{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:M7S4GN22ZLYCZ7TRMKSTNVFGBI","short_pith_number":"pith:M7S4GN22","schema_version":"1.0","canonical_sha256":"67e5c3375acaf02cfe7162a536d4a60a2eb687acf4b78966e4105dc20ba129de","source":{"kind":"arxiv","id":"1805.11290","version":1},"attestation_state":"computed","paper":{"title":"A Class of Infinite Horizon Mean Field Games on Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manh-Khang Dao (IRMAR), Nicoletta Tchou (IRMAR), Olivier Ley (IRMAR), Yves Achdou (LJLL)","submitted_at":"2018-05-29T08:05:44Z","abstract_excerpt":"We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant measure m, a value function u, and the ergodic constant $\\rho$. The function u is continuous and satisfies general Kirchhoff conditions at the vertices. The invariant measure m satisfies dual transmission conditions: in particular, m is discontinuous across the vertices in general, and the values of m on each side of the vertices satisfy special compatibility"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.11290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-29T08:05:44Z","cross_cats_sorted":[],"title_canon_sha256":"62aa0c71b0761c7ea20470061d48cf554a8ab07f54422d0e247cb599337fc9d2","abstract_canon_sha256":"9ff660f2ec13b65033548b33edd91095273e1d15fc101a4081a9d41d47111bea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:43.055998Z","signature_b64":"YXl1omh8PBrcHRChDcu1zS+0RSdKzLqG/r0zvkI6DpfwwU8s8sdOBLrb9ouoC2BAoEnSeWPyTXEwXRw70H0QDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67e5c3375acaf02cfe7162a536d4a60a2eb687acf4b78966e4105dc20ba129de","last_reissued_at":"2026-05-18T00:14:43.055553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:43.055553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Class of Infinite Horizon Mean Field Games on Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Manh-Khang Dao (IRMAR), Nicoletta Tchou (IRMAR), Olivier Ley (IRMAR), Yves Achdou (LJLL)","submitted_at":"2018-05-29T08:05:44Z","abstract_excerpt":"We consider stochastic mean field games for which the state space is a network. In the ergodic case, they are described by a system coupling a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation, whose unknowns are the invariant measure m, a value function u, and the ergodic constant $\\rho$. The function u is continuous and satisfies general Kirchhoff conditions at the vertices. The invariant measure m satisfies dual transmission conditions: in particular, m is discontinuous across the vertices in general, and the values of m on each side of the vertices satisfy special compatibility"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11290","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.11290","created_at":"2026-05-18T00:14:43.055622+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.11290v1","created_at":"2026-05-18T00:14:43.055622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.11290","created_at":"2026-05-18T00:14:43.055622+00:00"},{"alias_kind":"pith_short_12","alias_value":"M7S4GN22ZLYC","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"M7S4GN22ZLYCZ7TR","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"M7S4GN22","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI","json":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI.json","graph_json":"https://pith.science/api/pith-number/M7S4GN22ZLYCZ7TRMKSTNVFGBI/graph.json","events_json":"https://pith.science/api/pith-number/M7S4GN22ZLYCZ7TRMKSTNVFGBI/events.json","paper":"https://pith.science/paper/M7S4GN22"},"agent_actions":{"view_html":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI","download_json":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI.json","view_paper":"https://pith.science/paper/M7S4GN22","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.11290&json=true","fetch_graph":"https://pith.science/api/pith-number/M7S4GN22ZLYCZ7TRMKSTNVFGBI/graph.json","fetch_events":"https://pith.science/api/pith-number/M7S4GN22ZLYCZ7TRMKSTNVFGBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI/action/storage_attestation","attest_author":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI/action/author_attestation","sign_citation":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI/action/citation_signature","submit_replication":"https://pith.science/pith/M7S4GN22ZLYCZ7TRMKSTNVFGBI/action/replication_record"}},"created_at":"2026-05-18T00:14:43.055622+00:00","updated_at":"2026-05-18T00:14:43.055622+00:00"}