{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ES26W4PSKKOUJZWOMS6J2IZAQA","short_pith_number":"pith:ES26W4PS","canonical_record":{"source":{"id":"1906.03553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-06-09T03:01:43Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"efe8f1f0fae7125a281e47e24395d29999b357562d0285b9df70ef9bdc541d22","abstract_canon_sha256":"356205a9695831b1dfb86606ec13ee71ffdc5b02f2817053bddc76c9a1f5ba6f"},"schema_version":"1.0"},"canonical_sha256":"24b5eb71f2529d44e6ce64bc9d2320801867363c1c667bd603dc3d033fd62d12","source":{"kind":"arxiv","id":"1906.03553","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03553","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03553v1","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03553","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"ES26W4PSKKOU","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ES26W4PSKKOUJZWO","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ES26W4PS","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ES26W4PSKKOUJZWOMS6J2IZAQA","target":"record","payload":{"canonical_record":{"source":{"id":"1906.03553","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-06-09T03:01:43Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"efe8f1f0fae7125a281e47e24395d29999b357562d0285b9df70ef9bdc541d22","abstract_canon_sha256":"356205a9695831b1dfb86606ec13ee71ffdc5b02f2817053bddc76c9a1f5ba6f"},"schema_version":"1.0"},"canonical_sha256":"24b5eb71f2529d44e6ce64bc9d2320801867363c1c667bd603dc3d033fd62d12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:48.120408Z","signature_b64":"pFelfz0cWkLh+NGTrrZnW4vnCEjzf1vfm0iCBLlvnrwplcHoGNFUczoJcCHRgeCGWL4KkuONiOgukRRPH+YHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24b5eb71f2529d44e6ce64bc9d2320801867363c1c667bd603dc3d033fd62d12","last_reissued_at":"2026-05-17T23:43:48.119715Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:48.119715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.03553","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":"2026-05-17T23:43:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyTnd7tzU7pYituy5hZHBABenB6zpUtmqpbukgKorVYcwqj4Droe8kT+F8lFoaSyQKXZydEoZvFJoYiXDGL0DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:15:26.588744Z"},"content_sha256":"5c3cf4285b0ac2fcd650baca038cf89f64c54e6d7c4c9b2df4229eb273ee2af1","schema_version":"1.0","event_id":"sha256:5c3cf4285b0ac2fcd650baca038cf89f64c54e6d7c4c9b2df4229eb273ee2af1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ES26W4PSKKOUJZWOMS6J2IZAQA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toward Solving 2-TBSG Efficiently","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.GT","authors_text":"Yinyu Ye, Zaiwen Wen, Zeyu Jia","submitted_at":"2019-06-09T03:01:43Z","abstract_excerpt":"2-TBSG is a two-player game model which aims to find Nash equilibriums and is widely utilized in reinforced learning and AI. Inspired by the fact that the simplex method for solving the deterministic discounted Markov decision processes (MDPs) is strongly polynomial independent of the discounted factor, we are trying to answer an open problem whether there is a similar algorithm for 2-TBSG. We develop a simplex strategy iteration where one player updates its strategy with a simplex step while the other player finds an optimal counterstrategy in turn, and a modified simplex strategy iteration. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03553","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":"2026-05-17T23:43:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0eod/Z79tYCTr8qXmJOUWgcX6vt9PSIFf7mo2KeXk+ofzR6ogq8O53ZKTFbKAUEaAP8QV5q3UP4Ij49bI6STCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:15:26.589422Z"},"content_sha256":"542226c93df62381ebb282fbcb97d386cc2b9473587599f0758ef1aa7a876aa6","schema_version":"1.0","event_id":"sha256:542226c93df62381ebb282fbcb97d386cc2b9473587599f0758ef1aa7a876aa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ES26W4PSKKOUJZWOMS6J2IZAQA/bundle.json","state_url":"https://pith.science/pith/ES26W4PSKKOUJZWOMS6J2IZAQA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ES26W4PSKKOUJZWOMS6J2IZAQA/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":"2026-05-31T02:15:26Z","links":{"resolver":"https://pith.science/pith/ES26W4PSKKOUJZWOMS6J2IZAQA","bundle":"https://pith.science/pith/ES26W4PSKKOUJZWOMS6J2IZAQA/bundle.json","state":"https://pith.science/pith/ES26W4PSKKOUJZWOMS6J2IZAQA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ES26W4PSKKOUJZWOMS6J2IZAQA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ES26W4PSKKOUJZWOMS6J2IZAQA","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":"356205a9695831b1dfb86606ec13ee71ffdc5b02f2817053bddc76c9a1f5ba6f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-06-09T03:01:43Z","title_canon_sha256":"efe8f1f0fae7125a281e47e24395d29999b357562d0285b9df70ef9bdc541d22"},"schema_version":"1.0","source":{"id":"1906.03553","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.03553","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"arxiv_version","alias_value":"1906.03553v1","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.03553","created_at":"2026-05-17T23:43:48Z"},{"alias_kind":"pith_short_12","alias_value":"ES26W4PSKKOU","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ES26W4PSKKOUJZWO","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ES26W4PS","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:542226c93df62381ebb282fbcb97d386cc2b9473587599f0758ef1aa7a876aa6","target":"graph","created_at":"2026-05-17T23:43:48Z","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":"2-TBSG is a two-player game model which aims to find Nash equilibriums and is widely utilized in reinforced learning and AI. Inspired by the fact that the simplex method for solving the deterministic discounted Markov decision processes (MDPs) is strongly polynomial independent of the discounted factor, we are trying to answer an open problem whether there is a similar algorithm for 2-TBSG. We develop a simplex strategy iteration where one player updates its strategy with a simplex step while the other player finds an optimal counterstrategy in turn, and a modified simplex strategy iteration. ","authors_text":"Yinyu Ye, Zaiwen Wen, Zeyu Jia","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-06-09T03:01:43Z","title":"Toward Solving 2-TBSG Efficiently"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.03553","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":"sha256:5c3cf4285b0ac2fcd650baca038cf89f64c54e6d7c4c9b2df4229eb273ee2af1","target":"record","created_at":"2026-05-17T23:43:48Z","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":"356205a9695831b1dfb86606ec13ee71ffdc5b02f2817053bddc76c9a1f5ba6f","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2019-06-09T03:01:43Z","title_canon_sha256":"efe8f1f0fae7125a281e47e24395d29999b357562d0285b9df70ef9bdc541d22"},"schema_version":"1.0","source":{"id":"1906.03553","kind":"arxiv","version":1}},"canonical_sha256":"24b5eb71f2529d44e6ce64bc9d2320801867363c1c667bd603dc3d033fd62d12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24b5eb71f2529d44e6ce64bc9d2320801867363c1c667bd603dc3d033fd62d12","first_computed_at":"2026-05-17T23:43:48.119715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:48.119715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pFelfz0cWkLh+NGTrrZnW4vnCEjzf1vfm0iCBLlvnrwplcHoGNFUczoJcCHRgeCGWL4KkuONiOgukRRPH+YHCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:48.120408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.03553","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c3cf4285b0ac2fcd650baca038cf89f64c54e6d7c4c9b2df4229eb273ee2af1","sha256:542226c93df62381ebb282fbcb97d386cc2b9473587599f0758ef1aa7a876aa6"],"state_sha256":"8ba2d45cd8cc501b1d587c916e9e859e6e6e4ff78949cf115ee152749a3a8412"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jASiGYgc39eOQsR8g/Y1fiwLYtzOcb0UEwSuAFu1ynytzdvg/jcBM1PqXWQW+oxx2y1pRR/1KHlKQBqC9Ra9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:15:26.592793Z","bundle_sha256":"213cf2f8eca5f6ede6417d8b782cde708c26e277227cbaac64c7914579d724b5"}}