{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RC6CTLNNNS7XJF6LR2EFYS5KLP","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":"a648b5d31f3407ce885e573b69e87709adf534a8f5f94f8ad1aa9520057332a2","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-28T09:05:12Z","title_canon_sha256":"4e3162fad1b3703cef76be754ca44d640a0f2b48d00d6bae4e133ecec114e704"},"schema_version":"1.0","source":{"id":"1302.7116","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7116","created_at":"2026-05-18T03:32:07Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7116v1","created_at":"2026-05-18T03:32:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7116","created_at":"2026-05-18T03:32:07Z"},{"alias_kind":"pith_short_12","alias_value":"RC6CTLNNNS7X","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RC6CTLNNNS7XJF6L","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RC6CTLNN","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:9b8b50c442defce5ad992c026fb84a7fac3a430db1db117e4fc8bf16c24c636f","target":"graph","created_at":"2026-05-18T03:32:07Z","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":"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","authors_text":"Grigori Olshanski","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-28T09:05:12Z","title":"Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7116","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:e2f3428be3679ae45df29d3bd7bdc9902d2976bbe29b68ceac565f484a697292","target":"record","created_at":"2026-05-18T03:32:07Z","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":"a648b5d31f3407ce885e573b69e87709adf534a8f5f94f8ad1aa9520057332a2","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-02-28T09:05:12Z","title_canon_sha256":"4e3162fad1b3703cef76be754ca44d640a0f2b48d00d6bae4e133ecec114e704"},"schema_version":"1.0","source":{"id":"1302.7116","kind":"arxiv","version":1}},"canonical_sha256":"88bc29adad6cbf7497cb8e885c4baa5bdaa482c3c7200cf71eea3d60686c8a63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88bc29adad6cbf7497cb8e885c4baa5bdaa482c3c7200cf71eea3d60686c8a63","first_computed_at":"2026-05-18T03:32:07.184005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:07.184005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XC2OaMr7gFpi3wfTtJrHi44loqTJSPI3mvGgIdNi/NsnhYWVY7+QQjanYqsS/j1Hh1P8gTTYvtSQ8W+DaX3FDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:07.184776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7116","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2f3428be3679ae45df29d3bd7bdc9902d2976bbe29b68ceac565f484a697292","sha256:9b8b50c442defce5ad992c026fb84a7fac3a430db1db117e4fc8bf16c24c636f"],"state_sha256":"65dbd91bc738b6a16307c6b47b39c4dd2254c60908c7c5b5c5621f2bc67ad41a"}