{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RYY3J7LJ2ILVB6SFNQZWN5BGLM","short_pith_number":"pith:RYY3J7LJ","schema_version":"1.0","canonical_sha256":"8e31b4fd69d21750fa456c3366f4265b33123abdd9b2be497a8ded8cad0aab4b","source":{"kind":"arxiv","id":"2505.13632","version":1},"attestation_state":"computed","paper":{"title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.OC","authors_text":"Hui Huang, Jethro Warnett","submitted_at":"2025-05-19T18:09:10Z","abstract_excerpt":"Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This paper aims to address theoretical gaps in [12], specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics."},"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":"2505.13632","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2025-05-19T18:09:10Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"44bf4dd70346239a11a923f8dbd32777a9030c869ffc6dc134dbca9bcad61b49","abstract_canon_sha256":"0ed4b8d91abe92029ff9a5f960d229bcc054c2f0e9f8b66a7898f7692dde6692"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:48.732048Z","signature_b64":"vXr4CnLvstznguK0Ib8SsBzkmHzZ4/V71M66SEDgJh05UcJfQYfJgo4/VK2wV+TiDSAz4og01iGDCoX2RAXzAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e31b4fd69d21750fa456c3366f4265b33123abdd9b2be497a8ded8cad0aab4b","last_reissued_at":"2026-07-05T11:05:48.731618Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:48.731618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Well-posedness and mean-field limit estimate of a consensus-based algorithm for multiplayer games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.OC","authors_text":"Hui Huang, Jethro Warnett","submitted_at":"2025-05-19T18:09:10Z","abstract_excerpt":"Recently, the paper [12] introduces a derivative-free consensus-based particle method that finds the Nash equilibrium of non-convex multiplayer games, where it proves the global exponential convergence in the sense of mean-field law. This paper aims to address theoretical gaps in [12], specifically by providing a quantitative estimate of the mean-field limit with respect to the number of particles, as well as establishing the well-posedness of both the finite particle model and the corresponding mean-field dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13632","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/2505.13632/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":"2505.13632","created_at":"2026-07-05T11:05:48.731670+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.13632v1","created_at":"2026-07-05T11:05:48.731670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13632","created_at":"2026-07-05T11:05:48.731670+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYY3J7LJ2ILV","created_at":"2026-07-05T11:05:48.731670+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYY3J7LJ2ILVB6SF","created_at":"2026-07-05T11:05:48.731670+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYY3J7LJ","created_at":"2026-07-05T11:05:48.731670+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/RYY3J7LJ2ILVB6SFNQZWN5BGLM","json":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM.json","graph_json":"https://pith.science/api/pith-number/RYY3J7LJ2ILVB6SFNQZWN5BGLM/graph.json","events_json":"https://pith.science/api/pith-number/RYY3J7LJ2ILVB6SFNQZWN5BGLM/events.json","paper":"https://pith.science/paper/RYY3J7LJ"},"agent_actions":{"view_html":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM","download_json":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM.json","view_paper":"https://pith.science/paper/RYY3J7LJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.13632&json=true","fetch_graph":"https://pith.science/api/pith-number/RYY3J7LJ2ILVB6SFNQZWN5BGLM/graph.json","fetch_events":"https://pith.science/api/pith-number/RYY3J7LJ2ILVB6SFNQZWN5BGLM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM/action/storage_attestation","attest_author":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM/action/author_attestation","sign_citation":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM/action/citation_signature","submit_replication":"https://pith.science/pith/RYY3J7LJ2ILVB6SFNQZWN5BGLM/action/replication_record"}},"created_at":"2026-07-05T11:05:48.731670+00:00","updated_at":"2026-07-05T11:05:48.731670+00:00"}