{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:S46RSENO2IOVYQLTOPR7V4V25G","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"70c44a2cc5fe6f385f748f68c57737eb791108133ce0510cba3446733b7df0bf","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-11-02T19:10:19Z","title_canon_sha256":"2378e651f370c619ddd14f15cc8d49199303a080fbc705590bf91eaaa9a8a934"},"schema_version":"1.0","source":{"id":"2111.01848","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.01848","created_at":"2026-07-05T03:30:42Z"},{"alias_kind":"arxiv_version","alias_value":"2111.01848v2","created_at":"2026-07-05T03:30:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.01848","created_at":"2026-07-05T03:30:42Z"},{"alias_kind":"pith_short_12","alias_value":"S46RSENO2IOV","created_at":"2026-07-05T03:30:42Z"},{"alias_kind":"pith_short_16","alias_value":"S46RSENO2IOVYQLT","created_at":"2026-07-05T03:30:42Z"},{"alias_kind":"pith_short_8","alias_value":"S46RSENO","created_at":"2026-07-05T03:30:42Z"}],"graph_snapshots":[{"event_id":"sha256:40ed404d8316a9a27cb2114e1287f3de22f5ff01ccb74a29698489bcdf163052","target":"graph","created_at":"2026-07-05T03:30:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.01848/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we obtain improved iteration complexities for solving $\\ell_p$ regression. We provide methods which given any full-rank $\\mathbf{A} \\in \\mathbb{R}^{n \\times d}$ with $n \\geq d$, $b \\in \\mathbb{R}^n$, and $p \\geq 2$ solve $\\min_{x \\in \\mathbb{R}^d} \\left\\|\\mathbf{A} x - b\\right\\|_p$ to high precision in time dominated by that of solving $\\widetilde{O}_p(d^{\\frac{p-2}{3p-2}})$ linear systems in $\\mathbf{A}^\\top \\mathbf{D} \\mathbf{A}$ for positive diagonal matrices $\\mathbf{D}$. This improves upon the previous best iteration complexity of $\\widetilde{O}_p(n^{\\frac{p-2}{3p-2}})$ (Adi","authors_text":"Aaron Sidford, Arun Jambulapati, Yang P. Liu","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-11-02T19:10:19Z","title":"Improved Iteration Complexities for Overconstrained $p$-Norm Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.01848","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b56cb0af627f75bd8de486043ee54e719980d1352b5decba62173ae72131e3c4","target":"record","created_at":"2026-07-05T03:30:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"70c44a2cc5fe6f385f748f68c57737eb791108133ce0510cba3446733b7df0bf","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-11-02T19:10:19Z","title_canon_sha256":"2378e651f370c619ddd14f15cc8d49199303a080fbc705590bf91eaaa9a8a934"},"schema_version":"1.0","source":{"id":"2111.01848","kind":"arxiv","version":2}},"canonical_sha256":"973d1911aed21d5c417373e3faf2bae9b2216b27389b4043a42a12ec40e3201f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"973d1911aed21d5c417373e3faf2bae9b2216b27389b4043a42a12ec40e3201f","first_computed_at":"2026-07-05T03:30:42.472034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:30:42.472034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5yeE8HwG7LihT2KXzBfC55n0P++gSDEmx2+J8R4dphoP84zqeoaQO0Cb5LEFtLvNQktt4desrttqVCgPk0JiCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:30:42.472517Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.01848","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b56cb0af627f75bd8de486043ee54e719980d1352b5decba62173ae72131e3c4","sha256:40ed404d8316a9a27cb2114e1287f3de22f5ff01ccb74a29698489bcdf163052"],"state_sha256":"3fed2938f18f0339e41c003911d51f4c11701ed42188527f5febe2c55316a797"}