{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:TQVPJTEJ3X3WCTH64ZCZWIT77W","short_pith_number":"pith:TQVPJTEJ","schema_version":"1.0","canonical_sha256":"9c2af4cc89ddf7614cfee6459b227ffdbd7c82d04a677b5d1c8f1fca843a8d9b","source":{"kind":"arxiv","id":"2312.07598","version":1},"attestation_state":"computed","paper":{"title":"Differential Equation Approximations for Population Games using Elementary Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","cs.SY","eess.SY","math.DS","math.PR","stat.AP"],"primary_cat":"cs.GT","authors_text":"Nuno C. Martins, Semih Kara","submitted_at":"2023-12-11T13:28:24Z","abstract_excerpt":"Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary differential equations. This mean-field approach has found to be an effective tool of analysis. However its current proofs rely on advanced mathematical techniques, making them less accessible. In this article, we present a simpler derivation, using only undergraduate-level probability."},"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":"2312.07598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2023-12-11T13:28:24Z","cross_cats_sorted":["cs.MA","cs.SY","eess.SY","math.DS","math.PR","stat.AP"],"title_canon_sha256":"799076714abf8c17d282f353d1b91e160239c5a526de596a5a155f295baa0492","abstract_canon_sha256":"1fac070f8754474490e0b27fcdd05cfca79910937cd220be7b5c5248dc770527"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:23:33.250033Z","signature_b64":"H+HM3farbp/YDCttFfNnic5Z6yyJdKTcfeBNodlpC7D1vskNCdvHtkuE2AzH3FWGiTndGuJaTeNF7Klca961Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c2af4cc89ddf7614cfee6459b227ffdbd7c82d04a677b5d1c8f1fca843a8d9b","last_reissued_at":"2026-07-05T07:23:33.249625Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:23:33.249625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differential Equation Approximations for Population Games using Elementary Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","cs.SY","eess.SY","math.DS","math.PR","stat.AP"],"primary_cat":"cs.GT","authors_text":"Nuno C. Martins, Semih Kara","submitted_at":"2023-12-11T13:28:24Z","abstract_excerpt":"Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary differential equations. This mean-field approach has found to be an effective tool of analysis. However its current proofs rely on advanced mathematical techniques, making them less accessible. In this article, we present a simpler derivation, using only undergraduate-level probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.07598","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/2312.07598/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":"2312.07598","created_at":"2026-07-05T07:23:33.249687+00:00"},{"alias_kind":"arxiv_version","alias_value":"2312.07598v1","created_at":"2026-07-05T07:23:33.249687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.07598","created_at":"2026-07-05T07:23:33.249687+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQVPJTEJ3X3W","created_at":"2026-07-05T07:23:33.249687+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQVPJTEJ3X3WCTH6","created_at":"2026-07-05T07:23:33.249687+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQVPJTEJ","created_at":"2026-07-05T07:23:33.249687+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.19371","citing_title":"Aggregate Fictitious Play for Learning in Anonymous Polymatrix Games (Extended Version)","ref_index":20,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W","json":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W.json","graph_json":"https://pith.science/api/pith-number/TQVPJTEJ3X3WCTH64ZCZWIT77W/graph.json","events_json":"https://pith.science/api/pith-number/TQVPJTEJ3X3WCTH64ZCZWIT77W/events.json","paper":"https://pith.science/paper/TQVPJTEJ"},"agent_actions":{"view_html":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W","download_json":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W.json","view_paper":"https://pith.science/paper/TQVPJTEJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2312.07598&json=true","fetch_graph":"https://pith.science/api/pith-number/TQVPJTEJ3X3WCTH64ZCZWIT77W/graph.json","fetch_events":"https://pith.science/api/pith-number/TQVPJTEJ3X3WCTH64ZCZWIT77W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W/action/storage_attestation","attest_author":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W/action/author_attestation","sign_citation":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W/action/citation_signature","submit_replication":"https://pith.science/pith/TQVPJTEJ3X3WCTH64ZCZWIT77W/action/replication_record"}},"created_at":"2026-07-05T07:23:33.249687+00:00","updated_at":"2026-07-05T07:23:33.249687+00:00"}