{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JBI6RNYTGDCJ4FNHV2ZEQRNBAI","short_pith_number":"pith:JBI6RNYT","schema_version":"1.0","canonical_sha256":"4851e8b71330c49e15a7aeb24845a1021f9f5ceeaaa41d190f7b4513f4aabd0e","source":{"kind":"arxiv","id":"1512.02863","version":2},"attestation_state":"computed","paper":{"title":"On the eigenvalues of the spatial sign covariance matrix in more than two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.CO","authors_text":"Alexander D\\\"urre, Daniel Vogel, David E. Tyler","submitted_at":"2015-12-09T14:14:56Z","abstract_excerpt":"We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation."},"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":"1512.02863","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.CO","submitted_at":"2015-12-09T14:14:56Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"37baa4f64baa42ae744f24e07e57d4e576037f428da410e3876bfcf97aa046f0","abstract_canon_sha256":"1817b8fd3897c17b3e796c95fd0953f9ec2f942276e1cd04ac390380680dcaff"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:54.031054Z","signature_b64":"O44lArFa9Le4/tglg0oQvdD7v4Som+R75G1AWudDVuvSRBTw9un5dInBSyPfKcQsZtl5rA5GaBvHvyXyzgONBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4851e8b71330c49e15a7aeb24845a1021f9f5ceeaaa41d190f7b4513f4aabd0e","last_reissued_at":"2026-05-18T01:18:54.030546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:54.030546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the eigenvalues of the spatial sign covariance matrix in more than two dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.CO","authors_text":"Alexander D\\\"urre, Daniel Vogel, David E. Tyler","submitted_at":"2015-12-09T14:14:56Z","abstract_excerpt":"We gather several results on the eigenvalues of the spatial sign covariance matrix of an elliptical distribution. It is shown that the eigenvalues are a one-to-one function of the eigenvalues of the shape matrix and that they are closer together than the latter. We further provide a one-dimensional integral representation of the eigenvalues, which facilitates their numerical computation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02863","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":""},"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":"1512.02863","created_at":"2026-05-18T01:18:54.030626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.02863v2","created_at":"2026-05-18T01:18:54.030626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02863","created_at":"2026-05-18T01:18:54.030626+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBI6RNYTGDCJ","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBI6RNYTGDCJ4FNH","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBI6RNYT","created_at":"2026-05-18T12:29:27.538025+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/JBI6RNYTGDCJ4FNHV2ZEQRNBAI","json":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI.json","graph_json":"https://pith.science/api/pith-number/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/graph.json","events_json":"https://pith.science/api/pith-number/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/events.json","paper":"https://pith.science/paper/JBI6RNYT"},"agent_actions":{"view_html":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI","download_json":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI.json","view_paper":"https://pith.science/paper/JBI6RNYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.02863&json=true","fetch_graph":"https://pith.science/api/pith-number/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/graph.json","fetch_events":"https://pith.science/api/pith-number/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/action/storage_attestation","attest_author":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/action/author_attestation","sign_citation":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/action/citation_signature","submit_replication":"https://pith.science/pith/JBI6RNYTGDCJ4FNHV2ZEQRNBAI/action/replication_record"}},"created_at":"2026-05-18T01:18:54.030626+00:00","updated_at":"2026-05-18T01:18:54.030626+00:00"}