{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:D5ZEXU24HP4BVUTI4K4L2JOV4O","short_pith_number":"pith:D5ZEXU24","canonical_record":{"source":{"id":"1609.00056","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-08-31T22:14:14Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7f5731c5142ef1cf47e9c8fd6c57ac0ae06b244dcf9f88d3971f1cf7cc71909f","abstract_canon_sha256":"b71ad7879446aefed686c934c411db479bb27e6ac1b728181f857563fd14d185"},"schema_version":"1.0"},"canonical_sha256":"1f724bd35c3bf81ad268e2b8bd25d5e3a48ba61a1590069e1df7d6037d900841","source":{"kind":"arxiv","id":"1609.00056","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00056","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00056v5","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00056","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"D5ZEXU24HP4B","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D5ZEXU24HP4BVUTI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D5ZEXU24","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:D5ZEXU24HP4BVUTI4K4L2JOV4O","target":"record","payload":{"canonical_record":{"source":{"id":"1609.00056","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-08-31T22:14:14Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7f5731c5142ef1cf47e9c8fd6c57ac0ae06b244dcf9f88d3971f1cf7cc71909f","abstract_canon_sha256":"b71ad7879446aefed686c934c411db479bb27e6ac1b728181f857563fd14d185"},"schema_version":"1.0"},"canonical_sha256":"1f724bd35c3bf81ad268e2b8bd25d5e3a48ba61a1590069e1df7d6037d900841","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:34.709742Z","signature_b64":"h18gYUU/o9GnkJWEOt9o+6+0v/nU+v4WwM793xzAl3X+BEAHmEMtFkXCLjAxUqMRQ0ToHVDTyDMksEOpaiX0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f724bd35c3bf81ad268e2b8bd25d5e3a48ba61a1590069e1df7d6037d900841","last_reissued_at":"2026-05-18T00:05:34.709275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:34.709275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.00056","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PXu2uFCTxTzHaOfazapfOCb60oUS8/qzqOjjo9dD/H0V3SEH0nWAkRvIoswGBP+PbzzkMGNdXFFAUMXz7I9IAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:19:02.547418Z"},"content_sha256":"bdd7d13f186e03cd2d1d7035257f351ed34a9d9fd50c7cf6dfe70a888ba76f2c","schema_version":"1.0","event_id":"sha256:bdd7d13f186e03cd2d1d7035257f351ed34a9d9fd50c7cf6dfe70a888ba76f2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:D5ZEXU24HP4BVUTI4K4L2JOV4O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Quadratic Mean Field Teams: Optimal and Approximately Optimal Decentralized Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.SY","authors_text":"Aditya Mahajan, Jalal Arabneydi","submitted_at":"2016-08-31T22:14:14Z","abstract_excerpt":"We consider team optimal control of decentralized systems with linear dynamics, quadratic costs, and arbitrary disturbance that consist of multiple sub-populations with exchangeable agents (i.e., exchanging two agents within the same sub-population does not affect the dynamics or the cost). Such a system is equivalent to one where the dynamics and costs are coupled across agents through the mean-field (or empirical mean) of the states and actions (even when the primitive random variables are non-exchangeable). Two information structures are investigated. In the first, all agents observe their "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00056","kind":"arxiv","version":5},"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":"2026-05-18T00:05:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJR7sy79qdYpICg+7UCs4e0xmqP+Kfn4u5TwvV37lVWgT5PQKadVTONNYjj4WchG1PylIXcPaFTEumbEosv0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:19:02.547777Z"},"content_sha256":"01f411305b515a3e50acdd35d1ca3f8c03cd5abd43e6acb892382840adde1dec","schema_version":"1.0","event_id":"sha256:01f411305b515a3e50acdd35d1ca3f8c03cd5abd43e6acb892382840adde1dec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O/bundle.json","state_url":"https://pith.science/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O/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":"2026-06-25T23:19:02Z","links":{"resolver":"https://pith.science/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O","bundle":"https://pith.science/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O/bundle.json","state":"https://pith.science/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5ZEXU24HP4BVUTI4K4L2JOV4O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D5ZEXU24HP4BVUTI4K4L2JOV4O","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":"b71ad7879446aefed686c934c411db479bb27e6ac1b728181f857563fd14d185","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-08-31T22:14:14Z","title_canon_sha256":"7f5731c5142ef1cf47e9c8fd6c57ac0ae06b244dcf9f88d3971f1cf7cc71909f"},"schema_version":"1.0","source":{"id":"1609.00056","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00056","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00056v5","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00056","created_at":"2026-05-18T00:05:34Z"},{"alias_kind":"pith_short_12","alias_value":"D5ZEXU24HP4B","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D5ZEXU24HP4BVUTI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D5ZEXU24","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:01f411305b515a3e50acdd35d1ca3f8c03cd5abd43e6acb892382840adde1dec","target":"graph","created_at":"2026-05-18T00:05:34Z","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 consider team optimal control of decentralized systems with linear dynamics, quadratic costs, and arbitrary disturbance that consist of multiple sub-populations with exchangeable agents (i.e., exchanging two agents within the same sub-population does not affect the dynamics or the cost). Such a system is equivalent to one where the dynamics and costs are coupled across agents through the mean-field (or empirical mean) of the states and actions (even when the primitive random variables are non-exchangeable). Two information structures are investigated. In the first, all agents observe their ","authors_text":"Aditya Mahajan, Jalal Arabneydi","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-08-31T22:14:14Z","title":"Linear Quadratic Mean Field Teams: Optimal and Approximately Optimal Decentralized Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00056","kind":"arxiv","version":5},"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:bdd7d13f186e03cd2d1d7035257f351ed34a9d9fd50c7cf6dfe70a888ba76f2c","target":"record","created_at":"2026-05-18T00:05:34Z","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":"b71ad7879446aefed686c934c411db479bb27e6ac1b728181f857563fd14d185","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2016-08-31T22:14:14Z","title_canon_sha256":"7f5731c5142ef1cf47e9c8fd6c57ac0ae06b244dcf9f88d3971f1cf7cc71909f"},"schema_version":"1.0","source":{"id":"1609.00056","kind":"arxiv","version":5}},"canonical_sha256":"1f724bd35c3bf81ad268e2b8bd25d5e3a48ba61a1590069e1df7d6037d900841","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f724bd35c3bf81ad268e2b8bd25d5e3a48ba61a1590069e1df7d6037d900841","first_computed_at":"2026-05-18T00:05:34.709275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:34.709275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h18gYUU/o9GnkJWEOt9o+6+0v/nU+v4WwM793xzAl3X+BEAHmEMtFkXCLjAxUqMRQ0ToHVDTyDMksEOpaiX0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:34.709742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00056","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdd7d13f186e03cd2d1d7035257f351ed34a9d9fd50c7cf6dfe70a888ba76f2c","sha256:01f411305b515a3e50acdd35d1ca3f8c03cd5abd43e6acb892382840adde1dec"],"state_sha256":"ca597ff03a7bcd461783dcab38fd895dca9a367cf48d1e2c83e97e44a22e0675"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JdTbL2eTyeAloy0jO53e9eGc0HQuPwbU92vcZbzCFhbqRf3L9m+hlRS8ASSsvan/e1CBcHzhAKTDVwX93floBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:19:02.549849Z","bundle_sha256":"2d0333cb6babea8f4c5d586744cc97c7dfa1c2ef41da20272173910c8f657b45"}}