{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:WF3RGOKJ5LDDBU5NEC4YLCOZS4","short_pith_number":"pith:WF3RGOKJ","schema_version":"1.0","canonical_sha256":"b177133949eac630d3ad20b98589d9971300d520fe412f4b758b529cfa8c10f7","source":{"kind":"arxiv","id":"1301.6607","version":2},"attestation_state":"computed","paper":{"title":"Estimating the covariance of random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pierre Youssef","submitted_at":"2013-01-28T17:02:59Z","abstract_excerpt":"We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be in- terpreted as a quantified version of the law of large numbers for positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we dis- cuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices."},"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":"1301.6607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-28T17:02:59Z","cross_cats_sorted":[],"title_canon_sha256":"4e4aa4f035409491612240531b634a8977702b61b68cae9938204ebbbe0624d3","abstract_canon_sha256":"c008c42bbe434053d4db1d36d51910c442c83106fa4f0caa78768769af2204c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:05.887995Z","signature_b64":"U0teuDgkSlXwf4/oKszcgJzn0iccsdacKH+dzwlR+BFQ9OzjNvTCn53dw4ltlMB41mG48Htfil4N3tNP3pRRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b177133949eac630d3ad20b98589d9971300d520fe412f4b758b529cfa8c10f7","last_reissued_at":"2026-05-18T01:27:05.887423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:05.887423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating the covariance of random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pierre Youssef","submitted_at":"2013-01-28T17:02:59Z","abstract_excerpt":"We extend to the matrix setting a recent result of Srivastava-Vershynin about estimating the covariance matrix of a random vector. The result can be in- terpreted as a quantified version of the law of large numbers for positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we dis- cuss the notion of log-concave matrices and give estimates on the smallest and largest eigenvalues of a sum of such matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6607","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":"1301.6607","created_at":"2026-05-18T01:27:05.887535+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.6607v2","created_at":"2026-05-18T01:27:05.887535+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6607","created_at":"2026-05-18T01:27:05.887535+00:00"},{"alias_kind":"pith_short_12","alias_value":"WF3RGOKJ5LDD","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"WF3RGOKJ5LDDBU5N","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"WF3RGOKJ","created_at":"2026-05-18T12:28:04.890932+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/WF3RGOKJ5LDDBU5NEC4YLCOZS4","json":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4.json","graph_json":"https://pith.science/api/pith-number/WF3RGOKJ5LDDBU5NEC4YLCOZS4/graph.json","events_json":"https://pith.science/api/pith-number/WF3RGOKJ5LDDBU5NEC4YLCOZS4/events.json","paper":"https://pith.science/paper/WF3RGOKJ"},"agent_actions":{"view_html":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4","download_json":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4.json","view_paper":"https://pith.science/paper/WF3RGOKJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.6607&json=true","fetch_graph":"https://pith.science/api/pith-number/WF3RGOKJ5LDDBU5NEC4YLCOZS4/graph.json","fetch_events":"https://pith.science/api/pith-number/WF3RGOKJ5LDDBU5NEC4YLCOZS4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4/action/storage_attestation","attest_author":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4/action/author_attestation","sign_citation":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4/action/citation_signature","submit_replication":"https://pith.science/pith/WF3RGOKJ5LDDBU5NEC4YLCOZS4/action/replication_record"}},"created_at":"2026-05-18T01:27:05.887535+00:00","updated_at":"2026-05-18T01:27:05.887535+00:00"}