{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OPUG4KD6PBOMDIUAMZ7GTDHT4Q","short_pith_number":"pith:OPUG4KD6","canonical_record":{"source":{"id":"2507.10112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-14T09:57:19Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a7e23126ac217351ee8b0725f675e3da1e6c246292b429252366a0e8c8c102f2","abstract_canon_sha256":"706ce9db131e793b742f27a22cf70b8c61969c967684bb713e1e275eaf29c160"},"schema_version":"1.0"},"canonical_sha256":"73e86e287e785cc1a280667e698cf3e421b579de0eb4ea685430815c1ad0c000","source":{"kind":"arxiv","id":"2507.10112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10112","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10112v1","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10112","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"pith_short_12","alias_value":"OPUG4KD6PBOM","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"pith_short_16","alias_value":"OPUG4KD6PBOMDIUA","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"pith_short_8","alias_value":"OPUG4KD6","created_at":"2026-07-05T11:36:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OPUG4KD6PBOMDIUAMZ7GTDHT4Q","target":"record","payload":{"canonical_record":{"source":{"id":"2507.10112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-14T09:57:19Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a7e23126ac217351ee8b0725f675e3da1e6c246292b429252366a0e8c8c102f2","abstract_canon_sha256":"706ce9db131e793b742f27a22cf70b8c61969c967684bb713e1e275eaf29c160"},"schema_version":"1.0"},"canonical_sha256":"73e86e287e785cc1a280667e698cf3e421b579de0eb4ea685430815c1ad0c000","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:45.258595Z","signature_b64":"hUXXFnnBw/ECWmbnOcCYYbD1DuHTDlyeuhM4rzevJqlBvneSQlfSw3+NJGb5VsZ5MpBTnrsPdfhwTxM/CN4dAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73e86e287e785cc1a280667e698cf3e421b579de0eb4ea685430815c1ad0c000","last_reissued_at":"2026-07-05T11:36:45.258061Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:45.258061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.10112","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":"2026-07-05T11:36:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LFKu7UP2Ghe2w/HJbjSqzAoRT6Gk3SEyxDBfbvD+ASFLkXp40V246i4gS6MXNeJ/vl6JOcT3beuO/Sv6vXPRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:56:54.396837Z"},"content_sha256":"ce0a215768d493b4f0bf0ede55686d2ad1b475f992e3f74bb2b5cc4d245c6272","schema_version":"1.0","event_id":"sha256:ce0a215768d493b4f0bf0ede55686d2ad1b475f992e3f74bb2b5cc4d245c6272"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OPUG4KD6PBOMDIUAMZ7GTDHT4Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of Solutions and Selection Problem for Quasi-stationary Contact Mean Field Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AP","authors_text":"Xiaotian Hu","submitted_at":"2025-07-14T09:57:19Z","abstract_excerpt":"First, we study the existence of solutions for a class of first order mean field games systems\n\\begin{equation*} \\left\\{\\begin{aligned} &H(x,u,Du)=F(x,m(t)),\\quad &&x\\in M,\\ \\forall\\ t\\in[0,T],\\\\ &\\partial_t m-\\text{div}\\left(m\\dfrac{\\partial H}{\\partial p}(x,u,Du)\\right)=0,\\quad &&(x,t)\\in M\\times(0,T],\\\\ &m(0)=m_0, \\end{aligned}\\right. \\end{equation*} where the system comprises a stationary Hamilton-Jacobi equation in the contact case and an evolutionary continuity equation.\n  Then, for any fixed $\\lambda>0$, let $(u^\\lambda,m^\\lambda)$ be a solution of the system \\begin{equation*} \\left\\{ \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10112","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/2507.10112/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:36:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AcbVMDRwsrNnPsuenfsIcYafbgsM/b2tn0v7KT2w5e1vJMgzV2g2YSBB+zl01eAp90eqn2VJRuscK7zwzajRCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T12:56:54.397374Z"},"content_sha256":"648122f0285ce68b68276c7757663715c1066bc750996032a551cece2049cf3b","schema_version":"1.0","event_id":"sha256:648122f0285ce68b68276c7757663715c1066bc750996032a551cece2049cf3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q/bundle.json","state_url":"https://pith.science/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q/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":"2026-08-11T12:56:54Z","links":{"resolver":"https://pith.science/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q","bundle":"https://pith.science/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q/bundle.json","state":"https://pith.science/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPUG4KD6PBOMDIUAMZ7GTDHT4Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OPUG4KD6PBOMDIUAMZ7GTDHT4Q","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":"706ce9db131e793b742f27a22cf70b8c61969c967684bb713e1e275eaf29c160","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-14T09:57:19Z","title_canon_sha256":"a7e23126ac217351ee8b0725f675e3da1e6c246292b429252366a0e8c8c102f2"},"schema_version":"1.0","source":{"id":"2507.10112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.10112","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"arxiv_version","alias_value":"2507.10112v1","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10112","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"pith_short_12","alias_value":"OPUG4KD6PBOM","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"pith_short_16","alias_value":"OPUG4KD6PBOMDIUA","created_at":"2026-07-05T11:36:45Z"},{"alias_kind":"pith_short_8","alias_value":"OPUG4KD6","created_at":"2026-07-05T11:36:45Z"}],"graph_snapshots":[{"event_id":"sha256:648122f0285ce68b68276c7757663715c1066bc750996032a551cece2049cf3b","target":"graph","created_at":"2026-07-05T11:36:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.10112/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"First, we study the existence of solutions for a class of first order mean field games systems\n\\begin{equation*} \\left\\{\\begin{aligned} &H(x,u,Du)=F(x,m(t)),\\quad &&x\\in M,\\ \\forall\\ t\\in[0,T],\\\\ &\\partial_t m-\\text{div}\\left(m\\dfrac{\\partial H}{\\partial p}(x,u,Du)\\right)=0,\\quad &&(x,t)\\in M\\times(0,T],\\\\ &m(0)=m_0, \\end{aligned}\\right. \\end{equation*} where the system comprises a stationary Hamilton-Jacobi equation in the contact case and an evolutionary continuity equation.\n  Then, for any fixed $\\lambda>0$, let $(u^\\lambda,m^\\lambda)$ be a solution of the system \\begin{equation*} \\left\\{ \\","authors_text":"Xiaotian Hu","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-14T09:57:19Z","title":"Existence of Solutions and Selection Problem for Quasi-stationary Contact Mean Field Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10112","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:ce0a215768d493b4f0bf0ede55686d2ad1b475f992e3f74bb2b5cc4d245c6272","target":"record","created_at":"2026-07-05T11:36:45Z","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":"706ce9db131e793b742f27a22cf70b8c61969c967684bb713e1e275eaf29c160","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-07-14T09:57:19Z","title_canon_sha256":"a7e23126ac217351ee8b0725f675e3da1e6c246292b429252366a0e8c8c102f2"},"schema_version":"1.0","source":{"id":"2507.10112","kind":"arxiv","version":1}},"canonical_sha256":"73e86e287e785cc1a280667e698cf3e421b579de0eb4ea685430815c1ad0c000","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73e86e287e785cc1a280667e698cf3e421b579de0eb4ea685430815c1ad0c000","first_computed_at":"2026-07-05T11:36:45.258061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:36:45.258061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hUXXFnnBw/ECWmbnOcCYYbD1DuHTDlyeuhM4rzevJqlBvneSQlfSw3+NJGb5VsZ5MpBTnrsPdfhwTxM/CN4dAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:36:45.258595Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.10112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce0a215768d493b4f0bf0ede55686d2ad1b475f992e3f74bb2b5cc4d245c6272","sha256:648122f0285ce68b68276c7757663715c1066bc750996032a551cece2049cf3b"],"state_sha256":"c27cbda143a605409d244a1be9e310527ce8bd85b0accc303bb1a5a42b1a5d94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/EyKRqYyUeEOaet/ly6VpTrYc+vAMjD7GhdaL52HY9uMQX+J/pV+i3nvP7Jn45qrkavCTa62u4SgrEQvi8tAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T12:56:54.403265Z","bundle_sha256":"b51b06baaad86854451115e5c33e251c6a82cf3458449d5aa7e691694e5e7395"}}