{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:Y2FYORXUZX6OTMML6VZ2PZ52RZ","short_pith_number":"pith:Y2FYORXU","schema_version":"1.0","canonical_sha256":"c68b8746f4cdfce9b18bf573a7e7ba8e64cbab0a8f7310143d53ae12a725eca4","source":{"kind":"arxiv","id":"2004.06505","version":1},"attestation_state":"computed","paper":{"title":"Weak KAM approach to first-order Mean Field Games with state constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Cristian Mendico, Kaizhi Wang, Piermarco Cannarsa, Wei Cheng","submitted_at":"2020-04-14T13:48:10Z","abstract_excerpt":"We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on $[0,T]$ converges to the solution of the ergodic system as $T \\to +\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2004.06505","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-04-14T13:48:10Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"194afdcd617ec874d96e4eeae6f42e4f9a85773d221488a3b92c0589a2ba5b4d","abstract_canon_sha256":"984dce7cb0131921b091690c1a2c0a553aab2e4f2966a062b93f9808dcb74e3a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:57:08.579670Z","signature_b64":"9GT+l5c5/ADVuZzG+LsOPZilXViTI3s8FfZ8Y8NZCMlgMOGzq1uQhmCa90se+PvRUML5hCquJayIKglNTJ6CDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c68b8746f4cdfce9b18bf573a7e7ba8e64cbab0a8f7310143d53ae12a725eca4","last_reissued_at":"2026-07-05T05:57:08.579288Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:57:08.579288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak KAM approach to first-order Mean Field Games with state constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Cristian Mendico, Kaizhi Wang, Piermarco Cannarsa, Wei Cheng","submitted_at":"2020-04-14T13:48:10Z","abstract_excerpt":"We study the asymptotic behavior of solutions to the constrained MFG system as the time horizon $T$ goes to infinity. For this purpose, we analyze first Hamilton-Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on $[0,T]$ converges to the solution of the ergodic system as $T \\to +\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.06505","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.06505/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2004.06505","created_at":"2026-07-05T05:57:08.579367+00:00"},{"alias_kind":"arxiv_version","alias_value":"2004.06505v1","created_at":"2026-07-05T05:57:08.579367+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.06505","created_at":"2026-07-05T05:57:08.579367+00:00"},{"alias_kind":"pith_short_12","alias_value":"Y2FYORXUZX6O","created_at":"2026-07-05T05:57:08.579367+00:00"},{"alias_kind":"pith_short_16","alias_value":"Y2FYORXUZX6OTMML","created_at":"2026-07-05T05:57:08.579367+00:00"},{"alias_kind":"pith_short_8","alias_value":"Y2FYORXU","created_at":"2026-07-05T05:57:08.579367+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ","json":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ.json","graph_json":"https://pith.science/api/pith-number/Y2FYORXUZX6OTMML6VZ2PZ52RZ/graph.json","events_json":"https://pith.science/api/pith-number/Y2FYORXUZX6OTMML6VZ2PZ52RZ/events.json","paper":"https://pith.science/paper/Y2FYORXU"},"agent_actions":{"view_html":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ","download_json":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ.json","view_paper":"https://pith.science/paper/Y2FYORXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2004.06505&json=true","fetch_graph":"https://pith.science/api/pith-number/Y2FYORXUZX6OTMML6VZ2PZ52RZ/graph.json","fetch_events":"https://pith.science/api/pith-number/Y2FYORXUZX6OTMML6VZ2PZ52RZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ/action/storage_attestation","attest_author":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ/action/author_attestation","sign_citation":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ/action/citation_signature","submit_replication":"https://pith.science/pith/Y2FYORXUZX6OTMML6VZ2PZ52RZ/action/replication_record"}},"created_at":"2026-07-05T05:57:08.579367+00:00","updated_at":"2026-07-05T05:57:08.579367+00:00"}