{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4UE73YU4WSAOU4KU7EMBRW5NWL","short_pith_number":"pith:4UE73YU4","schema_version":"1.0","canonical_sha256":"e509fde29cb480ea7154f91818dbadb2dd1d83cdccc2fc9548810a8ddf4f5a9a","source":{"kind":"arxiv","id":"1502.05946","version":3},"attestation_state":"computed","paper":{"title":"The Singular Values of the GOE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Folkmar Bornemann, Michael La Croix","submitted_at":"2015-02-20T17:38:59Z","abstract_excerpt":"As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are distributed as the positive eigenvalues of a Gaussian ensemble with chiral unitary symmetry (anti-GUE), while the odd-location singular values, conditioned on the even-location ones, can be algebraically transformed into a set of independent $\\chi$-distributed random variables. We discuss three applications of this structure: first, there is a pair of bidiagonal squa"},"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":"1502.05946","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-02-20T17:38:59Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"13ec30643997be14625f0e50f48f8e43af568d04e0ce3f47d7840bd842987471","abstract_canon_sha256":"fc5f647c50b7bd069be71482e881d9782cceee7244ddcf2129b23b34f8a54b3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:54.165877Z","signature_b64":"uRwJyM21ilAt6yAc1qynFRNtg2qiGdCnZ1gvghhNS093eFoRJ0uJfJB1KE9Ygyd7p/JRLqbP+UQCocc4JXHsAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e509fde29cb480ea7154f91818dbadb2dd1d83cdccc2fc9548810a8ddf4f5a9a","last_reissued_at":"2026-05-18T02:17:54.165205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:54.165205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Singular Values of the GOE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Folkmar Bornemann, Michael La Croix","submitted_at":"2015-02-20T17:38:59Z","abstract_excerpt":"As a unifying framework for examining several properties that nominally involve eigenvalues, we present a particular structure of the singular values of the Gaussian orthogonal ensemble (GOE): the even-location singular values are distributed as the positive eigenvalues of a Gaussian ensemble with chiral unitary symmetry (anti-GUE), while the odd-location singular values, conditioned on the even-location ones, can be algebraically transformed into a set of independent $\\chi$-distributed random variables. We discuss three applications of this structure: first, there is a pair of bidiagonal squa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05946","kind":"arxiv","version":3},"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":"1502.05946","created_at":"2026-05-18T02:17:54.165304+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.05946v3","created_at":"2026-05-18T02:17:54.165304+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05946","created_at":"2026-05-18T02:17:54.165304+00:00"},{"alias_kind":"pith_short_12","alias_value":"4UE73YU4WSAO","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4UE73YU4WSAOU4KU","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4UE73YU4","created_at":"2026-05-18T12:29:05.191682+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/4UE73YU4WSAOU4KU7EMBRW5NWL","json":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL.json","graph_json":"https://pith.science/api/pith-number/4UE73YU4WSAOU4KU7EMBRW5NWL/graph.json","events_json":"https://pith.science/api/pith-number/4UE73YU4WSAOU4KU7EMBRW5NWL/events.json","paper":"https://pith.science/paper/4UE73YU4"},"agent_actions":{"view_html":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL","download_json":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL.json","view_paper":"https://pith.science/paper/4UE73YU4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.05946&json=true","fetch_graph":"https://pith.science/api/pith-number/4UE73YU4WSAOU4KU7EMBRW5NWL/graph.json","fetch_events":"https://pith.science/api/pith-number/4UE73YU4WSAOU4KU7EMBRW5NWL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL/action/storage_attestation","attest_author":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL/action/author_attestation","sign_citation":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL/action/citation_signature","submit_replication":"https://pith.science/pith/4UE73YU4WSAOU4KU7EMBRW5NWL/action/replication_record"}},"created_at":"2026-05-18T02:17:54.165304+00:00","updated_at":"2026-05-18T02:17:54.165304+00:00"}