{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A3TOYEYKMGQ6KUA2CI2KXXKWVA","short_pith_number":"pith:A3TOYEYK","canonical_record":{"source":{"id":"1605.03281","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-11T04:54:07Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"fe484e816c94c16b53c587825dcfb60cd8f93e1be115429be981c0dd5bdd5b13","abstract_canon_sha256":"1ed53698a3b038e7a5468a03a6e2c77acfadf3bb37f9ef37214b0f05493bdb00"},"schema_version":"1.0"},"canonical_sha256":"06e6ec130a61a1e5501a1234abdd56a805844f6ba6c3a537024a51425d0c37d9","source":{"kind":"arxiv","id":"1605.03281","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03281","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03281v3","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03281","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"A3TOYEYKMGQ6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A3TOYEYKMGQ6KUA2","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A3TOYEYK","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A3TOYEYKMGQ6KUA2CI2KXXKWVA","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03281","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-11T04:54:07Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"fe484e816c94c16b53c587825dcfb60cd8f93e1be115429be981c0dd5bdd5b13","abstract_canon_sha256":"1ed53698a3b038e7a5468a03a6e2c77acfadf3bb37f9ef37214b0f05493bdb00"},"schema_version":"1.0"},"canonical_sha256":"06e6ec130a61a1e5501a1234abdd56a805844f6ba6c3a537024a51425d0c37d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:21.284058Z","signature_b64":"Q0tW+EfeyaS1nOq/pC7JMSDnIn1Vi8qnuuGOYxOiRcCVStNT0t5XMR63rYGIY1myJ3KbyLZLZ5mjiBSIIbGfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06e6ec130a61a1e5501a1234abdd56a805844f6ba6c3a537024a51425d0c37d9","last_reissued_at":"2026-05-18T00:29:21.283467Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:21.283467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03281","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZTc5D+mN1uH/dWzdr3CVizVRStJk8J7kwxfx3W9KNoz6eHwCJr9DRZkOWOIM2NSDbIVRZReI/AFb+UmlHlzUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T09:13:33.662371Z"},"content_sha256":"170e6b4be6ee5c0a06d1013f8541234e69fb896bcef3f376c31193d5cd564339","schema_version":"1.0","event_id":"sha256:170e6b4be6ee5c0a06d1013f8541234e69fb896bcef3f376c31193d5cd564339"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A3TOYEYKMGQ6KUA2CI2KXXKWVA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-Field-Type Games in Engineering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"math.OC","authors_text":"Alain Tcheukam, Boualem Djehiche, Hamidou Tembine","submitted_at":"2016-05-11T04:54:07Z","abstract_excerpt":"A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03281","kind":"arxiv","version":3},"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":"2026-05-18T00:29:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y070ReXVcDfXyfyWo+sQIyLHCl6ebqNxeMhfpLLriW6jm1Mz1tPLYuaVoeNfZf8yRNxUrQ/B672vqynRqSa9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T09:13:33.662716Z"},"content_sha256":"8da0a852f9ebcb4e4bd45d42aa2a1e4ea9d374e9bf1b95c7f90711bd6e83f7f2","schema_version":"1.0","event_id":"sha256:8da0a852f9ebcb4e4bd45d42aa2a1e4ea9d374e9bf1b95c7f90711bd6e83f7f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA/bundle.json","state_url":"https://pith.science/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA/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":"2026-06-04T09:13:33Z","links":{"resolver":"https://pith.science/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA","bundle":"https://pith.science/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA/bundle.json","state":"https://pith.science/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3TOYEYKMGQ6KUA2CI2KXXKWVA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A3TOYEYKMGQ6KUA2CI2KXXKWVA","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":"1ed53698a3b038e7a5468a03a6e2c77acfadf3bb37f9ef37214b0f05493bdb00","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-11T04:54:07Z","title_canon_sha256":"fe484e816c94c16b53c587825dcfb60cd8f93e1be115429be981c0dd5bdd5b13"},"schema_version":"1.0","source":{"id":"1605.03281","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03281","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03281v3","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03281","created_at":"2026-05-18T00:29:21Z"},{"alias_kind":"pith_short_12","alias_value":"A3TOYEYKMGQ6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A3TOYEYKMGQ6KUA2","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A3TOYEYK","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:8da0a852f9ebcb4e4bd45d42aa2a1e4ea9d374e9bf1b95c7f90711bd6e83f7f2","target":"graph","created_at":"2026-05-18T00:29:21Z","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":"A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsens","authors_text":"Alain Tcheukam, Boualem Djehiche, Hamidou Tembine","cross_cats":["cs.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-11T04:54:07Z","title":"Mean-Field-Type Games in Engineering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03281","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":"sha256:170e6b4be6ee5c0a06d1013f8541234e69fb896bcef3f376c31193d5cd564339","target":"record","created_at":"2026-05-18T00:29:21Z","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":"1ed53698a3b038e7a5468a03a6e2c77acfadf3bb37f9ef37214b0f05493bdb00","cross_cats_sorted":["cs.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-11T04:54:07Z","title_canon_sha256":"fe484e816c94c16b53c587825dcfb60cd8f93e1be115429be981c0dd5bdd5b13"},"schema_version":"1.0","source":{"id":"1605.03281","kind":"arxiv","version":3}},"canonical_sha256":"06e6ec130a61a1e5501a1234abdd56a805844f6ba6c3a537024a51425d0c37d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06e6ec130a61a1e5501a1234abdd56a805844f6ba6c3a537024a51425d0c37d9","first_computed_at":"2026-05-18T00:29:21.283467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:21.283467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q0tW+EfeyaS1nOq/pC7JMSDnIn1Vi8qnuuGOYxOiRcCVStNT0t5XMR63rYGIY1myJ3KbyLZLZ5mjiBSIIbGfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:21.284058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03281","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:170e6b4be6ee5c0a06d1013f8541234e69fb896bcef3f376c31193d5cd564339","sha256:8da0a852f9ebcb4e4bd45d42aa2a1e4ea9d374e9bf1b95c7f90711bd6e83f7f2"],"state_sha256":"20581585a6451823ee63a170dd3d828c781a55035edb3a82b4cb1426c2989498"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whgrJXdsXbT40TKFd+KP/NJT32GiPO5S8YGlxn7PisVq7kcGOeW+a2HcWiKFMDBBqm6FyaU3K6+cy+Gt/vDXDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T09:13:33.664694Z","bundle_sha256":"493835a9b9482ffea5be8b4b4ccacd54c9814c23ac5b29f469537e584e0c9fc5"}}