{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZJTQJ4VPEG7IYO7DWDH26JK2TE","short_pith_number":"pith:ZJTQJ4VP","canonical_record":{"source":{"id":"1503.06445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-22T17:10:47Z","cross_cats_sorted":[],"title_canon_sha256":"47cfc5c1926a0a8e38385a9d83008537a43fdffdf153e8885a2c6feae2188bda","abstract_canon_sha256":"f92bf2385bb3e40b546f82d7693f8d1c1a1efb1c968ddd68486089292e554500"},"schema_version":"1.0"},"canonical_sha256":"ca6704f2af21be8c3be3b0cfaf255a99261c5728e232e2008194eddd151cc9ab","source":{"kind":"arxiv","id":"1503.06445","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06445","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06445v1","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06445","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZJTQJ4VPEG7I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZJTQJ4VPEG7IYO7D","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZJTQJ4VP","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZJTQJ4VPEG7IYO7DWDH26JK2TE","target":"record","payload":{"canonical_record":{"source":{"id":"1503.06445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-22T17:10:47Z","cross_cats_sorted":[],"title_canon_sha256":"47cfc5c1926a0a8e38385a9d83008537a43fdffdf153e8885a2c6feae2188bda","abstract_canon_sha256":"f92bf2385bb3e40b546f82d7693f8d1c1a1efb1c968ddd68486089292e554500"},"schema_version":"1.0"},"canonical_sha256":"ca6704f2af21be8c3be3b0cfaf255a99261c5728e232e2008194eddd151cc9ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:38.400507Z","signature_b64":"FM89M9CS1e0LCSwxeQf0xCkMaiB95RZ2dFCGWBr9j7ubZIdK8PEg67322FsCpBjazQRtfgl7kDQ/L5ZSqSitBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca6704f2af21be8c3be3b0cfaf255a99261c5728e232e2008194eddd151cc9ab","last_reissued_at":"2026-05-18T02:20:38.399849Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:38.399849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.06445","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":"2026-05-18T02:20:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vwT2XZ88dcAE0Bgy/h9YE01alHL+CAIFvb4KS8r8DtjPT0PIATx0OesiBE0xGkk8rAa9N7QkC2pOmKd+PjidDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:36:12.349397Z"},"content_sha256":"4c804ddb67b9f1a1cf77dca6ac3f8e6f90371b83011c8829b0ead2601913b8cc","schema_version":"1.0","event_id":"sha256:4c804ddb67b9f1a1cf77dca6ac3f8e6f90371b83011c8829b0ead2601913b8cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZJTQJ4VPEG7IYO7DWDH26JK2TE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity for second order stationary mean-field games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edgard A. Pimentel, Vardan Voskanyan","submitted_at":"2015-03-22T17:10:47Z","abstract_excerpt":"In this paper, we prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of long-time behavior of time-dependent mean-field games. Our argument is based on the interplay between the regularity of solutions of the Hamilton-Jacobi equation in terms of the solutions of the Fokker-Planck equation and vice-versa. Because we consider different classes of couplings, distinct techniques are used to obtain a priori estimates for the density"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06445","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":"2026-05-18T02:20:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpSd3/rOdrI4HeKgRHgzucCGeA7Bx7Jnfjhfvi5MhAgGb/WTGhgNvi0Ou/+BxmqPid5EnVdFxexF1oiifZ1sBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:36:12.349752Z"},"content_sha256":"160df9883ba35d4ebf376aff5a1a751bae4be168ce537f45e742d269d4c88b09","schema_version":"1.0","event_id":"sha256:160df9883ba35d4ebf376aff5a1a751bae4be168ce537f45e742d269d4c88b09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE/bundle.json","state_url":"https://pith.science/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE/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":"2026-06-01T09:36:12Z","links":{"resolver":"https://pith.science/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE","bundle":"https://pith.science/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE/bundle.json","state":"https://pith.science/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJTQJ4VPEG7IYO7DWDH26JK2TE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZJTQJ4VPEG7IYO7DWDH26JK2TE","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":"f92bf2385bb3e40b546f82d7693f8d1c1a1efb1c968ddd68486089292e554500","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-22T17:10:47Z","title_canon_sha256":"47cfc5c1926a0a8e38385a9d83008537a43fdffdf153e8885a2c6feae2188bda"},"schema_version":"1.0","source":{"id":"1503.06445","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06445","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06445v1","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06445","created_at":"2026-05-18T02:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZJTQJ4VPEG7I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZJTQJ4VPEG7IYO7D","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZJTQJ4VP","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:160df9883ba35d4ebf376aff5a1a751bae4be168ce537f45e742d269d4c88b09","target":"graph","created_at":"2026-05-18T02:20:38Z","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 prove the existence of classical solutions for second order stationary mean-field game systems. These arise in ergodic (mean-field) optimal control, convex degenerate problems in calculus of variations, and in the study of long-time behavior of time-dependent mean-field games. Our argument is based on the interplay between the regularity of solutions of the Hamilton-Jacobi equation in terms of the solutions of the Fokker-Planck equation and vice-versa. Because we consider different classes of couplings, distinct techniques are used to obtain a priori estimates for the density","authors_text":"Edgard A. Pimentel, Vardan Voskanyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-22T17:10:47Z","title":"Regularity for second order stationary mean-field games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06445","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":"sha256:4c804ddb67b9f1a1cf77dca6ac3f8e6f90371b83011c8829b0ead2601913b8cc","target":"record","created_at":"2026-05-18T02:20:38Z","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":"f92bf2385bb3e40b546f82d7693f8d1c1a1efb1c968ddd68486089292e554500","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-22T17:10:47Z","title_canon_sha256":"47cfc5c1926a0a8e38385a9d83008537a43fdffdf153e8885a2c6feae2188bda"},"schema_version":"1.0","source":{"id":"1503.06445","kind":"arxiv","version":1}},"canonical_sha256":"ca6704f2af21be8c3be3b0cfaf255a99261c5728e232e2008194eddd151cc9ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca6704f2af21be8c3be3b0cfaf255a99261c5728e232e2008194eddd151cc9ab","first_computed_at":"2026-05-18T02:20:38.399849Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:38.399849Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FM89M9CS1e0LCSwxeQf0xCkMaiB95RZ2dFCGWBr9j7ubZIdK8PEg67322FsCpBjazQRtfgl7kDQ/L5ZSqSitBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:38.400507Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06445","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c804ddb67b9f1a1cf77dca6ac3f8e6f90371b83011c8829b0ead2601913b8cc","sha256:160df9883ba35d4ebf376aff5a1a751bae4be168ce537f45e742d269d4c88b09"],"state_sha256":"bfa02080100218d43e7a768c9d09425611adee1960a1b35f639a6aca2fa08217"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYILZQCJuApxTA37cHrl76/GqgsQnrhtZqTWErcNqpm/003AOF7bDxZ80QK/xdKHCpf9ecIUmp7CfV0NQEowAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:36:12.351731Z","bundle_sha256":"f94cd6e2b6e96f053d98684c3ec2356f284f4d64487731b6248b0c0a1b641890"}}