{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:KLFRJ6YVE7Q7US5ZRYVGBBS6LF","short_pith_number":"pith:KLFRJ6YV","canonical_record":{"source":{"id":"cs/0205035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.CC","submitted_at":"2002-05-18T03:41:40Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dec117448d5cbc0e3cd99730f3243659541d79b712d08e814a6a923a589bbf9e","abstract_canon_sha256":"e7a1a048fa9788dccecc343ba2d40beaa389ee6ef77456530ea81eb395312370"},"schema_version":"1.0"},"canonical_sha256":"52cb14fb1527e1fa4bb98e2a60865e597a1b26b35abb8f4bb73f90ea97c87e89","source":{"kind":"arxiv","id":"cs/0205035","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0205035","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0205035v1","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0205035","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"KLFRJ6YVE7Q7","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"KLFRJ6YVE7Q7US5Z","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"KLFRJ6YV","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:KLFRJ6YVE7Q7US5ZRYVGBBS6LF","target":"record","payload":{"canonical_record":{"source":{"id":"cs/0205035","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cs.CC","submitted_at":"2002-05-18T03:41:40Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dec117448d5cbc0e3cd99730f3243659541d79b712d08e814a6a923a589bbf9e","abstract_canon_sha256":"e7a1a048fa9788dccecc343ba2d40beaa389ee6ef77456530ea81eb395312370"},"schema_version":"1.0"},"canonical_sha256":"52cb14fb1527e1fa4bb98e2a60865e597a1b26b35abb8f4bb73f90ea97c87e89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:53.981812Z","signature_b64":"XhqhKp4kfdxIQjYuy9XMlyBwV0NOMTM/cy7GYeLlx3j13WkW/ahQ9Ct67GJchxNom9d5eMlTIug9Z3DYSu8WAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52cb14fb1527e1fa4bb98e2a60865e597a1b26b35abb8f4bb73f90ea97c87e89","last_reissued_at":"2026-05-18T01:59:53.981238Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:53.981238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cs/0205035","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6+dwCqRMZw9sokEbT+GpY8E2ysDUXDOlN6J7Lcb7WTSAmVEIK7MUnK1mY/I6jIgvXBKPIjc+XEsLddYCMZsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:08:18.302652Z"},"content_sha256":"cf6af4174754bbb13f94237431910883ef1f33454384719b8f4915e767650887","schema_version":"1.0","event_id":"sha256:cf6af4174754bbb13f94237431910883ef1f33454384719b8f4915e767650887"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:KLFRJ6YVE7Q7US5ZRYVGBBS6LF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple Strategies for Large Zero-Sum Games with Applications to Complexity Theory","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Neal E. Young, Richard Lipton","submitted_at":"2002-05-18T03:41:40Z","abstract_excerpt":"Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from a multiset of pure strategies of size logarithmic in the number of pure strategies available to the opponent.\n  For exponentially large games, for which even representing an optimal mixed strategy can require exponential space, it follows that there are near-optimal, linear-size strategies. These strategies are easy to play and serve as small witnesses to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0205035","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RoSly648TbiLap2/CtMg/fpOBKLq/4gTofQ1uFx+o24Kbu2+zGy87bJAUqyjWw0rlme9OUxpBEfgAcTIxaCjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:08:18.303278Z"},"content_sha256":"8277a0a4dca1bfcfbb8c90299173bf1f9c9fb630f472afe0fbdda887f9b0e50b","schema_version":"1.0","event_id":"sha256:8277a0a4dca1bfcfbb8c90299173bf1f9c9fb630f472afe0fbdda887f9b0e50b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF/bundle.json","state_url":"https://pith.science/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T17:08:18Z","links":{"resolver":"https://pith.science/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF","bundle":"https://pith.science/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF/bundle.json","state":"https://pith.science/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLFRJ6YVE7Q7US5ZRYVGBBS6LF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:KLFRJ6YVE7Q7US5ZRYVGBBS6LF","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":"e7a1a048fa9788dccecc343ba2d40beaa389ee6ef77456530ea81eb395312370","cross_cats_sorted":["cs.DM"],"license":"","primary_cat":"cs.CC","submitted_at":"2002-05-18T03:41:40Z","title_canon_sha256":"dec117448d5cbc0e3cd99730f3243659541d79b712d08e814a6a923a589bbf9e"},"schema_version":"1.0","source":{"id":"cs/0205035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0205035","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0205035v1","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0205035","created_at":"2026-05-18T01:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"KLFRJ6YVE7Q7","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"KLFRJ6YVE7Q7US5Z","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"KLFRJ6YV","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:8277a0a4dca1bfcfbb8c90299173bf1f9c9fb630f472afe0fbdda887f9b0e50b","target":"graph","created_at":"2026-05-18T01:59:53Z","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"},"paper":{"abstract_excerpt":"Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from a multiset of pure strategies of size logarithmic in the number of pure strategies available to the opponent.\n  For exponentially large games, for which even representing an optimal mixed strategy can require exponential space, it follows that there are near-optimal, linear-size strategies. These strategies are easy to play and serve as small witnesses to t","authors_text":"Neal E. Young, Richard Lipton","cross_cats":["cs.DM"],"headline":"","license":"","primary_cat":"cs.CC","submitted_at":"2002-05-18T03:41:40Z","title":"Simple Strategies for Large Zero-Sum Games with Applications to Complexity Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0205035","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:cf6af4174754bbb13f94237431910883ef1f33454384719b8f4915e767650887","target":"record","created_at":"2026-05-18T01:59:53Z","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":"e7a1a048fa9788dccecc343ba2d40beaa389ee6ef77456530ea81eb395312370","cross_cats_sorted":["cs.DM"],"license":"","primary_cat":"cs.CC","submitted_at":"2002-05-18T03:41:40Z","title_canon_sha256":"dec117448d5cbc0e3cd99730f3243659541d79b712d08e814a6a923a589bbf9e"},"schema_version":"1.0","source":{"id":"cs/0205035","kind":"arxiv","version":1}},"canonical_sha256":"52cb14fb1527e1fa4bb98e2a60865e597a1b26b35abb8f4bb73f90ea97c87e89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52cb14fb1527e1fa4bb98e2a60865e597a1b26b35abb8f4bb73f90ea97c87e89","first_computed_at":"2026-05-18T01:59:53.981238Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:53.981238Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XhqhKp4kfdxIQjYuy9XMlyBwV0NOMTM/cy7GYeLlx3j13WkW/ahQ9Ct67GJchxNom9d5eMlTIug9Z3DYSu8WAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:53.981812Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0205035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf6af4174754bbb13f94237431910883ef1f33454384719b8f4915e767650887","sha256:8277a0a4dca1bfcfbb8c90299173bf1f9c9fb630f472afe0fbdda887f9b0e50b"],"state_sha256":"04758638790759a2db77699ca58ecefce86fc9ac323b857582320d6321c02b6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aypndR8j60yzkuzknRr74Ky1xUO3yDHx/NBrGS7uw5g1qDwIeUi23wQ/iqIgV43aLb3sTH0pqCYN/5I97HqSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:08:18.306197Z","bundle_sha256":"656d355df43063a8dbcc68c4cb2235339be11e5446387ea2450e6501519d729e"}}