{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:H3HJWE3ECZVMIFCDZ25TAG4P7H","short_pith_number":"pith:H3HJWE3E","schema_version":"1.0","canonical_sha256":"3ece9b1364166ac41443cebb301b8ff9e656c9981522f76a196354abfe1f2797","source":{"kind":"arxiv","id":"2506.10748","version":1},"attestation_state":"computed","paper":{"title":"Computational Complexity of Statistics: New Insights from Low-Degree Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander S. Wein","submitted_at":"2025-06-12T14:35:26Z","abstract_excerpt":"This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a statistical task by the minimum degree that a polynomial function must have in order to solve it. The main goals of this survey are to (1) describe the types of problems where the low-degree framework can be applied, encompassing questions of detection (hypothesis testing), recovery (estimation), and more; (2) discuss some philosophical questions surrounding 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":"2506.10748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-06-12T14:35:26Z","cross_cats_sorted":["cs.CC","stat.ML","stat.TH"],"title_canon_sha256":"6f772ed409c0b178f565640c8f6ab36bb5d81199ef40ab33f64c42d84dbe8783","abstract_canon_sha256":"ef3f871637f3eb9a2b8c2bcf702b681a84006c37b88cbdff48742bbfda970714"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:29.792924Z","signature_b64":"WtD7NkT8P7jdBAP0z3PSwqII8z3h9aqI1+KWShJE1aZahK509rtLnFAwR6yHL7hTdq+Xrl1iKJjHtiN+QN+ZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ece9b1364166ac41443cebb301b8ff9e656c9981522f76a196354abfe1f2797","last_reissued_at":"2026-07-05T11:20:29.792390Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:29.792390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computational Complexity of Statistics: New Insights from Low-Degree Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Alexander S. Wein","submitted_at":"2025-06-12T14:35:26Z","abstract_excerpt":"This is a survey on the use of low-degree polynomials to predict and explain the apparent statistical-computational tradeoffs in a variety of average-case computational problems. In a nutshell, this framework measures the complexity of a statistical task by the minimum degree that a polynomial function must have in order to solve it. The main goals of this survey are to (1) describe the types of problems where the low-degree framework can be applied, encompassing questions of detection (hypothesis testing), recovery (estimation), and more; (2) discuss some philosophical questions surrounding t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.10748","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/2506.10748/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":"2506.10748","created_at":"2026-07-05T11:20:29.792456+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.10748v1","created_at":"2026-07-05T11:20:29.792456+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.10748","created_at":"2026-07-05T11:20:29.792456+00:00"},{"alias_kind":"pith_short_12","alias_value":"H3HJWE3ECZVM","created_at":"2026-07-05T11:20:29.792456+00:00"},{"alias_kind":"pith_short_16","alias_value":"H3HJWE3ECZVMIFCD","created_at":"2026-07-05T11:20:29.792456+00:00"},{"alias_kind":"pith_short_8","alias_value":"H3HJWE3E","created_at":"2026-07-05T11:20:29.792456+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":11,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08538","citing_title":"High-Dimensional Procrustes Matching via Tree Counts","ref_index":3,"is_internal_anchor":true},{"citing_arxiv_id":"2606.11149","citing_title":"Efficiently Learning Drifting Halfspaces with Massart Noise","ref_index":42,"is_internal_anchor":false},{"citing_arxiv_id":"2606.05266","citing_title":"Sharp Low-Degree Thresholds for Planted-vs-Planted Testing","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.30113","citing_title":"Low-degree estimation thresholds in planted hypergraphs and tensor PCA","ref_index":19,"is_internal_anchor":false},{"citing_arxiv_id":"2502.14407","citing_title":"Sharp Phase Transitions in Estimation with Low-Degree Polynomials","ref_index":30,"is_internal_anchor":false},{"citing_arxiv_id":"2605.21360","citing_title":"Linear Functional Testing with General Loadings in Sparse Regression: Separation Rates and Computational Barriers","ref_index":59,"is_internal_anchor":false},{"citing_arxiv_id":"2605.18042","citing_title":"On efficient robust regression with subquadratic samples","ref_index":40,"is_internal_anchor":false},{"citing_arxiv_id":"2603.26029","citing_title":"Detection Is Harder Than Estimation in Certain Regimes: Inference for Moment and Cumulant Tensors","ref_index":64,"is_internal_anchor":false},{"citing_arxiv_id":"2605.05618","citing_title":"Algorithmic Phase Transition for Large Independent Sets in Dense Hypergraphs","ref_index":107,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06109","citing_title":"Learning $\\mathsf{AC}^0$ Under Graphical Models","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"2604.17410","citing_title":"Algorithmic Contiguity from Low-Degree Heuristic II: Predicting Detection-Recovery Gaps","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H","json":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H.json","graph_json":"https://pith.science/api/pith-number/H3HJWE3ECZVMIFCDZ25TAG4P7H/graph.json","events_json":"https://pith.science/api/pith-number/H3HJWE3ECZVMIFCDZ25TAG4P7H/events.json","paper":"https://pith.science/paper/H3HJWE3E"},"agent_actions":{"view_html":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H","download_json":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H.json","view_paper":"https://pith.science/paper/H3HJWE3E","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.10748&json=true","fetch_graph":"https://pith.science/api/pith-number/H3HJWE3ECZVMIFCDZ25TAG4P7H/graph.json","fetch_events":"https://pith.science/api/pith-number/H3HJWE3ECZVMIFCDZ25TAG4P7H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H/action/storage_attestation","attest_author":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H/action/author_attestation","sign_citation":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H/action/citation_signature","submit_replication":"https://pith.science/pith/H3HJWE3ECZVMIFCDZ25TAG4P7H/action/replication_record"}},"created_at":"2026-07-05T11:20:29.792456+00:00","updated_at":"2026-07-05T11:20:29.792456+00:00"}