{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:H2FX2YUFVA7HGYC57EX2SJ265F","short_pith_number":"pith:H2FX2YUF","canonical_record":{"source":{"id":"1908.06485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T17:18:11Z","cross_cats_sorted":[],"title_canon_sha256":"88481a350f38a97b6f6e6f11ab19e1396c5cbe17e641e240d717fbc84a549db5","abstract_canon_sha256":"cefacad53e6e0d6b20d3d1329401ba1a95a89db54655b329673efad123cf5d82"},"schema_version":"1.0"},"canonical_sha256":"3e8b7d6285a83e73605df92fa9275ee942466b5b3710c09686a3a72698f8ffe6","source":{"kind":"arxiv","id":"1908.06485","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06485","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06485v1","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06485","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"pith_short_12","alias_value":"H2FX2YUFVA7H","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"pith_short_16","alias_value":"H2FX2YUFVA7HGYC5","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"pith_short_8","alias_value":"H2FX2YUF","created_at":"2026-07-04T23:58:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:H2FX2YUFVA7HGYC57EX2SJ265F","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06485","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T17:18:11Z","cross_cats_sorted":[],"title_canon_sha256":"88481a350f38a97b6f6e6f11ab19e1396c5cbe17e641e240d717fbc84a549db5","abstract_canon_sha256":"cefacad53e6e0d6b20d3d1329401ba1a95a89db54655b329673efad123cf5d82"},"schema_version":"1.0"},"canonical_sha256":"3e8b7d6285a83e73605df92fa9275ee942466b5b3710c09686a3a72698f8ffe6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:16.213549Z","signature_b64":"ZMUWvqo02v+I8Hh+3D24u+RebwpJelgdpFUSGKr/SQ+5IgiupxhAZmlPLYqF1IX3t51+afDXGUanAbGA9o6nDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e8b7d6285a83e73605df92fa9275ee942466b5b3710c09686a3a72698f8ffe6","last_reissued_at":"2026-07-04T23:58:16.213198Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:16.213198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06485","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":"2026-07-04T23:58:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KNiKusjDggrpPdYORKFx2mvTp+hdSD51KbGxt6l/51OTRVFYaJ154t+6+l8NpjfPg9l0YZdqo4592JiIvFgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:24:02.181885Z"},"content_sha256":"95e39b31314663e431ca3f52c0236bdb39e8b9938896f3bfc6ab81e3223df3fe","schema_version":"1.0","event_id":"sha256:95e39b31314663e431ca3f52c0236bdb39e8b9938896f3bfc6ab81e3223df3fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:H2FX2YUFVA7HGYC57EX2SJ265F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The selection problem for some first-order stationary mean-field games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Diogo A. Gomes, Hiroyoshi Mitake, Kengo Terai","submitted_at":"2019-08-18T17:18:11Z","abstract_excerpt":"Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence of the vanishing-discount limit to a unique solution up to constants. Then, we establish refined asymptotics for the limit. When those conditions do not hold, the limit problem may not have a unique solution and its solutions may not be smooth, as we illustrate in an elementary example. Finally, we investigate the stability of regular weak solutions and addre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06485","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/1908.06485/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":"2026-07-04T23:58:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDr55kaAzuPLbGYrmABeT/ZUbi/wmJebotazj+1tO8o6NkLJ4n3y0DKOXAXFCzyUwRAaLl/y9Cg4RQbBK+KbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:24:02.182413Z"},"content_sha256":"4b97291e352b897b778fb166a16be1f905f79d1401b6a53be9ee6453207b33f5","schema_version":"1.0","event_id":"sha256:4b97291e352b897b778fb166a16be1f905f79d1401b6a53be9ee6453207b33f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2FX2YUFVA7HGYC57EX2SJ265F/bundle.json","state_url":"https://pith.science/pith/H2FX2YUFVA7HGYC57EX2SJ265F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2FX2YUFVA7HGYC57EX2SJ265F/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":"2026-08-16T05:24:02Z","links":{"resolver":"https://pith.science/pith/H2FX2YUFVA7HGYC57EX2SJ265F","bundle":"https://pith.science/pith/H2FX2YUFVA7HGYC57EX2SJ265F/bundle.json","state":"https://pith.science/pith/H2FX2YUFVA7HGYC57EX2SJ265F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2FX2YUFVA7HGYC57EX2SJ265F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:H2FX2YUFVA7HGYC57EX2SJ265F","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":"cefacad53e6e0d6b20d3d1329401ba1a95a89db54655b329673efad123cf5d82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T17:18:11Z","title_canon_sha256":"88481a350f38a97b6f6e6f11ab19e1396c5cbe17e641e240d717fbc84a549db5"},"schema_version":"1.0","source":{"id":"1908.06485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06485","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06485v1","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06485","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"pith_short_12","alias_value":"H2FX2YUFVA7H","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"pith_short_16","alias_value":"H2FX2YUFVA7HGYC5","created_at":"2026-07-04T23:58:16Z"},{"alias_kind":"pith_short_8","alias_value":"H2FX2YUF","created_at":"2026-07-04T23:58:16Z"}],"graph_snapshots":[{"event_id":"sha256:4b97291e352b897b778fb166a16be1f905f79d1401b6a53be9ee6453207b33f5","target":"graph","created_at":"2026-07-04T23:58:16Z","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/1908.06485/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Here, we study the existence and the convergence of solutions for the vanishing discount MFG problem with a quadratic Hamiltonian. We give conditions under which the discounted problem has a unique classical solution and prove convergence of the vanishing-discount limit to a unique solution up to constants. Then, we establish refined asymptotics for the limit. When those conditions do not hold, the limit problem may not have a unique solution and its solutions may not be smooth, as we illustrate in an elementary example. Finally, we investigate the stability of regular weak solutions and addre","authors_text":"Diogo A. Gomes, Hiroyoshi Mitake, Kengo Terai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T17:18:11Z","title":"The selection problem for some first-order stationary mean-field games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06485","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":"sha256:95e39b31314663e431ca3f52c0236bdb39e8b9938896f3bfc6ab81e3223df3fe","target":"record","created_at":"2026-07-04T23:58:16Z","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":"cefacad53e6e0d6b20d3d1329401ba1a95a89db54655b329673efad123cf5d82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T17:18:11Z","title_canon_sha256":"88481a350f38a97b6f6e6f11ab19e1396c5cbe17e641e240d717fbc84a549db5"},"schema_version":"1.0","source":{"id":"1908.06485","kind":"arxiv","version":1}},"canonical_sha256":"3e8b7d6285a83e73605df92fa9275ee942466b5b3710c09686a3a72698f8ffe6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e8b7d6285a83e73605df92fa9275ee942466b5b3710c09686a3a72698f8ffe6","first_computed_at":"2026-07-04T23:58:16.213198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:16.213198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZMUWvqo02v+I8Hh+3D24u+RebwpJelgdpFUSGKr/SQ+5IgiupxhAZmlPLYqF1IX3t51+afDXGUanAbGA9o6nDw==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:16.213549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95e39b31314663e431ca3f52c0236bdb39e8b9938896f3bfc6ab81e3223df3fe","sha256:4b97291e352b897b778fb166a16be1f905f79d1401b6a53be9ee6453207b33f5"],"state_sha256":"c6491f67f729cca00a0a97b1b22bf3907882c9f2f821a2ef6c39fee5fc067a3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xpzNvaAdH8FLb6BjCtjE0YyFUg8v4Wo500GLAjX94U/gJ/m4fLwsvFSe9pUHDfZzqhab/2Re/9WOcTc+9pIVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:24:02.187884Z","bundle_sha256":"608ca7e31bd8a8e46c3964af2ade311a67d2a7eeb7d17733b5988ed9594f3605"}}