{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SS3SFKQ4IJKC3476OP427LYYPK","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":"ba7b66034fe952996e36a575b74e37f22fd8a290858ac7fb978e4f6fa33cef3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-07-22T13:58:04Z","title_canon_sha256":"91c3df1994f19a5dbe2d33276cb9121db363cbe875666f9a0d7ab8161de81f37"},"schema_version":"1.0","source":{"id":"1007.3886","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.3886","created_at":"2026-05-18T02:06:11Z"},{"alias_kind":"arxiv_version","alias_value":"1007.3886v1","created_at":"2026-05-18T02:06:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.3886","created_at":"2026-05-18T02:06:11Z"},{"alias_kind":"pith_short_12","alias_value":"SS3SFKQ4IJKC","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SS3SFKQ4IJKC3476","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SS3SFKQ4","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:3cb81dc7d9b936c22c375ab0ef308dd8f08e623019ecd1ef334eb75eb37a4eed","target":"graph","created_at":"2026-05-18T02:06:11Z","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"},"paper":{"abstract_excerpt":"We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no u","authors_text":"Inbal Talgam-Cohen, Uriel Feige","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-07-22T13:58:04Z","title":"A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3886","kind":"arxiv","version":1},"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:f3296654717af266b66a2e3360d33705b84e79fe1df60996a57f682418f49c2d","target":"record","created_at":"2026-05-18T02:06:11Z","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":"ba7b66034fe952996e36a575b74e37f22fd8a290858ac7fb978e4f6fa33cef3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2010-07-22T13:58:04Z","title_canon_sha256":"91c3df1994f19a5dbe2d33276cb9121db363cbe875666f9a0d7ab8161de81f37"},"schema_version":"1.0","source":{"id":"1007.3886","kind":"arxiv","version":1}},"canonical_sha256":"94b722aa1c42542df3fe73f9afaf187ab50f184f0736ec97136b297becd243c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94b722aa1c42542df3fe73f9afaf187ab50f184f0736ec97136b297becd243c7","first_computed_at":"2026-05-18T02:06:11.587878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:11.587878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zgun7+2apcuI5ORjOO64Xx4Ae13z5oRFZwBEtQOaxTZlYyW28oVOBA6x4LDqeWy8tpZ9lMrfWiFf4TjHGCqTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:11.588488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.3886","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3296654717af266b66a2e3360d33705b84e79fe1df60996a57f682418f49c2d","sha256:3cb81dc7d9b936c22c375ab0ef308dd8f08e623019ecd1ef334eb75eb37a4eed"],"state_sha256":"e7dd689c3d1f8fb6b6d8ac51552bfb7d3a880ce393678a31707e5ebc523c29ec"}