{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:S2YCN7GAVFNDWVG6TEHSVUSSTI","short_pith_number":"pith:S2YCN7GA","schema_version":"1.0","canonical_sha256":"96b026fcc0a95a3b54de990f2ad2529a38390dc005d9600d2de8fb3082f0fd69","source":{"kind":"arxiv","id":"2304.06673","version":1},"attestation_state":"computed","paper":{"title":"Lipschitz stability for determination of states and inverse source problem for the mean field game equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Masahiro Yamamoto, Oleg Imanuvilov","submitted_at":"2023-04-13T17:00:37Z","abstract_excerpt":"We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\\Omega \\times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where $\\Omega$ is a bounded domain in $\\Bbb R^d$ and $(0,T)$ is the time interval. We first prove the Lipschitz stability in $\\Omega \\times (\\varepsilon, T-\\varepsilon)$ with given $\\varepsilon>0$ for the determination of the solutions by Dirichlet data on arbitrarily chosen subboundary of $\\partial\\Omega$. Next we prove the Lipschitz stability for an inverse proble"},"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":"2304.06673","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-04-13T17:00:37Z","cross_cats_sorted":[],"title_canon_sha256":"2ad2185705e9ca3f0f41ccde0e9c785a6cb33ee2b5e14441d700910ef8856fcc","abstract_canon_sha256":"b798b723a69e186e1914a9e3bfcbe192a11bfc2fc07bd5fb8e4bdb1101ea332d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:00:52.572688Z","signature_b64":"dfeJZh6ChjJQBbqd6DMa1FFefii9iUNqX4ESr28WskJHO1ESpBSRegrfqZS1g1Xh5na1EiBvdXXQNOj+O9tjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b026fcc0a95a3b54de990f2ad2529a38390dc005d9600d2de8fb3082f0fd69","last_reissued_at":"2026-07-05T06:00:52.572231Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:00:52.572231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lipschitz stability for determination of states and inverse source problem for the mean field game equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongyu Liu, Masahiro Yamamoto, Oleg Imanuvilov","submitted_at":"2023-04-13T17:00:37Z","abstract_excerpt":"We consider solutions satisfying the zero Neumann boundary condition and a linearized mean field game equation in $\\Omega \\times (0,T)$ whose principal coefficients depend on the time and spatial variables with general Hamiltonian, where $\\Omega$ is a bounded domain in $\\Bbb R^d$ and $(0,T)$ is the time interval. We first prove the Lipschitz stability in $\\Omega \\times (\\varepsilon, T-\\varepsilon)$ with given $\\varepsilon>0$ for the determination of the solutions by Dirichlet data on arbitrarily chosen subboundary of $\\partial\\Omega$. Next we prove the Lipschitz stability for an inverse proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.06673","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/2304.06673/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2304.06673","created_at":"2026-07-05T06:00:52.572286+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.06673v1","created_at":"2026-07-05T06:00:52.572286+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.06673","created_at":"2026-07-05T06:00:52.572286+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2YCN7GAVFND","created_at":"2026-07-05T06:00:52.572286+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2YCN7GAVFNDWVG6","created_at":"2026-07-05T06:00:52.572286+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2YCN7GA","created_at":"2026-07-05T06:00:52.572286+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.00909","citing_title":"Gaussian process policy iteration with additive Schwarz acceleration for forward and inverse HJB and mean field game problems","ref_index":35,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI","json":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI.json","graph_json":"https://pith.science/api/pith-number/S2YCN7GAVFNDWVG6TEHSVUSSTI/graph.json","events_json":"https://pith.science/api/pith-number/S2YCN7GAVFNDWVG6TEHSVUSSTI/events.json","paper":"https://pith.science/paper/S2YCN7GA"},"agent_actions":{"view_html":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI","download_json":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI.json","view_paper":"https://pith.science/paper/S2YCN7GA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.06673&json=true","fetch_graph":"https://pith.science/api/pith-number/S2YCN7GAVFNDWVG6TEHSVUSSTI/graph.json","fetch_events":"https://pith.science/api/pith-number/S2YCN7GAVFNDWVG6TEHSVUSSTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI/action/storage_attestation","attest_author":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI/action/author_attestation","sign_citation":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI/action/citation_signature","submit_replication":"https://pith.science/pith/S2YCN7GAVFNDWVG6TEHSVUSSTI/action/replication_record"}},"created_at":"2026-07-05T06:00:52.572286+00:00","updated_at":"2026-07-05T06:00:52.572286+00:00"}