{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VJ7UHRZS55HDFUFNDJ5CTJUNZT","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":"f2eb53866dddacf634a00218069400fb982cc48f79df333944a12fd7d29cc217","cross_cats_sorted":["math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-23T16:26:55Z","title_canon_sha256":"e7bef1a1d04aba29f9ab62fbc8110dc6902a31a25f8c90cc3cc7257689e86170"},"schema_version":"1.0","source":{"id":"2606.24766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24766","created_at":"2026-06-24T01:15:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24766v1","created_at":"2026-06-24T01:15:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24766","created_at":"2026-06-24T01:15:41Z"},{"alias_kind":"pith_short_12","alias_value":"VJ7UHRZS55HD","created_at":"2026-06-24T01:15:41Z"},{"alias_kind":"pith_short_16","alias_value":"VJ7UHRZS55HDFUFN","created_at":"2026-06-24T01:15:41Z"},{"alias_kind":"pith_short_8","alias_value":"VJ7UHRZS","created_at":"2026-06-24T01:15:41Z"}],"graph_snapshots":[{"event_id":"sha256:b27e9ce8232351ec5b44d80dfaf18ed935f63bfad9413fa44077844344876162","target":"graph","created_at":"2026-06-24T01:15:41Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.24766/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Concentration inequalities for sample covariance matrices are fundamental tools in high-dimensional probability. Classical results typically assume that the selected random vectors are independent of the selection rule. In this paper, we study spectral concentration for sample covariance matrices formed from arbitrary, possibly data-dependent subsets of i.i.d. random vectors. Such data-dependent selection destroys the usual independence structure and makes standard covariance concentration bounds inapplicable. For i.i.d. Gaussian random vectors, we prove high-probability lower and upper bounds","authors_text":"Huikang Liu, Laura Balzano, Peng Wang","cross_cats":["math.OC","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-23T16:26:55Z","title":"A Concentration Inequality for the Covariance Matrix of an Arbitrary Subset of Random Vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24766","kind":"arxiv","version":1},"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":"sha256:34a9e0418d2de3c67dce3586052ba86c866d4f74608e622dc41d456aa76143f9","target":"record","created_at":"2026-06-24T01:15:41Z","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":"f2eb53866dddacf634a00218069400fb982cc48f79df333944a12fd7d29cc217","cross_cats_sorted":["math.OC","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2026-06-23T16:26:55Z","title_canon_sha256":"e7bef1a1d04aba29f9ab62fbc8110dc6902a31a25f8c90cc3cc7257689e86170"},"schema_version":"1.0","source":{"id":"2606.24766","kind":"arxiv","version":1}},"canonical_sha256":"aa7f43c732ef4e32d0ad1a7a29a68dccf3f14ec414cdf2970c8b324d971739e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa7f43c732ef4e32d0ad1a7a29a68dccf3f14ec414cdf2970c8b324d971739e8","first_computed_at":"2026-06-24T01:15:41.661037Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:41.661037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PLQy3CN7hEpVKLozaeZ32BHo/FgTkh/P0IhAtn1B1z0xa6LAOd8DzoxwEwm+x30kCpojx3LyHP0OFCsWtzZxDg==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:41.661459Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34a9e0418d2de3c67dce3586052ba86c866d4f74608e622dc41d456aa76143f9","sha256:b27e9ce8232351ec5b44d80dfaf18ed935f63bfad9413fa44077844344876162"],"state_sha256":"9a451cfeb7a58dd27887bc98f0702e2957d0de4aa6a27444e7efb2f8262c8c0a"}