+CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:51.600958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3856ad3dae544907fc694465534f15f5ffedfcbcb91c2a5f19404c24a2f7eb2e","sha256:627d58b1599b7ea47c681bb8cdd2414c4fb8134ae4addb1bb2c2f7ac613c6fde"],"state_sha256":"e6a026991e994dc42648d36e7c7cea78801f71488890930fe8245ce8c008c63c"}