{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:QYWSHER4F7C3GTDNTWONXU3Y2H","short_pith_number":"pith:QYWSHER4","schema_version":"1.0","canonical_sha256":"862d23923c2fc5b34c6d9d9cdbd378d1ded9fa7e8578d321c572886c0e5195f3","source":{"kind":"arxiv","id":"1905.02046","version":1},"attestation_state":"computed","paper":{"title":"Two-scale homogenization of a stationary mean-field game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diogo Gomes, Rita Ferreira, Xianjin Yang","submitted_at":"2019-05-06T13:48:51Z","abstract_excerpt":"In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems."},"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":"1905.02046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-06T13:48:51Z","cross_cats_sorted":[],"title_canon_sha256":"9c6952667480162d42a12da89b7ee5e0abab44cf2802e5f49dcb95242db4720a","abstract_canon_sha256":"ebd2fb3e1e5428f588d064bdf09866ea97122b91eceb0f009f140cea31170612"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:56.576991Z","signature_b64":"YEj2/O5nKvcCVRiLxpZSW8n8wwK1yHT3ybWmWCPtMcNxfEtrGJF7rgR1g6ZGMs73TTMOlNH0T/LNqN8bOTfgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"862d23923c2fc5b34c6d9d9cdbd378d1ded9fa7e8578d321c572886c0e5195f3","last_reissued_at":"2026-05-17T23:46:56.576422Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:56.576422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two-scale homogenization of a stationary mean-field game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diogo Gomes, Rita Ferreira, Xianjin Yang","submitted_at":"2019-05-06T13:48:51Z","abstract_excerpt":"In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.02046","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.02046","created_at":"2026-05-17T23:46:56.576508+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.02046v1","created_at":"2026-05-17T23:46:56.576508+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.02046","created_at":"2026-05-17T23:46:56.576508+00:00"},{"alias_kind":"pith_short_12","alias_value":"QYWSHER4F7C3","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"QYWSHER4F7C3GTDN","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"QYWSHER4","created_at":"2026-05-18T12:33:27.125529+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/QYWSHER4F7C3GTDNTWONXU3Y2H","json":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H.json","graph_json":"https://pith.science/api/pith-number/QYWSHER4F7C3GTDNTWONXU3Y2H/graph.json","events_json":"https://pith.science/api/pith-number/QYWSHER4F7C3GTDNTWONXU3Y2H/events.json","paper":"https://pith.science/paper/QYWSHER4"},"agent_actions":{"view_html":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H","download_json":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H.json","view_paper":"https://pith.science/paper/QYWSHER4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.02046&json=true","fetch_graph":"https://pith.science/api/pith-number/QYWSHER4F7C3GTDNTWONXU3Y2H/graph.json","fetch_events":"https://pith.science/api/pith-number/QYWSHER4F7C3GTDNTWONXU3Y2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H/action/storage_attestation","attest_author":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H/action/author_attestation","sign_citation":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H/action/citation_signature","submit_replication":"https://pith.science/pith/QYWSHER4F7C3GTDNTWONXU3Y2H/action/replication_record"}},"created_at":"2026-05-17T23:46:56.576508+00:00","updated_at":"2026-05-17T23:46:56.576508+00:00"}