{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NFQB5SRKRU4FCLV7MAH7H37TBO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6f80d7abf450b8ee566accc9b227d8cda561794981d0a88f6a3b0757ee6a7cee","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2022-03-03T03:22:38Z","title_canon_sha256":"3fb6d3b93932b908d5c50dd18f9ce500eac1ebfcb558f0878f068cd47ea66c79"},"schema_version":"1.0","source":{"id":"2203.01500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.01500","created_at":"2026-07-05T04:01:48Z"},{"alias_kind":"arxiv_version","alias_value":"2203.01500v1","created_at":"2026-07-05T04:01:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.01500","created_at":"2026-07-05T04:01:48Z"},{"alias_kind":"pith_short_12","alias_value":"NFQB5SRKRU4F","created_at":"2026-07-05T04:01:48Z"},{"alias_kind":"pith_short_16","alias_value":"NFQB5SRKRU4FCLV7","created_at":"2026-07-05T04:01:48Z"},{"alias_kind":"pith_short_8","alias_value":"NFQB5SRK","created_at":"2026-07-05T04:01:48Z"}],"graph_snapshots":[{"event_id":"sha256:072d4b6c9b3c9fd3cfea5ee9658b999a50e3b3f5241b04e9f6e99de245ba0a42","target":"graph","created_at":"2026-07-05T04:01:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2203.01500/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Although learning has found wide application in multi-agent systems, its effects on the temporal evolution of a system are far from understood. This paper focuses on the dynamics of Q-learning in large-scale multi-agent systems modeled as population games. We revisit the replicator equation model for Q-learning dynamics and observe that this model is inappropriate for our concerned setting. Motivated by this, we develop a new formal model, which bears a formal connection with the continuity equation in physics. We show that our model always accurately describes the Q-learning dynamics in popul","authors_text":"Chin-wing Leung, Harold Soh, Ho-fung Leung, Shuyue Hu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2022-03-03T03:22:38Z","title":"The Dynamics of Q-learning in Population Games: a Physics-Inspired Continuity Equation Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.01500","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2146fd836e54e5f5b213031d3375df993a5f2341cf196090072786c919d9d4ce","target":"record","created_at":"2026-07-05T04:01:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6f80d7abf450b8ee566accc9b227d8cda561794981d0a88f6a3b0757ee6a7cee","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.MA","submitted_at":"2022-03-03T03:22:38Z","title_canon_sha256":"3fb6d3b93932b908d5c50dd18f9ce500eac1ebfcb558f0878f068cd47ea66c79"},"schema_version":"1.0","source":{"id":"2203.01500","kind":"arxiv","version":1}},"canonical_sha256":"69601eca2a8d38512ebf600ff3eff30b87612f153e004ff32437842fcdfcb810","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"69601eca2a8d38512ebf600ff3eff30b87612f153e004ff32437842fcdfcb810","first_computed_at":"2026-07-05T04:01:48.575559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:01:48.575559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWxAWJFoQLZYeo/aukwNpx8qnX86DKMGj2yBGXEXJ47JQjhytJwojJ0ZBeU5dFLviirf6bt7D+wfY4Traq6PAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:01:48.576056Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.01500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2146fd836e54e5f5b213031d3375df993a5f2341cf196090072786c919d9d4ce","sha256:072d4b6c9b3c9fd3cfea5ee9658b999a50e3b3f5241b04e9f6e99de245ba0a42"],"state_sha256":"647bbc0daa47b107f7a2633031fc2fef65ca9972e6695ff89dc3ed31a74987b2"}