{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B37P6BLWQQCLR3PKA735EAUFSB","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":"a6f65794523c6e295b36a9f618bcd92704ae432adb2f177342a2f666961c2518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-22T00:17:48Z","title_canon_sha256":"c2525232055a3ffe25ce4dc2495bcee94a66b2371ba127f97f530fa69af5aa53"},"schema_version":"1.0","source":{"id":"1707.07078","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.07078","created_at":"2026-05-18T00:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1707.07078v3","created_at":"2026-05-18T00:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.07078","created_at":"2026-05-18T00:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"B37P6BLWQQCL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B37P6BLWQQCLR3PK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B37P6BLW","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:a57c8be541c9d8cfc5661f8e0119a9e60ee4a907d9523bcb0d8cc465628005f0","target":"graph","created_at":"2026-05-18T00:29:05Z","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":"We prove existence of solutions for a class of systems of subelliptic PDEs arising from Mean Field Game systems with H\\\"ormander diffusion. These results are motivated by the feedback synthesis Mean Field Game solutions and the Nash equilibria of a large class of $N$-player differential games.","authors_text":"Ermal Feleqi, Federica Dragoni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-22T00:17:48Z","title":"Ergodic Mean Field Games with H\\\"ormander diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07078","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":"sha256:84e3563b27b5e23d6c110ae9323785b9e5c8819ed81853b4011ea2e8f37767a0","target":"record","created_at":"2026-05-18T00:29:05Z","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":"a6f65794523c6e295b36a9f618bcd92704ae432adb2f177342a2f666961c2518","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-22T00:17:48Z","title_canon_sha256":"c2525232055a3ffe25ce4dc2495bcee94a66b2371ba127f97f530fa69af5aa53"},"schema_version":"1.0","source":{"id":"1707.07078","kind":"arxiv","version":3}},"canonical_sha256":"0efeff05768404b8edea07f7d20285907aba13ecbadb82d4ee5b2c1975570f56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0efeff05768404b8edea07f7d20285907aba13ecbadb82d4ee5b2c1975570f56","first_computed_at":"2026-05-18T00:29:05.596862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:05.596862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qYbI8Q6c1p9YCh7HFr1mAyd1ussJD8qUHXQXTu5RuxcuAIZeBUX5I1nKUm6NBGtDAqLts0fb/GxnLC1UPK4kCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:05.597445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.07078","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84e3563b27b5e23d6c110ae9323785b9e5c8819ed81853b4011ea2e8f37767a0","sha256:a57c8be541c9d8cfc5661f8e0119a9e60ee4a907d9523bcb0d8cc465628005f0"],"state_sha256":"ae064569e4b971ae5d78f0c1cba6e46d895ba68b77c5917a89a97162722acd3f"}