{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:GLZKDJD3THOSREMJBI4ZR34PXM","short_pith_number":"pith:GLZKDJD3","schema_version":"1.0","canonical_sha256":"32f2a1a47b99dd2891890a3998ef8fbb30aaa957b9c0d6f6652321d6c3e3ebc5","source":{"kind":"arxiv","id":"math/0110131","version":2},"attestation_state":"computed","paper":{"title":"Birkhoff's theorem and multidimensional numerical range","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Yuri Safarov","submitted_at":"2001-10-12T14:01:03Z","abstract_excerpt":"We study the relation between the spectrum of a self-adjoint operator and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex set whose extreme points are sequences of eigenvalues of the operator. Every collection of eigenvalues which can be obtained by the Rayleigh--Ritz formula generates an extreme point of the multidimensional numerical range. However, it may also have other extreme points."},"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":"math/0110131","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.SP","submitted_at":"2001-10-12T14:01:03Z","cross_cats_sorted":[],"title_canon_sha256":"91ce944146d5cdd775979dfcf97f6433e8ecb754b49ef78d1e696d27a51a70f4","abstract_canon_sha256":"0ac26ac7a65430a94107495f6a1c8444f4c13f3500784ad076e0a139f8c2d088"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:49:40.907852Z","signature_b64":"qR8ZWQuz668i+4izJar+X8e6C7/BJAL3bm3V53k9oBbpIvC4YON+w4ZZYIq10KWDuVmfyxlPp9lWNyjSAXWuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32f2a1a47b99dd2891890a3998ef8fbb30aaa957b9c0d6f6652321d6c3e3ebc5","last_reissued_at":"2026-07-04T14:49:40.907483Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:49:40.907483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Birkhoff's theorem and multidimensional numerical range","license":"","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Yuri Safarov","submitted_at":"2001-10-12T14:01:03Z","abstract_excerpt":"We study the relation between the spectrum of a self-adjoint operator and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex set whose extreme points are sequences of eigenvalues of the operator. Every collection of eigenvalues which can be obtained by the Rayleigh--Ritz formula generates an extreme point of the multidimensional numerical range. However, it may also have other extreme points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110131","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0110131/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"math/0110131","created_at":"2026-07-04T14:49:40.907538+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0110131v2","created_at":"2026-07-04T14:49:40.907538+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110131","created_at":"2026-07-04T14:49:40.907538+00:00"},{"alias_kind":"pith_short_12","alias_value":"GLZKDJD3THOS","created_at":"2026-07-04T14:49:40.907538+00:00"},{"alias_kind":"pith_short_16","alias_value":"GLZKDJD3THOSREMJ","created_at":"2026-07-04T14:49:40.907538+00:00"},{"alias_kind":"pith_short_8","alias_value":"GLZKDJD3","created_at":"2026-07-04T14:49:40.907538+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/GLZKDJD3THOSREMJBI4ZR34PXM","json":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM.json","graph_json":"https://pith.science/api/pith-number/GLZKDJD3THOSREMJBI4ZR34PXM/graph.json","events_json":"https://pith.science/api/pith-number/GLZKDJD3THOSREMJBI4ZR34PXM/events.json","paper":"https://pith.science/paper/GLZKDJD3"},"agent_actions":{"view_html":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM","download_json":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM.json","view_paper":"https://pith.science/paper/GLZKDJD3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0110131&json=true","fetch_graph":"https://pith.science/api/pith-number/GLZKDJD3THOSREMJBI4ZR34PXM/graph.json","fetch_events":"https://pith.science/api/pith-number/GLZKDJD3THOSREMJBI4ZR34PXM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM/action/storage_attestation","attest_author":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM/action/author_attestation","sign_citation":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM/action/citation_signature","submit_replication":"https://pith.science/pith/GLZKDJD3THOSREMJBI4ZR34PXM/action/replication_record"}},"created_at":"2026-07-04T14:49:40.907538+00:00","updated_at":"2026-07-04T14:49:40.907538+00:00"}