{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YFKBD3CPKJEL7JCJDAG7W3A4EF","short_pith_number":"pith:YFKBD3CP","schema_version":"1.0","canonical_sha256":"c15411ec4f5248bfa449180dfb6c1c2167bdb95a0700da63e5d713eaa73d81a4","source":{"kind":"arxiv","id":"2605.16733","version":1},"attestation_state":"computed","paper":{"title":"Concentration Inequalities for Sample Cross-Covariances","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Sub-Gaussian sample cross-covariances deviate from their mean in operator norm at a rate governed by the effective ranks of the marginal covariances.","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Daniel Sanz-Alonso, Jiaheng Chen","submitted_at":"2026-05-16T00:58:51Z","abstract_excerpt":"This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed by the effective ranks of the two marginal covariance matrices. In the Gaussian case, we prove a matching expectation lower bound, allowing arbitrary correlation between the two random vectors."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.16733","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-16T00:58:51Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"8a55c7cc866c63fccaad65c949f84013bc2e0a95f1ee04e29e49d044d09c639e","abstract_canon_sha256":"137281ba770c67bb41bad533352187752afcdd22cd6c60844e6b112c91b8a50c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:02:38.923464Z","signature_b64":"iBPELxHH3aale3tSRfVxgBNr6Hf+DA+5pkC67VUVsSkCacMxQ18t0qkoghHEjW8yeLDOWT//GHC89IXhjfANDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c15411ec4f5248bfa449180dfb6c1c2167bdb95a0700da63e5d713eaa73d81a4","last_reissued_at":"2026-05-20T00:02:38.922606Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:02:38.922606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration Inequalities for Sample Cross-Covariances","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Sub-Gaussian sample cross-covariances deviate from their mean in operator norm at a rate governed by the effective ranks of the marginal covariances.","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Daniel Sanz-Alonso, Jiaheng Chen","submitted_at":"2026-05-16T00:58:51Z","abstract_excerpt":"This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed by the effective ranks of the two marginal covariance matrices. In the Gaussian case, we prove a matching expectation lower bound, allowing arbitrary correlation between the two random vectors."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For sub-Gaussian random vectors, a high-probability operator-norm bound for the deviation of the sample cross-covariance matrix governed by the effective ranks of the two marginal covariance matrices; in the Gaussian case, a matching expectation lower bound allowing arbitrary correlation between the two random vectors.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The two random vectors are sub-Gaussian (or jointly Gaussian), which supplies the tail and moment properties used to control the deviation of the sample cross-covariance in operator norm.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Sub-Gaussian sample cross-covariances deviate from their mean in operator norm at a rate governed by the effective ranks of the marginal covariances.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4510886d723251e9e70bf3fd9ae14e7f7bca3f373c70727ed48c320dde7bdc14"},"source":{"id":"2605.16733","kind":"arxiv","version":1},"verdict":{"id":"fac690fb-58ce-44ea-bd5c-889d3cb61b02","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:22:58.620406Z","strongest_claim":"For sub-Gaussian random vectors, a high-probability operator-norm bound for the deviation of the sample cross-covariance matrix governed by the effective ranks of the two marginal covariance matrices; in the Gaussian case, a matching expectation lower bound allowing arbitrary correlation between the two random vectors.","one_line_summary":"Proves sharp operator-norm concentration and expectation bounds for sample cross-covariances of sub-Gaussian and Gaussian vectors, governed by effective ranks of the marginal covariances.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The two random vectors are sub-Gaussian (or jointly Gaussian), which supplies the tail and moment properties used to control the deviation of the sample cross-covariance in operator norm.","pith_extraction_headline":"Sub-Gaussian sample cross-covariances deviate from their mean in operator norm at a rate governed by the effective ranks of the marginal covariances."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16733/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T20:32:04.423142Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.182600Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.340404Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.468225Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"5ad90af262bfe8349d90450147bd67660211cf9d3d65d87e802917577b249644"},"references":{"count":300,"sample":[{"doi":"","year":null,"title":"Ghattas, Omar Al and Bao, Jiajun and Sanz-Alonso, Daniel , journal=","work_id":"68c33f98-f3a4-4185-91ad-b588fc7c4eab","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Majda, A. J. and Tong, X. T. , journal=. 2018 , publisher=","work_id":"2eed246e-52d8-4de4-ba21-719c4ae051cd","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"Tong, X. T. , journal=. 2018 , publisher=","work_id":"3453c7d3-3d04-4a18-8872-9607ab9654b2","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Nonparametric estimation of large covariance matrices of longitudinal data , author=. Biometrika , volume=. 2003 , publisher=","work_id":"7d659169-41b6-45fe-860a-f1562d20adb7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"Advances In Statistics , pages=","work_id":"85bcc470-7947-4840-93e7-08fd071c8daf","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":300,"snapshot_sha256":"22bf80d6e967575b4f65d79b96d410682a6bd060ab2ced7c7d5d3e23867ab045","internal_anchors":4},"formal_canon":{"evidence_count":1,"snapshot_sha256":"64bbfe8357b9039d508ada7b909b515bb7190f8c8d48c400bd355e4a1b9ac5c3"},"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":"2605.16733","created_at":"2026-05-20T00:02:38.922750+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.16733v1","created_at":"2026-05-20T00:02:38.922750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16733","created_at":"2026-05-20T00:02:38.922750+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFKBD3CPKJEL","created_at":"2026-05-20T00:02:38.922750+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFKBD3CPKJEL7JCJ","created_at":"2026-05-20T00:02:38.922750+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFKBD3CP","created_at":"2026-05-20T00:02:38.922750+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":1,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF","json":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF.json","graph_json":"https://pith.science/api/pith-number/YFKBD3CPKJEL7JCJDAG7W3A4EF/graph.json","events_json":"https://pith.science/api/pith-number/YFKBD3CPKJEL7JCJDAG7W3A4EF/events.json","paper":"https://pith.science/paper/YFKBD3CP"},"agent_actions":{"view_html":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF","download_json":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF.json","view_paper":"https://pith.science/paper/YFKBD3CP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.16733&json=true","fetch_graph":"https://pith.science/api/pith-number/YFKBD3CPKJEL7JCJDAG7W3A4EF/graph.json","fetch_events":"https://pith.science/api/pith-number/YFKBD3CPKJEL7JCJDAG7W3A4EF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF/action/storage_attestation","attest_author":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF/action/author_attestation","sign_citation":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF/action/citation_signature","submit_replication":"https://pith.science/pith/YFKBD3CPKJEL7JCJDAG7W3A4EF/action/replication_record"}},"created_at":"2026-05-20T00:02:38.922750+00:00","updated_at":"2026-05-20T00:02:38.922750+00:00"}