{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EK3JI6AOIC7X3DF4CHORKSEJ5D","short_pith_number":"pith:EK3JI6AO","canonical_record":{"source":{"id":"1703.10211","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-29T19:36:52Z","cross_cats_sorted":[],"title_canon_sha256":"dab4cf0ccb8699b3fd8d9c928c21857be4fb4d92405a5de3356d4f6a26112eb6","abstract_canon_sha256":"c64ab000f46a6ae564530dbcb13b926344f758fc4d0e8fa82d9004a4b386d777"},"schema_version":"1.0"},"canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","source":{"kind":"arxiv","id":"1703.10211","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10211","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10211v8","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10211","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"EK3JI6AOIC7X","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EK3JI6AOIC7X3DF4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EK3JI6AO","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EK3JI6AOIC7X3DF4CHORKSEJ5D","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10211","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-29T19:36:52Z","cross_cats_sorted":[],"title_canon_sha256":"dab4cf0ccb8699b3fd8d9c928c21857be4fb4d92405a5de3356d4f6a26112eb6","abstract_canon_sha256":"c64ab000f46a6ae564530dbcb13b926344f758fc4d0e8fa82d9004a4b386d777"},"schema_version":"1.0"},"canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:23.337755Z","signature_b64":"NbacWq6t5AsyGOL7rmQqUygF7ZQWRSWOrvq3N+R0zJ71SIyQS0+X9iD2lBkDawLD418zsX44cdgAxuVWKcWDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","last_reissued_at":"2026-05-18T00:23:23.337140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:23.337140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10211","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FE7CSqCj3jslsVD9gwlSZk978SqRNjMXwiktu27wQJbPFKKZoJLmngeJH7ZyTOsDp2u/FbJ7odQh7TERYyfbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:11:18.229968Z"},"content_sha256":"1b4c669819462cd1647e3f7eebdbca2be9b8a572ad1d70af853fb1eac992f7fa","schema_version":"1.0","event_id":"sha256:1b4c669819462cd1647e3f7eebdbca2be9b8a572ad1d70af853fb1eac992f7fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EK3JI6AOIC7X3DF4CHORKSEJ5D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Connections between Mean-Field Game and Social Welfare Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lin Zhao, Sen Li, Wei Zhang","submitted_at":"2017-03-29T19:36:52Z","abstract_excerpt":"This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the $\\epsilon$-Nash equilibrium of the mean-field game coincides with the optimal solution to a social welfare optimizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10211","kind":"arxiv","version":8},"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":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S4vKAZ+TQj7fRa7Hf2MaZQnXzNMiMwwE6wxJMsQKA7jpxaoPhiAoxq9UU0TIkUJPQ0q/6lEhfIEqwmN57ytmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T05:11:18.230652Z"},"content_sha256":"715feca09ef3a0d429cfcbffdb49aee447cd2dd119fd6fd6e8a0d80082544707","schema_version":"1.0","event_id":"sha256:715feca09ef3a0d429cfcbffdb49aee447cd2dd119fd6fd6e8a0d80082544707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/bundle.json","state_url":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/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":"2026-06-05T05:11:18Z","links":{"resolver":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D","bundle":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/bundle.json","state":"https://pith.science/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EK3JI6AOIC7X3DF4CHORKSEJ5D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EK3JI6AOIC7X3DF4CHORKSEJ5D","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":"c64ab000f46a6ae564530dbcb13b926344f758fc4d0e8fa82d9004a4b386d777","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-29T19:36:52Z","title_canon_sha256":"dab4cf0ccb8699b3fd8d9c928c21857be4fb4d92405a5de3356d4f6a26112eb6"},"schema_version":"1.0","source":{"id":"1703.10211","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10211","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10211v8","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10211","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"EK3JI6AOIC7X","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EK3JI6AOIC7X3DF4","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EK3JI6AO","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:715feca09ef3a0d429cfcbffdb49aee447cd2dd119fd6fd6e8a0d80082544707","target":"graph","created_at":"2026-05-18T00:23:23Z","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":"This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the $\\epsilon$-Nash equilibrium of the mean-field game coincides with the optimal solution to a social welfare optimizat","authors_text":"Lin Zhao, Sen Li, Wei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-29T19:36:52Z","title":"Connections between Mean-Field Game and Social Welfare Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10211","kind":"arxiv","version":8},"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":"sha256:1b4c669819462cd1647e3f7eebdbca2be9b8a572ad1d70af853fb1eac992f7fa","target":"record","created_at":"2026-05-18T00:23:23Z","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":"c64ab000f46a6ae564530dbcb13b926344f758fc4d0e8fa82d9004a4b386d777","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-03-29T19:36:52Z","title_canon_sha256":"dab4cf0ccb8699b3fd8d9c928c21857be4fb4d92405a5de3356d4f6a26112eb6"},"schema_version":"1.0","source":{"id":"1703.10211","kind":"arxiv","version":8}},"canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22b694780e40bf7d8cbc11dd154889e8d542caa844b7263a305c8b23585c0453","first_computed_at":"2026-05-18T00:23:23.337140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:23.337140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbacWq6t5AsyGOL7rmQqUygF7ZQWRSWOrvq3N+R0zJ71SIyQS0+X9iD2lBkDawLD418zsX44cdgAxuVWKcWDCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:23.337755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10211","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b4c669819462cd1647e3f7eebdbca2be9b8a572ad1d70af853fb1eac992f7fa","sha256:715feca09ef3a0d429cfcbffdb49aee447cd2dd119fd6fd6e8a0d80082544707"],"state_sha256":"dc81bfcb0af7b1c709b14eb9ef7f22a54b2bb1a7c0aa27d7777714e4baa01dfe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezYwu2byswlLEl/8h79QAvsI3X7t/LvHXPvncIKlzagf3g+sYGMBwpivw+AlMvW2czLwxtmLoGKjv7TjuoK/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T05:11:18.234051Z","bundle_sha256":"a90b34802dec30553676e4243bb6e904fbfa0d0bb623b47b98a00e636cf1f62f"}}