{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2GJSJ57X2ITZGKEU3WWSZGDCWG","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":"c830b7b4f165bea7086a8c70d61d835342d1a71d4f2f71341da00cf0e01a842d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-01T15:14:18Z","title_canon_sha256":"b78cf2980b8797ee9b5a6c020289b1a879145b647dd7f5f9915493fd5caef1c5"},"schema_version":"1.0","source":{"id":"1708.00383","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.00383","created_at":"2026-05-17T23:56:15Z"},{"alias_kind":"arxiv_version","alias_value":"1708.00383v4","created_at":"2026-05-17T23:56:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.00383","created_at":"2026-05-17T23:56:15Z"},{"alias_kind":"pith_short_12","alias_value":"2GJSJ57X2ITZ","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2GJSJ57X2ITZGKEU","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2GJSJ57X","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:e2577a77c6ea538a6b14c80e999b04e657d05bce5083e2e1fc6c4a7c7738ed1f","target":"graph","created_at":"2026-05-17T23:56:15Z","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 $G$ be a complex connected simple algebraic group with a fixed real form $\\sigma$. Let $G(\\mathbb{R})=G^\\sigma$ be the corresponding group of real points. This paper reports a finiteness theorem for the classification of irreducible unitary Harish-Chandra modules of $G(\\mathbb{R})$ (up to equivalence) having non-vanishing Dirac cohomology. Moreover, we study the distribution of the spin norm along Vogan pencils for certain $G(\\mathbb{R})$, with particular attention paid to the unitarily small convex hull introduced by Salamanca-Riba and Vogan.","authors_text":"Chao-Ping Dong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-01T15:14:18Z","title":"Unitary representations with Dirac cohomology: finiteness in the real case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00383","kind":"arxiv","version":4},"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:c273833aeba75db3a9d8549d84120df3597c202515fce79c71ed184f3a8b48d2","target":"record","created_at":"2026-05-17T23:56:15Z","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":"c830b7b4f165bea7086a8c70d61d835342d1a71d4f2f71341da00cf0e01a842d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-08-01T15:14:18Z","title_canon_sha256":"b78cf2980b8797ee9b5a6c020289b1a879145b647dd7f5f9915493fd5caef1c5"},"schema_version":"1.0","source":{"id":"1708.00383","kind":"arxiv","version":4}},"canonical_sha256":"d19324f7f7d227932894ddad2c9862b1b113ab073b265fbe6bb7c64ca587ad57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d19324f7f7d227932894ddad2c9862b1b113ab073b265fbe6bb7c64ca587ad57","first_computed_at":"2026-05-17T23:56:15.499643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:15.499643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rkLvKAmb8+7JaoEO61jiOTyKWJKGjPitAg/TRlymEImvmnZUrzowJ9Ol1oWPXuVLX/fFtIPcIYY7Q1Tg1o0xDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:15.500111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.00383","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c273833aeba75db3a9d8549d84120df3597c202515fce79c71ed184f3a8b48d2","sha256:e2577a77c6ea538a6b14c80e999b04e657d05bce5083e2e1fc6c4a7c7738ed1f"],"state_sha256":"e8e05559e092cd3ffcd19b065e01bf56d69d33036bc4b8814d9a62cddbe44ac0"}