{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MUBFJECHBJB573REEGF46WPV2D","short_pith_number":"pith:MUBFJECH","canonical_record":{"source":{"id":"1410.6942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T17:44:58Z","cross_cats_sorted":[],"title_canon_sha256":"0389a0dfa4ddeb0f9177a346ddc79a82fcbbd13029691ea2fe1f6c31319bb9f8","abstract_canon_sha256":"05c603b73b63d4b27154c55cff229a397911e450bf760ea4da43bcea920b4896"},"schema_version":"1.0"},"canonical_sha256":"65025490470a43dfee24218bcf59f5d0c703070345ea129832c51f6bd244f91c","source":{"kind":"arxiv","id":"1410.6942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6942","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6942v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6942","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MUBFJECHBJB5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MUBFJECHBJB573RE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MUBFJECH","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MUBFJECHBJB573REEGF46WPV2D","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T17:44:58Z","cross_cats_sorted":[],"title_canon_sha256":"0389a0dfa4ddeb0f9177a346ddc79a82fcbbd13029691ea2fe1f6c31319bb9f8","abstract_canon_sha256":"05c603b73b63d4b27154c55cff229a397911e450bf760ea4da43bcea920b4896"},"schema_version":"1.0"},"canonical_sha256":"65025490470a43dfee24218bcf59f5d0c703070345ea129832c51f6bd244f91c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:18.271023Z","signature_b64":"KxuL6FNuCDy/pu2NNlQA8O/FPTiKOY8+Zoss/bJxQpvHdDktULai14M5dNMRrCtx9XAVVZBUUatgNMrIEo7sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65025490470a43dfee24218bcf59f5d0c703070345ea129832c51f6bd244f91c","last_reissued_at":"2026-05-18T02:39:18.270675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:18.270675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6942","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tlRyjNTK6y62U8/CZO3hhSiHsWO8MegWU+7U01tiskpdUzAI8IhjjbS3dfmraxhcezw/hmqzMdx6xhedtqunAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:14:10.162997Z"},"content_sha256":"141f487fb7881386f1f43b87692eb6b3e3d75c46306a43b2f20a5732cee63b14","schema_version":"1.0","event_id":"sha256:141f487fb7881386f1f43b87692eb6b3e3d75c46306a43b2f20a5732cee63b14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MUBFJECHBJB573REEGF46WPV2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Obstacle Mean-Field Game Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diogo Gomes, Stefania Patrizi","submitted_at":"2014-10-25T17:44:58Z","abstract_excerpt":"In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6942","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":"2026-05-18T02:39:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wwnkp5aaB4isjY2460ckhkx3N28020nZ4i8p5cBXcsil7b8k6LqlhcE8lj2ZCicxmNrE2iH5Tgy89x9y13jPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:14:10.163690Z"},"content_sha256":"6f8d43c4f721f1118ffa54baa0629331d9ef73318311d346f412ff0862b44beb","schema_version":"1.0","event_id":"sha256:6f8d43c4f721f1118ffa54baa0629331d9ef73318311d346f412ff0862b44beb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUBFJECHBJB573REEGF46WPV2D/bundle.json","state_url":"https://pith.science/pith/MUBFJECHBJB573REEGF46WPV2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUBFJECHBJB573REEGF46WPV2D/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":"2026-06-01T00:14:10Z","links":{"resolver":"https://pith.science/pith/MUBFJECHBJB573REEGF46WPV2D","bundle":"https://pith.science/pith/MUBFJECHBJB573REEGF46WPV2D/bundle.json","state":"https://pith.science/pith/MUBFJECHBJB573REEGF46WPV2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUBFJECHBJB573REEGF46WPV2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MUBFJECHBJB573REEGF46WPV2D","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":"05c603b73b63d4b27154c55cff229a397911e450bf760ea4da43bcea920b4896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T17:44:58Z","title_canon_sha256":"0389a0dfa4ddeb0f9177a346ddc79a82fcbbd13029691ea2fe1f6c31319bb9f8"},"schema_version":"1.0","source":{"id":"1410.6942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6942","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6942v1","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6942","created_at":"2026-05-18T02:39:18Z"},{"alias_kind":"pith_short_12","alias_value":"MUBFJECHBJB5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MUBFJECHBJB573RE","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MUBFJECH","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:6f8d43c4f721f1118ffa54baa0629331d9ef73318311d346f412ff0862b44beb","target":"graph","created_at":"2026-05-18T02:39:18Z","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":"In this paper, we introduce and study a first-order mean-field game obstacle problem. We examine the case of local dependence on the measure under assumptions that include both the logarithmic case and power-like nonlinearities. Since the obstacle operator is not differentiable, the equations for first-order mean field game problems have to be discussed carefully. Hence, we begin by considering a penalized problem. We prove this problem admits a unique solution satisfying uniform bounds. These bounds serve to pass to the limit in the penalized problem and to characterize the limiting equations","authors_text":"Diogo Gomes, Stefania Patrizi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T17:44:58Z","title":"Obstacle Mean-Field Game Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6942","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":"sha256:141f487fb7881386f1f43b87692eb6b3e3d75c46306a43b2f20a5732cee63b14","target":"record","created_at":"2026-05-18T02:39:18Z","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":"05c603b73b63d4b27154c55cff229a397911e450bf760ea4da43bcea920b4896","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-25T17:44:58Z","title_canon_sha256":"0389a0dfa4ddeb0f9177a346ddc79a82fcbbd13029691ea2fe1f6c31319bb9f8"},"schema_version":"1.0","source":{"id":"1410.6942","kind":"arxiv","version":1}},"canonical_sha256":"65025490470a43dfee24218bcf59f5d0c703070345ea129832c51f6bd244f91c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65025490470a43dfee24218bcf59f5d0c703070345ea129832c51f6bd244f91c","first_computed_at":"2026-05-18T02:39:18.270675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:18.270675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KxuL6FNuCDy/pu2NNlQA8O/FPTiKOY8+Zoss/bJxQpvHdDktULai14M5dNMRrCtx9XAVVZBUUatgNMrIEo7sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:18.271023Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:141f487fb7881386f1f43b87692eb6b3e3d75c46306a43b2f20a5732cee63b14","sha256:6f8d43c4f721f1118ffa54baa0629331d9ef73318311d346f412ff0862b44beb"],"state_sha256":"7523d11b6b738882506ff95d592bd06f5bf99704b0cd998862c69f823697fda2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WM7CGESiWxzzrgeaUK1k0VD9raHWLs6bERnRpwxrBy5OZ5HwqVz9F7Oj6KWVd7hmsgUohYTM/m6LEgg8YCB5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:14:10.167534Z","bundle_sha256":"2085da9df38af363b2c86546337604296974cc581d9a254e334696cb4231b3ac"}}