{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:IJPQSAGHY5ALAUNOO6FMWQ3KVN","short_pith_number":"pith:IJPQSAGH","schema_version":"1.0","canonical_sha256":"425f0900c7c740b051ae778acb436aab7a4bfdb906b61dc1d73c7a6233dce629","source":{"kind":"arxiv","id":"2506.20659","version":1},"attestation_state":"computed","paper":{"title":"A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Joshua Agterberg, Ren\\'e Vidal","submitted_at":"2025-06-25T17:53:52Z","abstract_excerpt":"The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In this work we provide a high-dimensional statistical analysis for symmetric low-rank matrix sensing observed under Gaussian"},"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":"2506.20659","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.ST","submitted_at":"2025-06-25T17:53:52Z","cross_cats_sorted":["math.OC","stat.TH"],"title_canon_sha256":"d2e97ff2300eef39e59b72c9b754232da72f2edfd20ac468157306eef88ba01f","abstract_canon_sha256":"a112b415d065a9861e27b6b5e0c9e09e5753673d050a1cb8c315a9413de4c560"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:27:15.968206Z","signature_b64":"5lHzBtFFpxbDpEYV2j2zBcPSUtrkdmcP3pRZ793jwHbUNUbJwOZA9n5HKHimMzmkoKXNfhrwytO8fsG5GgdlCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"425f0900c7c740b051ae778acb436aab7a4bfdb906b61dc1d73c7a6233dce629","last_reissued_at":"2026-07-05T11:27:15.967664Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:27:15.967664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A High-Dimensional Statistical Theory for Convex and Nonconvex Matrix Sensing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC","stat.TH"],"primary_cat":"math.ST","authors_text":"Joshua Agterberg, Ren\\'e Vidal","submitted_at":"2025-06-25T17:53:52Z","abstract_excerpt":"The problem of matrix sensing, or trace regression, is a problem wherein one wishes to estimate a low-rank matrix from linear measurements perturbed with noise. A number of existing works have studied both convex and nonconvex approaches to this problem, establishing minimax error rates when the number of measurements is sufficiently large relative to the rank and dimension of the low-rank matrix, though a precise comparison of these procedures still remains unexplored. In this work we provide a high-dimensional statistical analysis for symmetric low-rank matrix sensing observed under Gaussian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20659","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/2506.20659/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":"2506.20659","created_at":"2026-07-05T11:27:15.967734+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.20659v1","created_at":"2026-07-05T11:27:15.967734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20659","created_at":"2026-07-05T11:27:15.967734+00:00"},{"alias_kind":"pith_short_12","alias_value":"IJPQSAGHY5AL","created_at":"2026-07-05T11:27:15.967734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IJPQSAGHY5ALAUNO","created_at":"2026-07-05T11:27:15.967734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IJPQSAGH","created_at":"2026-07-05T11:27:15.967734+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/IJPQSAGHY5ALAUNOO6FMWQ3KVN","json":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN.json","graph_json":"https://pith.science/api/pith-number/IJPQSAGHY5ALAUNOO6FMWQ3KVN/graph.json","events_json":"https://pith.science/api/pith-number/IJPQSAGHY5ALAUNOO6FMWQ3KVN/events.json","paper":"https://pith.science/paper/IJPQSAGH"},"agent_actions":{"view_html":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN","download_json":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN.json","view_paper":"https://pith.science/paper/IJPQSAGH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.20659&json=true","fetch_graph":"https://pith.science/api/pith-number/IJPQSAGHY5ALAUNOO6FMWQ3KVN/graph.json","fetch_events":"https://pith.science/api/pith-number/IJPQSAGHY5ALAUNOO6FMWQ3KVN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN/action/storage_attestation","attest_author":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN/action/author_attestation","sign_citation":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN/action/citation_signature","submit_replication":"https://pith.science/pith/IJPQSAGHY5ALAUNOO6FMWQ3KVN/action/replication_record"}},"created_at":"2026-07-05T11:27:15.967734+00:00","updated_at":"2026-07-05T11:27:15.967734+00:00"}