{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:AD4NWPMTY6NPYVO4BSJBBFZJNV","short_pith_number":"pith:AD4NWPMT","schema_version":"1.0","canonical_sha256":"00f8db3d93c79afc55dc0c921097296d44845d8cba3397b3bd50364c0fef6e27","source":{"kind":"arxiv","id":"2607.14460","version":1},"attestation_state":"computed","paper":{"title":"Precise sample covariance spectral norm error -- an RDT view","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Mihailo Stojnic","submitted_at":"2026-07-16T01:16:31Z","abstract_excerpt":"We study the sample covariance error of centered Gaussians. A remarkable breakthrough [66] established the correct error scaling order and explicitly revealed the critical role of both the effective rank and the true covariance spectrum.\n  In this work, we move beyond scaling characterizations and determine the precise limiting value of the error's spectral norm. To do so, we develop a generic framework based on Random Duality Theory (RDT). Within this framework, we first determine closed-form, explicit RDT-based upper bounds. We then establish complementary lower bounds by introducing a novel"},"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":"2607.14460","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2026-07-16T01:16:31Z","cross_cats_sorted":["cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"title_canon_sha256":"b1aaae00e9510c7cb3d40841d186403e2927bc67fb1167f347832bee54fe9b86","abstract_canon_sha256":"0524bcdbfa0431d3b633600f960cd87320b4f36577ded7a5aee3bf4702877ebf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T00:21:13.577434Z","signature_b64":"4IuNO7AcaSbvZ3X+rBjrDYL3KD1jnVVjY3V3bc1vMHljnTJr5CYAZVCy+YmgjMCXC0gr5FPKhh2V6/NDl9gTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00f8db3d93c79afc55dc0c921097296d44845d8cba3397b3bd50364c0fef6e27","last_reissued_at":"2026-07-17T00:21:13.576499Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T00:21:13.576499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Precise sample covariance spectral norm error -- an RDT view","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT","math.PR","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Mihailo Stojnic","submitted_at":"2026-07-16T01:16:31Z","abstract_excerpt":"We study the sample covariance error of centered Gaussians. A remarkable breakthrough [66] established the correct error scaling order and explicitly revealed the critical role of both the effective rank and the true covariance spectrum.\n  In this work, we move beyond scaling characterizations and determine the precise limiting value of the error's spectral norm. To do so, we develop a generic framework based on Random Duality Theory (RDT). Within this framework, we first determine closed-form, explicit RDT-based upper bounds. We then establish complementary lower bounds by introducing a novel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14460","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.14460/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.14460","created_at":"2026-07-17T00:21:13.576971+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.14460v1","created_at":"2026-07-17T00:21:13.576971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14460","created_at":"2026-07-17T00:21:13.576971+00:00"},{"alias_kind":"pith_short_12","alias_value":"AD4NWPMTY6NP","created_at":"2026-07-17T00:21:13.576971+00:00"},{"alias_kind":"pith_short_16","alias_value":"AD4NWPMTY6NPYVO4","created_at":"2026-07-17T00:21:13.576971+00:00"},{"alias_kind":"pith_short_8","alias_value":"AD4NWPMT","created_at":"2026-07-17T00:21:13.576971+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/AD4NWPMTY6NPYVO4BSJBBFZJNV","json":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV.json","graph_json":"https://pith.science/api/pith-number/AD4NWPMTY6NPYVO4BSJBBFZJNV/graph.json","events_json":"https://pith.science/api/pith-number/AD4NWPMTY6NPYVO4BSJBBFZJNV/events.json","paper":"https://pith.science/paper/AD4NWPMT"},"agent_actions":{"view_html":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV","download_json":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV.json","view_paper":"https://pith.science/paper/AD4NWPMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.14460&json=true","fetch_graph":"https://pith.science/api/pith-number/AD4NWPMTY6NPYVO4BSJBBFZJNV/graph.json","fetch_events":"https://pith.science/api/pith-number/AD4NWPMTY6NPYVO4BSJBBFZJNV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV/action/storage_attestation","attest_author":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV/action/author_attestation","sign_citation":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV/action/citation_signature","submit_replication":"https://pith.science/pith/AD4NWPMTY6NPYVO4BSJBBFZJNV/action/replication_record"}},"created_at":"2026-07-17T00:21:13.576971+00:00","updated_at":"2026-07-17T00:21:13.576971+00:00"}