{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:RC6CTLNNNS7XJF6LR2EFYS5KLP","short_pith_number":"pith:RC6CTLNN","schema_version":"1.0","canonical_sha256":"88bc29adad6cbf7497cb8e885c4baa5bdaa482c3c7200cf71eea3d60686c8a63","source":{"kind":"arxiv","id":"1302.7116","version":1},"attestation_state":"computed","paper":{"title":"Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.RT","authors_text":"Grigori Olshanski","submitted_at":"2013-02-28T09:05:12Z","abstract_excerpt":"The unitary group U(N) acts by conjugations on the space H(N) of NxN Hermitian matrices, and every orbit of this action carries a unique invariant probability measure called an orbital measure. Consider the projection of the space H(N) onto the real line assigning to an Hermitian matrix its (1,1)-entry. Under this projection, the density of the pushforward of a generic orbital measure is a spline function with N knots. This fact was pointed out by Andrei Okounkov in 1996, and the goal of the paper is to propose a multidimensional generalization. Namely, it turns out that if instead of the (1,1"},"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":"1302.7116","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-28T09:05:12Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"4e3162fad1b3703cef76be754ca44d640a0f2b48d00d6bae4e133ecec114e704","abstract_canon_sha256":"a648b5d31f3407ce885e573b69e87709adf534a8f5f94f8ad1aa9520057332a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:07.184776Z","signature_b64":"XC2OaMr7gFpi3wfTtJrHi44loqTJSPI3mvGgIdNi/NsnhYWVY7+QQjanYqsS/j1Hh1P8gTTYvtSQ8W+DaX3FDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88bc29adad6cbf7497cb8e885c4baa5bdaa482c3c7200cf71eea3d60686c8a63","last_reissued_at":"2026-05-18T03:32:07.184005Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:07.184005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.RT","authors_text":"Grigori Olshanski","submitted_at":"2013-02-28T09:05:12Z","abstract_excerpt":"The unitary group U(N) acts by conjugations on the space H(N) of NxN Hermitian matrices, and every orbit of this action carries a unique invariant probability measure called an orbital measure. Consider the projection of the space H(N) onto the real line assigning to an Hermitian matrix its (1,1)-entry. Under this projection, the density of the pushforward of a generic orbital measure is a spline function with N knots. This fact was pointed out by Andrei Okounkov in 1996, and the goal of the paper is to propose a multidimensional generalization. Namely, it turns out that if instead of the (1,1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7116","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":"1302.7116","created_at":"2026-05-18T03:32:07.184127+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.7116v1","created_at":"2026-05-18T03:32:07.184127+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7116","created_at":"2026-05-18T03:32:07.184127+00:00"},{"alias_kind":"pith_short_12","alias_value":"RC6CTLNNNS7X","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"RC6CTLNNNS7XJF6L","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"RC6CTLNN","created_at":"2026-05-18T12:27:57.521954+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/RC6CTLNNNS7XJF6LR2EFYS5KLP","json":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP.json","graph_json":"https://pith.science/api/pith-number/RC6CTLNNNS7XJF6LR2EFYS5KLP/graph.json","events_json":"https://pith.science/api/pith-number/RC6CTLNNNS7XJF6LR2EFYS5KLP/events.json","paper":"https://pith.science/paper/RC6CTLNN"},"agent_actions":{"view_html":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP","download_json":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP.json","view_paper":"https://pith.science/paper/RC6CTLNN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.7116&json=true","fetch_graph":"https://pith.science/api/pith-number/RC6CTLNNNS7XJF6LR2EFYS5KLP/graph.json","fetch_events":"https://pith.science/api/pith-number/RC6CTLNNNS7XJF6LR2EFYS5KLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP/action/storage_attestation","attest_author":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP/action/author_attestation","sign_citation":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP/action/citation_signature","submit_replication":"https://pith.science/pith/RC6CTLNNNS7XJF6LR2EFYS5KLP/action/replication_record"}},"created_at":"2026-05-18T03:32:07.184127+00:00","updated_at":"2026-05-18T03:32:07.184127+00:00"}