{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:WHBH7ABB4UHLKCHC3G6GDABEX7","short_pith_number":"pith:WHBH7ABB","schema_version":"1.0","canonical_sha256":"b1c27f8021e50eb508e2d9bc618024bfea181a95b42558920d2707b9e1278fe3","source":{"kind":"arxiv","id":"2412.21203","version":1},"attestation_state":"computed","paper":{"title":"SoS Certificates for Sparse Singular Values and Their Applications: Robust Statistics, Subspace Distortion, and More","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Ankit Pensia, Ilias Diakonikolas, Samuel B. Hopkins, Stefan Tiegel","submitted_at":"2024-12-30T18:59:46Z","abstract_excerpt":"We study $\\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \\times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on the maximum of $\\|M u\\|$, where $u$ is a unit vector with at most $\\eta n$ nonzero entries for a given $\\eta \\in (0,1)$. This basic algorithmic primitive lies at the heart of a wide range of problems across algorithmic statistics and theoretical computer science.\n  Our algorithms certify a bound which is asymptotically smaller than the naive one, given by t"},"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":"2412.21203","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-12-30T18:59:46Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7c2473d7482e65b9734a92f13779ddc709fd2d9a09d59dffa43f1e34b6df263f","abstract_canon_sha256":"35ceb76d60a7d9d672d29125a07897565ecbbbaea86157194674d31b7df15c88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:55:28.781998Z","signature_b64":"8hByYIRynBaBXVm+uZ6ikDrLNr2pCI1lVekQ1g6/dFZh+7yYPHRc9eDRfU0xKAOXx35EvtQovDMe91oSyAD0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1c27f8021e50eb508e2d9bc618024bfea181a95b42558920d2707b9e1278fe3","last_reissued_at":"2026-07-05T09:55:28.781512Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:55:28.781512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SoS Certificates for Sparse Singular Values and Their Applications: Robust Statistics, Subspace Distortion, and More","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.DS","authors_text":"Ankit Pensia, Ilias Diakonikolas, Samuel B. Hopkins, Stefan Tiegel","submitted_at":"2024-12-30T18:59:46Z","abstract_excerpt":"We study $\\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \\times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on the maximum of $\\|M u\\|$, where $u$ is a unit vector with at most $\\eta n$ nonzero entries for a given $\\eta \\in (0,1)$. This basic algorithmic primitive lies at the heart of a wide range of problems across algorithmic statistics and theoretical computer science.\n  Our algorithms certify a bound which is asymptotically smaller than the naive one, given by t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21203","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/2412.21203/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":"2412.21203","created_at":"2026-07-05T09:55:28.781571+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.21203v1","created_at":"2026-07-05T09:55:28.781571+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.21203","created_at":"2026-07-05T09:55:28.781571+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHBH7ABB4UHL","created_at":"2026-07-05T09:55:28.781571+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHBH7ABB4UHLKCHC","created_at":"2026-07-05T09:55:28.781571+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHBH7ABB","created_at":"2026-07-05T09:55:28.781571+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/WHBH7ABB4UHLKCHC3G6GDABEX7","json":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7.json","graph_json":"https://pith.science/api/pith-number/WHBH7ABB4UHLKCHC3G6GDABEX7/graph.json","events_json":"https://pith.science/api/pith-number/WHBH7ABB4UHLKCHC3G6GDABEX7/events.json","paper":"https://pith.science/paper/WHBH7ABB"},"agent_actions":{"view_html":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7","download_json":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7.json","view_paper":"https://pith.science/paper/WHBH7ABB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.21203&json=true","fetch_graph":"https://pith.science/api/pith-number/WHBH7ABB4UHLKCHC3G6GDABEX7/graph.json","fetch_events":"https://pith.science/api/pith-number/WHBH7ABB4UHLKCHC3G6GDABEX7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7/action/storage_attestation","attest_author":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7/action/author_attestation","sign_citation":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7/action/citation_signature","submit_replication":"https://pith.science/pith/WHBH7ABB4UHLKCHC3G6GDABEX7/action/replication_record"}},"created_at":"2026-07-05T09:55:28.781571+00:00","updated_at":"2026-07-05T09:55:28.781571+00:00"}