{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HOMQDBMPPCDFHT3FN7DQNN2TBI","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":"0894a9b31caa6f44e2a2341d6ced5a08f4b13e2c8a4aaf5b36714790ac6af351","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2023-08-23T00:18:17Z","title_canon_sha256":"ed7474acaf723ca431524c068d2adb704aff2cebdf5a942a3fb545ab57e4b9dd"},"schema_version":"1.0","source":{"id":"2308.11842","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.11842","created_at":"2026-07-05T08:23:11Z"},{"alias_kind":"arxiv_version","alias_value":"2308.11842v3","created_at":"2026-07-05T08:23:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.11842","created_at":"2026-07-05T08:23:11Z"},{"alias_kind":"pith_short_12","alias_value":"HOMQDBMPPCDF","created_at":"2026-07-05T08:23:11Z"},{"alias_kind":"pith_short_16","alias_value":"HOMQDBMPPCDFHT3F","created_at":"2026-07-05T08:23:11Z"},{"alias_kind":"pith_short_8","alias_value":"HOMQDBMP","created_at":"2026-07-05T08:23:11Z"}],"graph_snapshots":[{"event_id":"sha256:fc1339bc2e947f3b8f0cc5d9ec7d8313b1d3c3075083b474075e23ad7bf835a7","target":"graph","created_at":"2026-07-05T08:23:11Z","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/2308.11842/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Identification and analysis of symmetrical patterns in the natural world have led to significant discoveries across various scientific fields, such as the formulation of gravitational laws in physics and advancements in the study of chemical structures. In this paper, we focus on exploiting Euclidean symmetries inherent in certain cooperative multi-agent reinforcement learning (MARL) problems and prevalent in many applications. We begin by formally characterizing a subclass of Markov games with a general notion of symmetries that admits the existence of symmetric optimal values and policies. M","authors_text":"Dingyang Chen, Qi Zhang","cross_cats":["cs.AI","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2023-08-23T00:18:17Z","title":"${\\rm E}(3)$-Equivariant Actor-Critic Methods for Cooperative Multi-Agent Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.11842","kind":"arxiv","version":3},"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":"sha256:9f63945703516bfe43cbf5630c1e5c33987926067c4d0230ed217397241d5910","target":"record","created_at":"2026-07-05T08:23:11Z","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":"0894a9b31caa6f44e2a2341d6ced5a08f4b13e2c8a4aaf5b36714790ac6af351","cross_cats_sorted":["cs.AI","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.MA","submitted_at":"2023-08-23T00:18:17Z","title_canon_sha256":"ed7474acaf723ca431524c068d2adb704aff2cebdf5a942a3fb545ab57e4b9dd"},"schema_version":"1.0","source":{"id":"2308.11842","kind":"arxiv","version":3}},"canonical_sha256":"3b9901858f788653cf656fc706b7530a107eb8f8e5ca6f11e149e3c6ffbe9c38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b9901858f788653cf656fc706b7530a107eb8f8e5ca6f11e149e3c6ffbe9c38","first_computed_at":"2026-07-05T08:23:11.373384Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:11.373384Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZpfyLBJo0I+6wwn9cwiqI3UazTCmzPc3RheQ8sQBaEXfJ+2haZGcgma4cBwuW8cizOOa89vCoLG0XIgJsuoKBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:11.373850Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.11842","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f63945703516bfe43cbf5630c1e5c33987926067c4d0230ed217397241d5910","sha256:fc1339bc2e947f3b8f0cc5d9ec7d8313b1d3c3075083b474075e23ad7bf835a7"],"state_sha256":"9725e47c974c7f9c2ec568423a1a999ddf17ba3295a52772a5a0cf40ec0396ce"}