{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:A7UHTE5VDQXKF44HJHKT7Q3TXC","short_pith_number":"pith:A7UHTE5V","canonical_record":{"source":{"id":"1804.03090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-04-09T16:30:43Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7a14bd08db401e97fdb3cde33fc3afa6479790baa2c56d5d1e4d6443667fc8f6","abstract_canon_sha256":"518e11475bdd9e89168395ebad77593d0417406abaed749e8343241a271c7b88"},"schema_version":"1.0"},"canonical_sha256":"07e87993b51c2ea2f38749d53fc373b8a6b781bd11b771ae87d1ec583cb15b80","source":{"kind":"arxiv","id":"1804.03090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03090","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03090v1","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03090","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"pith_short_12","alias_value":"A7UHTE5VDQXK","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A7UHTE5VDQXKF44H","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A7UHTE5V","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:A7UHTE5VDQXKF44HJHKT7Q3TXC","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-04-09T16:30:43Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"7a14bd08db401e97fdb3cde33fc3afa6479790baa2c56d5d1e4d6443667fc8f6","abstract_canon_sha256":"518e11475bdd9e89168395ebad77593d0417406abaed749e8343241a271c7b88"},"schema_version":"1.0"},"canonical_sha256":"07e87993b51c2ea2f38749d53fc373b8a6b781bd11b771ae87d1ec583cb15b80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:28.252452Z","signature_b64":"g2dXNH1tOX5xa7NdXYESIc+Uxw51WApID8TZUWYpL7A6OE4sur4j4D9HN7iDorM+Pbzyi2FsMyCNMKh+dvnuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07e87993b51c2ea2f38749d53fc373b8a6b781bd11b771ae87d1ec583cb15b80","last_reissued_at":"2026-05-17T23:50:28.251966Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:28.251966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03090","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":"2026-05-17T23:50:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hmj9EmqISy89JG3UUKyJZZsuTt7SoZ8RVxs2e7fJZYA+4N2UmHdbaxM2CuJdYeXDiGqrtAOh1DRSGLO9K5ovCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:36:20.720679Z"},"content_sha256":"48d5ed0a2994873548450741d7e6d3b10adae17dd580b2bfecfb2ae0d6b12640","schema_version":"1.0","event_id":"sha256:48d5ed0a2994873548450741d7e6d3b10adae17dd580b2bfecfb2ae0d6b12640"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:A7UHTE5VDQXKF44HJHKT7Q3TXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean Field Games in the weak noise limit : A WKB approach to the Fokker-Planck equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"physics.soc-ph","authors_text":"Denis Ullmo, Thibault Bonnemain","submitted_at":"2018-04-09T16:30:43Z","abstract_excerpt":"Motivated by the study of a Mean Field Game toy model called the \"seminar problem\", we consider the Fokker-Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach \"a la Maslov\", making it possible to solve directly the time dependant problem in an especially transparent way."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03090","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":"2026-05-17T23:50:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KKLHJI+a8kxb8bf23ZpZaRSloQwGstrrzndJDqhZlvnV0KynqoZLp1OXfBQ9kNzp8Efvi2vU2jnAnj4XhqRADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:36:20.721019Z"},"content_sha256":"eb9319907c31fce52e4b256bdf4985e032417678f2637c82ea7c48866a1008d7","schema_version":"1.0","event_id":"sha256:eb9319907c31fce52e4b256bdf4985e032417678f2637c82ea7c48866a1008d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC/bundle.json","state_url":"https://pith.science/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC/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":"2026-06-20T06:36:20Z","links":{"resolver":"https://pith.science/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC","bundle":"https://pith.science/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC/bundle.json","state":"https://pith.science/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A7UHTE5VDQXKF44HJHKT7Q3TXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:A7UHTE5VDQXKF44HJHKT7Q3TXC","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":"518e11475bdd9e89168395ebad77593d0417406abaed749e8343241a271c7b88","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-04-09T16:30:43Z","title_canon_sha256":"7a14bd08db401e97fdb3cde33fc3afa6479790baa2c56d5d1e4d6443667fc8f6"},"schema_version":"1.0","source":{"id":"1804.03090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03090","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03090v1","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03090","created_at":"2026-05-17T23:50:28Z"},{"alias_kind":"pith_short_12","alias_value":"A7UHTE5VDQXK","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"A7UHTE5VDQXKF44H","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"A7UHTE5V","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:eb9319907c31fce52e4b256bdf4985e032417678f2637c82ea7c48866a1008d7","target":"graph","created_at":"2026-05-17T23:50:28Z","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":"Motivated by the study of a Mean Field Game toy model called the \"seminar problem\", we consider the Fokker-Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach \"a la Maslov\", making it possible to solve directly the time dependant problem in an especially transparent way.","authors_text":"Denis Ullmo, Thibault Bonnemain","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-04-09T16:30:43Z","title":"Mean Field Games in the weak noise limit : A WKB approach to the Fokker-Planck equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03090","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":"sha256:48d5ed0a2994873548450741d7e6d3b10adae17dd580b2bfecfb2ae0d6b12640","target":"record","created_at":"2026-05-17T23:50:28Z","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":"518e11475bdd9e89168395ebad77593d0417406abaed749e8343241a271c7b88","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2018-04-09T16:30:43Z","title_canon_sha256":"7a14bd08db401e97fdb3cde33fc3afa6479790baa2c56d5d1e4d6443667fc8f6"},"schema_version":"1.0","source":{"id":"1804.03090","kind":"arxiv","version":1}},"canonical_sha256":"07e87993b51c2ea2f38749d53fc373b8a6b781bd11b771ae87d1ec583cb15b80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07e87993b51c2ea2f38749d53fc373b8a6b781bd11b771ae87d1ec583cb15b80","first_computed_at":"2026-05-17T23:50:28.251966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:28.251966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g2dXNH1tOX5xa7NdXYESIc+Uxw51WApID8TZUWYpL7A6OE4sur4j4D9HN7iDorM+Pbzyi2FsMyCNMKh+dvnuAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:28.252452Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48d5ed0a2994873548450741d7e6d3b10adae17dd580b2bfecfb2ae0d6b12640","sha256:eb9319907c31fce52e4b256bdf4985e032417678f2637c82ea7c48866a1008d7"],"state_sha256":"7273f61739901500c43eee3b7776668a124286395849a38df1db596c270183f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vLf8+ASTAZI2NTsZlb8SnURiDzRSGOB6nMQw4Of7gvXEZfhSoyU1/rVS73damwS4uYX55w4T6+bSvGFT+yPuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:36:20.722884Z","bundle_sha256":"fe242141291a39bbd0fd9544deac830f3288258e9cfe2e99ccacba27747429c0"}}