{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:AL3NC47JGMXEIYVN4JBP4YPVMH","short_pith_number":"pith:AL3NC47J","schema_version":"1.0","canonical_sha256":"02f6d173e9332e4462ade242fe61f561d0251795f0c0993a2ff5baf7faef0d4d","source":{"kind":"arxiv","id":"1908.03643","version":2},"attestation_state":"computed","paper":{"title":"Unique ergodicity of deterministic zero-sum differential games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antoine Hochart","submitted_at":"2019-08-09T21:58:29Z","abstract_excerpt":"We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or equivalently, the averaged finite-horizon value as the time goes to infinity. We provide necessary and sufficient conditions for the unique ergodicity of a game. This notion extends the classical one for dynamical systems, namely when ergodicity holds with any (suitable) perturbation of the running payoff function. Our main condition is symmetric between the two"},"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":"1908.03643","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-09T21:58:29Z","cross_cats_sorted":[],"title_canon_sha256":"66970029c9925679cf3054accacc9f963ed30f05459f94516c24776f65b3433d","abstract_canon_sha256":"c9a39fe698b6509e1d9abe258be3bc5c11b3ce56da84e4ba75174833b44d15fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:30:20.910685Z","signature_b64":"3z2LROIlZfZIlpyb68+3cerZXBTQ5ZlXGPNEfPMFPVgYu/RqdEvef1dxUvMhTg0iv2kMRtRWDWA/NsryOeopAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02f6d173e9332e4462ade242fe61f561d0251795f0c0993a2ff5baf7faef0d4d","last_reissued_at":"2026-07-05T00:30:20.910256Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:30:20.910256Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unique ergodicity of deterministic zero-sum differential games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antoine Hochart","submitted_at":"2019-08-09T21:58:29Z","abstract_excerpt":"We study the ergodicity of deterministic two-person zero-sum differential games. This property is defined by the uniform convergence to a constant of either the infinite-horizon discounted value as the discount factor tends to zero, or equivalently, the averaged finite-horizon value as the time goes to infinity. We provide necessary and sufficient conditions for the unique ergodicity of a game. This notion extends the classical one for dynamical systems, namely when ergodicity holds with any (suitable) perturbation of the running payoff function. Our main condition is symmetric between the two"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03643","kind":"arxiv","version":2},"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/1908.03643/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":"1908.03643","created_at":"2026-07-05T00:30:20.910326+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.03643v2","created_at":"2026-07-05T00:30:20.910326+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03643","created_at":"2026-07-05T00:30:20.910326+00:00"},{"alias_kind":"pith_short_12","alias_value":"AL3NC47JGMXE","created_at":"2026-07-05T00:30:20.910326+00:00"},{"alias_kind":"pith_short_16","alias_value":"AL3NC47JGMXEIYVN","created_at":"2026-07-05T00:30:20.910326+00:00"},{"alias_kind":"pith_short_8","alias_value":"AL3NC47J","created_at":"2026-07-05T00:30:20.910326+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/AL3NC47JGMXEIYVN4JBP4YPVMH","json":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH.json","graph_json":"https://pith.science/api/pith-number/AL3NC47JGMXEIYVN4JBP4YPVMH/graph.json","events_json":"https://pith.science/api/pith-number/AL3NC47JGMXEIYVN4JBP4YPVMH/events.json","paper":"https://pith.science/paper/AL3NC47J"},"agent_actions":{"view_html":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH","download_json":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH.json","view_paper":"https://pith.science/paper/AL3NC47J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.03643&json=true","fetch_graph":"https://pith.science/api/pith-number/AL3NC47JGMXEIYVN4JBP4YPVMH/graph.json","fetch_events":"https://pith.science/api/pith-number/AL3NC47JGMXEIYVN4JBP4YPVMH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH/action/storage_attestation","attest_author":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH/action/author_attestation","sign_citation":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH/action/citation_signature","submit_replication":"https://pith.science/pith/AL3NC47JGMXEIYVN4JBP4YPVMH/action/replication_record"}},"created_at":"2026-07-05T00:30:20.910326+00:00","updated_at":"2026-07-05T00:30:20.910326+00:00"}