{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OXFLGUSLU37UG4B6CK7UP2FVFY","short_pith_number":"pith:OXFLGUSL","schema_version":"1.0","canonical_sha256":"75cab3524ba6ff43703e12bf47e8b52e0dbdd3921fe414fcc8e5977c688e6576","source":{"kind":"arxiv","id":"1712.04173","version":1},"attestation_state":"computed","paper":{"title":"Computing the associatied cycles of certain Harish-Chandra modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Vogan, Pavle Pandzic, Roger Zierau, Salah Mehdi","submitted_at":"2017-12-12T08:36:14Z","abstract_excerpt":"Let $G_{\\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\\mathbb{R}}$ and assume that ${\\rm rank}(G_\\mathbb{R})={\\rm rank}(K_\\mathbb{R})$. In \\cite{MPVZ} we proved that for any representation $X$ of Gelfand-Kirillov dimension $\\frac{1}{2}\\dim(G_{\\mathbb{R}}/K_{\\mathbb{R}})$, the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing $X$ is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.04173","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-12-12T08:36:14Z","cross_cats_sorted":[],"title_canon_sha256":"03aabe8517d00c94eecb5837e1b143810ee441dab13aa4dca63a62110fbb4a2f","abstract_canon_sha256":"30bde9417bf6f9f8731746ceac50e1eac341e5cf0ee83d882dafb425c9e1b1e7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:08.891834Z","signature_b64":"pqJ9BwEUGpWrmByz7RtQ4+q7/9y7mOMOy3ahtGSS5lpRaQQ5OuJb6FDHD1b+Q21HzqI3VYzWjr9lnGoyHEPjDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75cab3524ba6ff43703e12bf47e8b52e0dbdd3921fe414fcc8e5977c688e6576","last_reissued_at":"2026-05-18T00:28:08.891146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:08.891146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the associatied cycles of certain Harish-Chandra modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Vogan, Pavle Pandzic, Roger Zierau, Salah Mehdi","submitted_at":"2017-12-12T08:36:14Z","abstract_excerpt":"Let $G_{\\mathbb{R}}$ be a simple real linear Lie group with maximal compact subgroup $K_{\\mathbb{R}}$ and assume that ${\\rm rank}(G_\\mathbb{R})={\\rm rank}(K_\\mathbb{R})$. In \\cite{MPVZ} we proved that for any representation $X$ of Gelfand-Kirillov dimension $\\frac{1}{2}\\dim(G_{\\mathbb{R}}/K_{\\mathbb{R}})$, the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing $X$ is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04173","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.04173","created_at":"2026-05-18T00:28:08.891254+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.04173v1","created_at":"2026-05-18T00:28:08.891254+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04173","created_at":"2026-05-18T00:28:08.891254+00:00"},{"alias_kind":"pith_short_12","alias_value":"OXFLGUSLU37U","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OXFLGUSLU37UG4B6","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OXFLGUSL","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY","json":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY.json","graph_json":"https://pith.science/api/pith-number/OXFLGUSLU37UG4B6CK7UP2FVFY/graph.json","events_json":"https://pith.science/api/pith-number/OXFLGUSLU37UG4B6CK7UP2FVFY/events.json","paper":"https://pith.science/paper/OXFLGUSL"},"agent_actions":{"view_html":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY","download_json":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY.json","view_paper":"https://pith.science/paper/OXFLGUSL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.04173&json=true","fetch_graph":"https://pith.science/api/pith-number/OXFLGUSLU37UG4B6CK7UP2FVFY/graph.json","fetch_events":"https://pith.science/api/pith-number/OXFLGUSLU37UG4B6CK7UP2FVFY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY/action/storage_attestation","attest_author":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY/action/author_attestation","sign_citation":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY/action/citation_signature","submit_replication":"https://pith.science/pith/OXFLGUSLU37UG4B6CK7UP2FVFY/action/replication_record"}},"created_at":"2026-05-18T00:28:08.891254+00:00","updated_at":"2026-05-18T00:28:08.891254+00:00"}