{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YL4MM5FEEHYHYGZYIT3GMUM5HK","short_pith_number":"pith:YL4MM5FE","canonical_record":{"source":{"id":"1810.00137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-29T02:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"a93af3cab8c9d0e6f84ec58e4109606aff20920c4b835734372c12b0546fbcdf","abstract_canon_sha256":"562fa1cfdb145ba485373896ff516744bbf4e499932e8be04ca479202e68be90"},"schema_version":"1.0"},"canonical_sha256":"c2f8c674a421f07c1b3844f666519d3abffc90a93292f7ad23c742edac17d5f9","source":{"kind":"arxiv","id":"1810.00137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00137","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00137v1","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00137","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"YL4MM5FEEHYH","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YL4MM5FEEHYHYGZY","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YL4MM5FE","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YL4MM5FEEHYHYGZYIT3GMUM5HK","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-29T02:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"a93af3cab8c9d0e6f84ec58e4109606aff20920c4b835734372c12b0546fbcdf","abstract_canon_sha256":"562fa1cfdb145ba485373896ff516744bbf4e499932e8be04ca479202e68be90"},"schema_version":"1.0"},"canonical_sha256":"c2f8c674a421f07c1b3844f666519d3abffc90a93292f7ad23c742edac17d5f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:28.674688Z","signature_b64":"0X5RZ7Wq3CHndvaqNy0WMrndfDcIE6DZlxZKqYO8QX+QpWcBLED0ELQ4KZXnrhVKordycQkwvN9VJIDxKdSSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2f8c674a421f07c1b3844f666519d3abffc90a93292f7ad23c742edac17d5f9","last_reissued_at":"2026-05-18T00:04:28.674128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:28.674128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00137","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":"2026-05-18T00:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"feIF2eUi8rI0+ty13XWGh1YZuMLiv7dmBwmivmWiExbPb74Au8y/paASAG0VNQlTLLGer5e8Dq69WgFDn2YECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:59:23.788637Z"},"content_sha256":"4ced3fdcd164670a164b33d5aa07e66d78c3e43e9aeac432c331979996b191d1","schema_version":"1.0","event_id":"sha256:4ced3fdcd164670a164b33d5aa07e66d78c3e43e9aeac432c331979996b191d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YL4MM5FEEHYHYGZYIT3GMUM5HK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean Field Production Output Control with Sticky Prices: Nash and Social Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bingchang Wang, Minyi Huang","submitted_at":"2018-09-29T02:38:18Z","abstract_excerpt":"This paper presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices and adjustment costs. By solving auxiliary limiting optimal control problems subject to consistent mean field approximations, two sets of decentralized strategies are obtained and further shown to asymptotically attain Nash equilibria and social optima, respectively. The performance estimate of the social optimum strategies exploits a passivity property of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00137","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":"2026-05-18T00:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R0TCCg12mY7gqKgHp73XxGS9mhBHYRuZUPI5jgxTlfAScsBA8d6gM0uCRQf8cHbT4XpVIRQjQcY08SIcqEZmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:59:23.788985Z"},"content_sha256":"57b7bfc5253b1f69611ac9db31fce5b23e472bae11fc91dbb5ef252448d6faae","schema_version":"1.0","event_id":"sha256:57b7bfc5253b1f69611ac9db31fce5b23e472bae11fc91dbb5ef252448d6faae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK/bundle.json","state_url":"https://pith.science/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK/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":"2026-06-22T17:59:23Z","links":{"resolver":"https://pith.science/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK","bundle":"https://pith.science/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK/bundle.json","state":"https://pith.science/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YL4MM5FEEHYHYGZYIT3GMUM5HK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YL4MM5FEEHYHYGZYIT3GMUM5HK","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":"562fa1cfdb145ba485373896ff516744bbf4e499932e8be04ca479202e68be90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-29T02:38:18Z","title_canon_sha256":"a93af3cab8c9d0e6f84ec58e4109606aff20920c4b835734372c12b0546fbcdf"},"schema_version":"1.0","source":{"id":"1810.00137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00137","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00137v1","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00137","created_at":"2026-05-18T00:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"YL4MM5FEEHYH","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YL4MM5FEEHYHYGZY","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YL4MM5FE","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:57b7bfc5253b1f69611ac9db31fce5b23e472bae11fc91dbb5ef252448d6faae","target":"graph","created_at":"2026-05-18T00:04:28Z","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 presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices and adjustment costs. By solving auxiliary limiting optimal control problems subject to consistent mean field approximations, two sets of decentralized strategies are obtained and further shown to asymptotically attain Nash equilibria and social optima, respectively. The performance estimate of the social optimum strategies exploits a passivity property of the","authors_text":"Bingchang Wang, Minyi Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-29T02:38:18Z","title":"Mean Field Production Output Control with Sticky Prices: Nash and Social Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00137","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":"sha256:4ced3fdcd164670a164b33d5aa07e66d78c3e43e9aeac432c331979996b191d1","target":"record","created_at":"2026-05-18T00:04:28Z","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":"562fa1cfdb145ba485373896ff516744bbf4e499932e8be04ca479202e68be90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-09-29T02:38:18Z","title_canon_sha256":"a93af3cab8c9d0e6f84ec58e4109606aff20920c4b835734372c12b0546fbcdf"},"schema_version":"1.0","source":{"id":"1810.00137","kind":"arxiv","version":1}},"canonical_sha256":"c2f8c674a421f07c1b3844f666519d3abffc90a93292f7ad23c742edac17d5f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2f8c674a421f07c1b3844f666519d3abffc90a93292f7ad23c742edac17d5f9","first_computed_at":"2026-05-18T00:04:28.674128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:28.674128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0X5RZ7Wq3CHndvaqNy0WMrndfDcIE6DZlxZKqYO8QX+QpWcBLED0ELQ4KZXnrhVKordycQkwvN9VJIDxKdSSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:28.674688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ced3fdcd164670a164b33d5aa07e66d78c3e43e9aeac432c331979996b191d1","sha256:57b7bfc5253b1f69611ac9db31fce5b23e472bae11fc91dbb5ef252448d6faae"],"state_sha256":"1cd6aaec9a1213c66202b44b8abc73f03a8f1514d148c9a974bbb696453dc64c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MljNAHhLppZXHZ25kOyYo6Bh90h7qwY0weWR1+7W+xkQNPVI/L4Eqdk84Dbu35RZr+x60Sy9yEMG20GGqaYAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:59:23.790821Z","bundle_sha256":"d0069f890984ae42288bcda4e7c871053b1909c803a121513862bfb66d0ec0cc"}}