{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MLXNJ2LXG2U3JI64ID7FP5J67R","short_pith_number":"pith:MLXNJ2LX","canonical_record":{"source":{"id":"1502.06026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T22:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"f40ada2f89e2d2b20b572fcf69de2a43dace3561d3eaaa5940046ef8f8dd62b7","abstract_canon_sha256":"b4f7642928b734e4d6b5e8915d2e377212ed0a27c754a738013dac3ff2cd273d"},"schema_version":"1.0"},"canonical_sha256":"62eed4e97736a9b4a3dc40fe57f53efc7b28eb77549c0c4a221f4bdf403b8a7d","source":{"kind":"arxiv","id":"1502.06026","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06026","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06026v3","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06026","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"MLXNJ2LXG2U3","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MLXNJ2LXG2U3JI64","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MLXNJ2LX","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MLXNJ2LXG2U3JI64ID7FP5J67R","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06026","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T22:40:38Z","cross_cats_sorted":[],"title_canon_sha256":"f40ada2f89e2d2b20b572fcf69de2a43dace3561d3eaaa5940046ef8f8dd62b7","abstract_canon_sha256":"b4f7642928b734e4d6b5e8915d2e377212ed0a27c754a738013dac3ff2cd273d"},"schema_version":"1.0"},"canonical_sha256":"62eed4e97736a9b4a3dc40fe57f53efc7b28eb77549c0c4a221f4bdf403b8a7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:42.433387Z","signature_b64":"de0GccPEb5/0o1U4GECB1FHZSlFwmUjJfELPtfrYaYJbZJaC4hN02qrkRqNDK3tz+iOJ4OOS0yHwEkul+umMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62eed4e97736a9b4a3dc40fe57f53efc7b28eb77549c0c4a221f4bdf403b8a7d","last_reissued_at":"2026-05-18T01:19:42.432879Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:42.432879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06026","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lD0rKwok+UgtHatclPjIE48Jmt8kBWv9pGuHq4Xj8eaj0IHwx2WzV/R/6ecdfXwr8M8cB4ZuhGdoPuP9I1UTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:40:42.123028Z"},"content_sha256":"05bf2898bf9f325a8db286c63043b31163138508d3034e03a41802234e5ffc9a","schema_version":"1.0","event_id":"sha256:05bf2898bf9f325a8db286c63043b31163138508d3034e03a41802234e5ffc9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MLXNJ2LXG2U3JI64ID7FP5J67R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variational approach to second order mean field games with density constraints: the stationary case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alp\\'ar Rich\\'ard M\\'esz\\'aros, Francisco J. Silva","submitted_at":"2015-02-20T22:40:38Z","abstract_excerpt":"In this paper we study second order stationary Mean Field Game systems under density constraints on a bounded domain $\\Omega \\subset \\mathbb{R}^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of growth. Our strategy is a variational one, i.e. we obtain the Mean Field Game system as the optimality condition of a convex optimization problem, which has a solution. When the Hamiltonian has a growth of order $q' \\in ]1, d/(d-1)[$, the solution of the optimization problem is continuous which implies that the problem constraints are qualified. Using this f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06026","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mSHgeKNTVwwqhWfYJ/phC9zRF/C1GdnE66boP7Sg3sNUCdNZYFTOXzTT11HZ4JEMtgmbVKG6CDN+Sq59zxvYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:40:42.123389Z"},"content_sha256":"61bcd2c7197a7de5d2feb574c823cc6cafb21fba60533eebec9b7c47d7afcb96","schema_version":"1.0","event_id":"sha256:61bcd2c7197a7de5d2feb574c823cc6cafb21fba60533eebec9b7c47d7afcb96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MLXNJ2LXG2U3JI64ID7FP5J67R/bundle.json","state_url":"https://pith.science/pith/MLXNJ2LXG2U3JI64ID7FP5J67R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MLXNJ2LXG2U3JI64ID7FP5J67R/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":"2026-05-27T20:40:42Z","links":{"resolver":"https://pith.science/pith/MLXNJ2LXG2U3JI64ID7FP5J67R","bundle":"https://pith.science/pith/MLXNJ2LXG2U3JI64ID7FP5J67R/bundle.json","state":"https://pith.science/pith/MLXNJ2LXG2U3JI64ID7FP5J67R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MLXNJ2LXG2U3JI64ID7FP5J67R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MLXNJ2LXG2U3JI64ID7FP5J67R","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":"b4f7642928b734e4d6b5e8915d2e377212ed0a27c754a738013dac3ff2cd273d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T22:40:38Z","title_canon_sha256":"f40ada2f89e2d2b20b572fcf69de2a43dace3561d3eaaa5940046ef8f8dd62b7"},"schema_version":"1.0","source":{"id":"1502.06026","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06026","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06026v3","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06026","created_at":"2026-05-18T01:19:42Z"},{"alias_kind":"pith_short_12","alias_value":"MLXNJ2LXG2U3","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MLXNJ2LXG2U3JI64","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MLXNJ2LX","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:61bcd2c7197a7de5d2feb574c823cc6cafb21fba60533eebec9b7c47d7afcb96","target":"graph","created_at":"2026-05-18T01:19:42Z","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 study second order stationary Mean Field Game systems under density constraints on a bounded domain $\\Omega \\subset \\mathbb{R}^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of growth. Our strategy is a variational one, i.e. we obtain the Mean Field Game system as the optimality condition of a convex optimization problem, which has a solution. When the Hamiltonian has a growth of order $q' \\in ]1, d/(d-1)[$, the solution of the optimization problem is continuous which implies that the problem constraints are qualified. Using this f","authors_text":"Alp\\'ar Rich\\'ard M\\'esz\\'aros, Francisco J. Silva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T22:40:38Z","title":"A variational approach to second order mean field games with density constraints: the stationary case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06026","kind":"arxiv","version":3},"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":"sha256:05bf2898bf9f325a8db286c63043b31163138508d3034e03a41802234e5ffc9a","target":"record","created_at":"2026-05-18T01:19:42Z","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":"b4f7642928b734e4d6b5e8915d2e377212ed0a27c754a738013dac3ff2cd273d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-20T22:40:38Z","title_canon_sha256":"f40ada2f89e2d2b20b572fcf69de2a43dace3561d3eaaa5940046ef8f8dd62b7"},"schema_version":"1.0","source":{"id":"1502.06026","kind":"arxiv","version":3}},"canonical_sha256":"62eed4e97736a9b4a3dc40fe57f53efc7b28eb77549c0c4a221f4bdf403b8a7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62eed4e97736a9b4a3dc40fe57f53efc7b28eb77549c0c4a221f4bdf403b8a7d","first_computed_at":"2026-05-18T01:19:42.432879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:42.432879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"de0GccPEb5/0o1U4GECB1FHZSlFwmUjJfELPtfrYaYJbZJaC4hN02qrkRqNDK3tz+iOJ4OOS0yHwEkul+umMCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:42.433387Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06026","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05bf2898bf9f325a8db286c63043b31163138508d3034e03a41802234e5ffc9a","sha256:61bcd2c7197a7de5d2feb574c823cc6cafb21fba60533eebec9b7c47d7afcb96"],"state_sha256":"5f8f4d3de40bcfdf39cbe29fed92a5947de05807804a094866044f9e6869ff08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9jG+3u2LDA7N4zpYhT7dpx9ocpfW0GGZeJpxzkN+QSJtKvL2RE0pjxuRF3lA6nO/9TDrc8Oi3Lh2OBF6YaaVDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:40:42.126556Z","bundle_sha256":"69d3362a2da79be04a63ff521559f787fdaf5933e56b238e9b6ef05cc7d49187"}}