{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2QUFHHZ2ODG75R6CXOVYXLGUQX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"5c1579bf067dab4d08145c4648d62cbb5cf185ad6025af44dc24fafd491a28e0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-15T23:20:37Z","title_canon_sha256":"ba961883ce24c5f16119b13c16a0365f170a108812f58f8f66ac2cab485a36e7"},"schema_version":"1.0","source":{"id":"1103.3063","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3063","created_at":"2026-05-18T03:59:47Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3063v3","created_at":"2026-05-18T03:59:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3063","created_at":"2026-05-18T03:59:47Z"},{"alias_kind":"pith_short_12","alias_value":"2QUFHHZ2ODG7","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2QUFHHZ2ODG75R6C","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2QUFHHZ2","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ee6814a35479c389312a6f281930e166f6afae3db36c09b96a925d8246d1894d","target":"graph","created_at":"2026-05-18T03:59:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $X$ be a $n\\times p$ matrix with coherence $\\mu(X)=\\max_{j\\neq j'} |X_j^tX_{j'}|$. We present a simplified and improved study of the quasi-isometry property for most submatrices of $X$ obtained by uniform column sampling. Our results depend on $\\mu(X)$, $\\|X\\|$ and the dimensions with explicit constants, which improve the previously known values by a large factor. The analysis relies on a tail decoupling argument, of independent interest, and a recent version of the Non-Commutative Chernoff inequality (NCCI).","authors_text":"S\\'ebastien Darses, St\\'ephane Chr\\'etien","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-15T23:20:37Z","title":"Invertibility of random submatrices via tail decoupling and a Matrix Chernoff Inequality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3063","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e70df90337cece89e45b6cf28a925e0e69624bf06c3d2df51a4f8152cf810ee7","target":"record","created_at":"2026-05-18T03:59:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"5c1579bf067dab4d08145c4648d62cbb5cf185ad6025af44dc24fafd491a28e0","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-15T23:20:37Z","title_canon_sha256":"ba961883ce24c5f16119b13c16a0365f170a108812f58f8f66ac2cab485a36e7"},"schema_version":"1.0","source":{"id":"1103.3063","kind":"arxiv","version":3}},"canonical_sha256":"d428539f3a70cdfec7c2bbab8bacd485d850fb03c89613c41632451ba66d2c1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d428539f3a70cdfec7c2bbab8bacd485d850fb03c89613c41632451ba66d2c1f","first_computed_at":"2026-05-18T03:59:47.818416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:47.818416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6p9mlIglhX1Csnx05XI+4duxTKELhqFe0vdvknyDQavrYHUc8LsU7NAlTteAr1BcV+6qflEV4OYR0rCUqJ9fDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:47.818863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3063","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e70df90337cece89e45b6cf28a925e0e69624bf06c3d2df51a4f8152cf810ee7","sha256:ee6814a35479c389312a6f281930e166f6afae3db36c09b96a925d8246d1894d"],"state_sha256":"27ff7578f76e9d48d60fa64300f9fd2a071463f5ac89d64cbd0ee87aaf203788"}