{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6YDXVOSEJOWDABZXULRSSULQME","short_pith_number":"pith:6YDXVOSE","schema_version":"1.0","canonical_sha256":"f6077aba444bac300737a2e3295170613279b2868bedb1cf21253c99e65f0b83","source":{"kind":"arxiv","id":"2606.29186","version":1},"attestation_state":"computed","paper":{"title":"Computing Lewis weights to high precision using local relative smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Chenyi Zhang, Sander Gribling","submitted_at":"2026-06-28T04:15:55Z","abstract_excerpt":"We provide algorithms that compute $\\epsilon$-estimates of the $\\ell_p$-Lewis weights of a matrix $A \\in \\mathbb{R}^{m \\times n}$ for $p \\geq 4$ using $O(p^2 \\log(m/\\epsilon))$ rounds of leverage score computation, where $\\ell_p$-Lewis weights and leverage scores are both standard measures of row importance. This improves upon the state-of-the-art round complexity of $O(p^3 \\log(m/\\epsilon))$ due to Fazel, Lee, Padmanabha, and Sidford (2022). We obtain our results by carefully applying a local variant of relatively smooth gradient descent to primal and dual forms of the $\\ell_p$-Lewis weight o"},"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":"2606.29186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-28T04:15:55Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"ab44bb10a24e791f961b697ccef8b108238ee31601632c83bc02be81be6ecf1e","abstract_canon_sha256":"a1b7eac7dd6df003f4afefc0ef02af7bb980805910d67b24dbb3747f20718e31"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T01:17:56.299198Z","signature_b64":"16E2PDpxkvGVPrhnY5tg+gOMDNdf1AcFrrgnMiV2xkHUTvRwuvSZfHa9aFItGZQxg3e37pKI3oTyXzM1ieP9Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6077aba444bac300737a2e3295170613279b2868bedb1cf21253c99e65f0b83","last_reissued_at":"2026-06-30T01:17:56.298086Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T01:17:56.298086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing Lewis weights to high precision using local relative smoothness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Aaron Sidford, Chenyi Zhang, Sander Gribling","submitted_at":"2026-06-28T04:15:55Z","abstract_excerpt":"We provide algorithms that compute $\\epsilon$-estimates of the $\\ell_p$-Lewis weights of a matrix $A \\in \\mathbb{R}^{m \\times n}$ for $p \\geq 4$ using $O(p^2 \\log(m/\\epsilon))$ rounds of leverage score computation, where $\\ell_p$-Lewis weights and leverage scores are both standard measures of row importance. This improves upon the state-of-the-art round complexity of $O(p^3 \\log(m/\\epsilon))$ due to Fazel, Lee, Padmanabha, and Sidford (2022). We obtain our results by carefully applying a local variant of relatively smooth gradient descent to primal and dual forms of the $\\ell_p$-Lewis weight o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29186","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/2606.29186/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":"2606.29186","created_at":"2026-06-30T01:17:56.298224+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29186v1","created_at":"2026-06-30T01:17:56.298224+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29186","created_at":"2026-06-30T01:17:56.298224+00:00"},{"alias_kind":"pith_short_12","alias_value":"6YDXVOSEJOWD","created_at":"2026-06-30T01:17:56.298224+00:00"},{"alias_kind":"pith_short_16","alias_value":"6YDXVOSEJOWDABZX","created_at":"2026-06-30T01:17:56.298224+00:00"},{"alias_kind":"pith_short_8","alias_value":"6YDXVOSE","created_at":"2026-06-30T01:17:56.298224+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/6YDXVOSEJOWDABZXULRSSULQME","json":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME.json","graph_json":"https://pith.science/api/pith-number/6YDXVOSEJOWDABZXULRSSULQME/graph.json","events_json":"https://pith.science/api/pith-number/6YDXVOSEJOWDABZXULRSSULQME/events.json","paper":"https://pith.science/paper/6YDXVOSE"},"agent_actions":{"view_html":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME","download_json":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME.json","view_paper":"https://pith.science/paper/6YDXVOSE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29186&json=true","fetch_graph":"https://pith.science/api/pith-number/6YDXVOSEJOWDABZXULRSSULQME/graph.json","fetch_events":"https://pith.science/api/pith-number/6YDXVOSEJOWDABZXULRSSULQME/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME/action/storage_attestation","attest_author":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME/action/author_attestation","sign_citation":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME/action/citation_signature","submit_replication":"https://pith.science/pith/6YDXVOSEJOWDABZXULRSSULQME/action/replication_record"}},"created_at":"2026-06-30T01:17:56.298224+00:00","updated_at":"2026-06-30T01:17:56.298224+00:00"}