{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EWBKT7JNS3D726R2UGF74GLBXJ","short_pith_number":"pith:EWBKT7JN","schema_version":"1.0","canonical_sha256":"2582a9fd2d96c7fd7a3aa18bfe1961ba66bc7ce1620458e92a0e626e94cf7711","source":{"kind":"arxiv","id":"1811.01156","version":3},"attestation_state":"computed","paper":{"title":"Fourier Approximation Methods for First-Order Nonlocal Mean-Field Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joao Saude, Levon Nurbekyan","submitted_at":"2018-11-03T04:13:02Z","abstract_excerpt":"In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem and arrive at a finite-dimensional saddle point problem. Finally, we solve this saddle-point problem by a variant of a primal dual hybrid gradient method."},"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":"1811.01156","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-03T04:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"15b46cfc544879599c69ab082f624b1978d358d49b283ae999f33a9c9bc5963c","abstract_canon_sha256":"4e9947cc86c2c2fc09a09745bd204b8f349561254fd029516f7146f63c2a6670"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:05.084860Z","signature_b64":"qsByQBFYcy8EJw9IpfNfLg0/JBluFsQrdebtFrjqjNz/SE3VESBHyVP5DXXprlex9sGVEidbAKU/5jy2gGE5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2582a9fd2d96c7fd7a3aa18bfe1961ba66bc7ce1620458e92a0e626e94cf7711","last_reissued_at":"2026-05-17T23:56:05.084195Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:05.084195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fourier Approximation Methods for First-Order Nonlocal Mean-Field Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joao Saude, Levon Nurbekyan","submitted_at":"2018-11-03T04:13:02Z","abstract_excerpt":"In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate a given MFG system by a simpler one that is equivalent to a convex optimization problem over a finite-dimensional subspace of continuous curves. Furthermore, we perform a time-discretization for this optimization problem and arrive at a finite-dimensional saddle point problem. Finally, we solve this saddle-point problem by a variant of a primal dual hybrid gradient method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01156","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1811.01156","created_at":"2026-05-17T23:56:05.084310+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01156v3","created_at":"2026-05-17T23:56:05.084310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01156","created_at":"2026-05-17T23:56:05.084310+00:00"},{"alias_kind":"pith_short_12","alias_value":"EWBKT7JNS3D7","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EWBKT7JNS3D726R2","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EWBKT7JN","created_at":"2026-05-18T12:32:22.470017+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/EWBKT7JNS3D726R2UGF74GLBXJ","json":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ.json","graph_json":"https://pith.science/api/pith-number/EWBKT7JNS3D726R2UGF74GLBXJ/graph.json","events_json":"https://pith.science/api/pith-number/EWBKT7JNS3D726R2UGF74GLBXJ/events.json","paper":"https://pith.science/paper/EWBKT7JN"},"agent_actions":{"view_html":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ","download_json":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ.json","view_paper":"https://pith.science/paper/EWBKT7JN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01156&json=true","fetch_graph":"https://pith.science/api/pith-number/EWBKT7JNS3D726R2UGF74GLBXJ/graph.json","fetch_events":"https://pith.science/api/pith-number/EWBKT7JNS3D726R2UGF74GLBXJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ/action/storage_attestation","attest_author":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ/action/author_attestation","sign_citation":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ/action/citation_signature","submit_replication":"https://pith.science/pith/EWBKT7JNS3D726R2UGF74GLBXJ/action/replication_record"}},"created_at":"2026-05-17T23:56:05.084310+00:00","updated_at":"2026-05-17T23:56:05.084310+00:00"}