{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RIHU2YBZW47MMFRCORCQ6JEGFG","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":"bb8d44b03d9d5dce85ca1826bf1ebe4a40a27461ebbd25cc7177fa141e60b37d","cross_cats_sorted":["cs.DS","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-05T18:44:27Z","title_canon_sha256":"0d2ca23f12cdae9ba78e8fdc26a8b77455414720123a34f3ece6857fbf1ef452"},"schema_version":"1.0","source":{"id":"2601.02347","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.02347","created_at":"2026-06-23T03:13:53Z"},{"alias_kind":"arxiv_version","alias_value":"2601.02347v3","created_at":"2026-06-23T03:13:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.02347","created_at":"2026-06-23T03:13:53Z"},{"alias_kind":"pith_short_12","alias_value":"RIHU2YBZW47M","created_at":"2026-06-23T03:13:53Z"},{"alias_kind":"pith_short_16","alias_value":"RIHU2YBZW47MMFRC","created_at":"2026-06-23T03:13:53Z"},{"alias_kind":"pith_short_8","alias_value":"RIHU2YBZ","created_at":"2026-06-23T03:13:53Z"}],"graph_snapshots":[{"event_id":"sha256:5c59c6735a75f065fbdf57aaa74d854469d1678c63eed36e82ee0f5b025468fa","target":"graph","created_at":"2026-06-23T03:13:53Z","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/2601.02347/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of computing an $\\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \\in \\mathbb{R}^{m \\times n}$, when the players' strategies are constrained to lie in simple sets. We provide algorithms which solve this problem in $\\tilde{O}(\\epsilon^{-2/3})$ matrix-vector multiplies (matvecs) in two well-studied cases: $\\ell_1$-$\\ell_1$ (or zero-sum) games, where the players' strategies are both in the probability simplex, and $\\ell_2$-$\\ell_1$ games (encompassing hard-margin SVMs), where the players' strategies are in the unit Euclidea","authors_text":"Aaron Sidford, Ishani Karmarkar, Liam O'Carroll","cross_cats":["cs.DS","cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-05T18:44:27Z","title":"Solving Matrix Games with Near-Optimal Matvec Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.02347","kind":"arxiv","version":3},"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":"sha256:4fbe4b863db6aa7018a1e916a46b5b37db2a17c8f2ea5f73b5eff3df6de9e790","target":"record","created_at":"2026-06-23T03:13:53Z","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":"bb8d44b03d9d5dce85ca1826bf1ebe4a40a27461ebbd25cc7177fa141e60b37d","cross_cats_sorted":["cs.DS","cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-01-05T18:44:27Z","title_canon_sha256":"0d2ca23f12cdae9ba78e8fdc26a8b77455414720123a34f3ece6857fbf1ef452"},"schema_version":"1.0","source":{"id":"2601.02347","kind":"arxiv","version":3}},"canonical_sha256":"8a0f4d6039b73ec6162274450f248629873e55147147ec917ee31c380e5bd81f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a0f4d6039b73ec6162274450f248629873e55147147ec917ee31c380e5bd81f","first_computed_at":"2026-06-23T03:13:53.072744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:53.072744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XvFfgpU9A7ZoeDBCuP+F+RLpKbFaNAOZA1sq59IzNse2tszlRRd7nxuiZemPU8S+6JHnXl2TwZUb+Cz0gWpkAQ==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:53.073201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.02347","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fbe4b863db6aa7018a1e916a46b5b37db2a17c8f2ea5f73b5eff3df6de9e790","sha256:5c59c6735a75f065fbdf57aaa74d854469d1678c63eed36e82ee0f5b025468fa"],"state_sha256":"767b58cb0c234ab83bcc7e67dcdfd00c89bff4d732b8cc8c9b8a94109376ded7"}