{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HG4LAJRT7ZNOB4NNO46K6YCA4B","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":"d8ca58e4402fbbb102737b06df90d813101ba7663eb1631b3b7beed2a6d8fb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-10T18:05:52Z","title_canon_sha256":"6e39022a56dd159b9253a782421d1c41effed90e696197b716c7685d5fc42142"},"schema_version":"1.0","source":{"id":"1201.2130","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.2130","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1201.2130v3","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.2130","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"HG4LAJRT7ZNO","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HG4LAJRT7ZNOB4NN","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HG4LAJRT","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:18abaea856e5a47d55812174429a196a2b0fdca1bd20ee5af7a9397886cf56d5","target":"graph","created_at":"2026-05-18T02:50:40Z","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":"We define the algebraic Dirac induction map $\\Ind_D$ for graded affine Hecke algebras. The map $\\Ind_D$ is a Hecke algebra analog of the explicit realization of the Baum-Connes assembly map in the $K$-theory of the reduced $C^*$-algebra of a real reductive group using Dirac operators. The definition of $\\Ind_D$ is uniform over the parameter space of the graded affine Hecke algebra. We show that the map $\\Ind_D$ defines an isometric isomorphism from the space of elliptic characters of the Weyl group (relative to its reflection representation) to the space of elliptic characters of the graded af","authors_text":"Dan Ciubotaru, Eric M. Opdam, Peter E. Trapa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-10T18:05:52Z","title":"Algebraic and analytic Dirac induction for graded affine Hecke algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2130","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":"sha256:241d977e0929069ef17494d6850b5a3fdf54fc7c67e4a2939f6150bf0c5f9ddd","target":"record","created_at":"2026-05-18T02:50:40Z","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":"d8ca58e4402fbbb102737b06df90d813101ba7663eb1631b3b7beed2a6d8fb54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-01-10T18:05:52Z","title_canon_sha256":"6e39022a56dd159b9253a782421d1c41effed90e696197b716c7685d5fc42142"},"schema_version":"1.0","source":{"id":"1201.2130","kind":"arxiv","version":3}},"canonical_sha256":"39b8b02633fe5ae0f1ad773caf6040e079562a95e11e100c999bc4896667e208","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39b8b02633fe5ae0f1ad773caf6040e079562a95e11e100c999bc4896667e208","first_computed_at":"2026-05-18T02:50:40.754166Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:40.754166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1TT3s74DRQXZw7j1EIQYot3aiffFdbiY8iLYQpYOBX8KTKx3WnY8UDy6T75WTjFk5Wlr0vecgNsfJ6qFznO1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:40.754808Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.2130","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:241d977e0929069ef17494d6850b5a3fdf54fc7c67e4a2939f6150bf0c5f9ddd","sha256:18abaea856e5a47d55812174429a196a2b0fdca1bd20ee5af7a9397886cf56d5"],"state_sha256":"b6c4cf216f95d308c7aa17f5ed2876c9c8e7d957374b7a1e98ec3d4bcc560425"}