{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:5V6UDXXLGDTDC4BMVJAGMPVYQB","short_pith_number":"pith:5V6UDXXL","canonical_record":{"source":{"id":"2110.04495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-09T07:46:25Z","cross_cats_sorted":["cs.MA"],"title_canon_sha256":"b60c0e940faa5e565b3f30d63f52c762968282d0a0e6ee2c4959ce2039d43751","abstract_canon_sha256":"4b1413bf3a8de9d6d5401a5c9279bcc218114f3623e4a1447b721a565d990af8"},"schema_version":"1.0"},"canonical_sha256":"ed7d41deeb30e631702caa40663eb880620df04d74d9e5bdcef308a97fbb8f3d","source":{"kind":"arxiv","id":"2110.04495","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.04495","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.04495v2","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.04495","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"5V6UDXXLGDTD","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"pith_short_16","alias_value":"5V6UDXXLGDTDC4BM","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"pith_short_8","alias_value":"5V6UDXXL","created_at":"2026-07-05T04:18:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:5V6UDXXLGDTDC4BMVJAGMPVYQB","target":"record","payload":{"canonical_record":{"source":{"id":"2110.04495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-09T07:46:25Z","cross_cats_sorted":["cs.MA"],"title_canon_sha256":"b60c0e940faa5e565b3f30d63f52c762968282d0a0e6ee2c4959ce2039d43751","abstract_canon_sha256":"4b1413bf3a8de9d6d5401a5c9279bcc218114f3623e4a1447b721a565d990af8"},"schema_version":"1.0"},"canonical_sha256":"ed7d41deeb30e631702caa40663eb880620df04d74d9e5bdcef308a97fbb8f3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:18:48.017691Z","signature_b64":"z2JaPK/7+m/SYuiql61fh2Et4L+QVnfIldqfPaWpyBrOkH+WkU5mc6igCsPpOcEnXUREpPHDeTyUwu2sM3rPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed7d41deeb30e631702caa40663eb880620df04d74d9e5bdcef308a97fbb8f3d","last_reissued_at":"2026-07-05T04:18:48.017255Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:18:48.017255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.04495","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:18:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Opcm0inv5Daswu5Y6X6in1PUECL4B98CB/2VF91GgbQ2bgO774dkxeW/aXEdXvARzOCoYS/E1LwBDT5EKP+YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:48:59.766595Z"},"content_sha256":"47c80efe315a6e49135e18ffb06065f48765107f379b8b51c236d560e77688e3","schema_version":"1.0","event_id":"sha256:47c80efe315a6e49135e18ffb06065f48765107f379b8b51c236d560e77688e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:5V6UDXXLGDTDC4BMVJAGMPVYQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Agent MDP Homomorphic Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"cs.LG","authors_text":"Elise van der Pol, Frans A. Oliehoek, Herke van Hoof, Max Welling","submitted_at":"2021-10-09T07:46:25Z","abstract_excerpt":"This paper introduces Multi-Agent MDP Homomorphic Networks, a class of networks that allows distributed execution using only local information, yet is able to share experience between global symmetries in the joint state-action space of cooperative multi-agent systems. In cooperative multi-agent systems, complex symmetries arise between different configurations of the agents and their local observations. For example, consider a group of agents navigating: rotating the state globally results in a permutation of the optimal joint policy. Existing work on symmetries in single agent reinforcement "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.04495","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/2110.04495/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:18:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2bMFz41xm/3oO0yzDQbWGV16MtZrQqHTO3Rsl6PgEqHRQknfSwnW/FWxe5UWIZrPQuyQD2NYFy3sVOs2BsaYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T12:48:59.767524Z"},"content_sha256":"0b75accc52cfde2e77fb0737d12a9be502c62599fa7403cd8bcbe71ff09e72bc","schema_version":"1.0","event_id":"sha256:0b75accc52cfde2e77fb0737d12a9be502c62599fa7403cd8bcbe71ff09e72bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB/bundle.json","state_url":"https://pith.science/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T12:48:59Z","links":{"resolver":"https://pith.science/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB","bundle":"https://pith.science/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB/bundle.json","state":"https://pith.science/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5V6UDXXLGDTDC4BMVJAGMPVYQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5V6UDXXLGDTDC4BMVJAGMPVYQB","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":"4b1413bf3a8de9d6d5401a5c9279bcc218114f3623e4a1447b721a565d990af8","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-09T07:46:25Z","title_canon_sha256":"b60c0e940faa5e565b3f30d63f52c762968282d0a0e6ee2c4959ce2039d43751"},"schema_version":"1.0","source":{"id":"2110.04495","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.04495","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"arxiv_version","alias_value":"2110.04495v2","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.04495","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"pith_short_12","alias_value":"5V6UDXXLGDTD","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"pith_short_16","alias_value":"5V6UDXXLGDTDC4BM","created_at":"2026-07-05T04:18:48Z"},{"alias_kind":"pith_short_8","alias_value":"5V6UDXXL","created_at":"2026-07-05T04:18:48Z"}],"graph_snapshots":[{"event_id":"sha256:0b75accc52cfde2e77fb0737d12a9be502c62599fa7403cd8bcbe71ff09e72bc","target":"graph","created_at":"2026-07-05T04:18:48Z","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/2110.04495/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces Multi-Agent MDP Homomorphic Networks, a class of networks that allows distributed execution using only local information, yet is able to share experience between global symmetries in the joint state-action space of cooperative multi-agent systems. In cooperative multi-agent systems, complex symmetries arise between different configurations of the agents and their local observations. For example, consider a group of agents navigating: rotating the state globally results in a permutation of the optimal joint policy. Existing work on symmetries in single agent reinforcement ","authors_text":"Elise van der Pol, Frans A. Oliehoek, Herke van Hoof, Max Welling","cross_cats":["cs.MA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-09T07:46:25Z","title":"Multi-Agent MDP Homomorphic Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.04495","kind":"arxiv","version":2},"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":"sha256:47c80efe315a6e49135e18ffb06065f48765107f379b8b51c236d560e77688e3","target":"record","created_at":"2026-07-05T04:18:48Z","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":"4b1413bf3a8de9d6d5401a5c9279bcc218114f3623e4a1447b721a565d990af8","cross_cats_sorted":["cs.MA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-10-09T07:46:25Z","title_canon_sha256":"b60c0e940faa5e565b3f30d63f52c762968282d0a0e6ee2c4959ce2039d43751"},"schema_version":"1.0","source":{"id":"2110.04495","kind":"arxiv","version":2}},"canonical_sha256":"ed7d41deeb30e631702caa40663eb880620df04d74d9e5bdcef308a97fbb8f3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed7d41deeb30e631702caa40663eb880620df04d74d9e5bdcef308a97fbb8f3d","first_computed_at":"2026-07-05T04:18:48.017255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:18:48.017255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2JaPK/7+m/SYuiql61fh2Et4L+QVnfIldqfPaWpyBrOkH+WkU5mc6igCsPpOcEnXUREpPHDeTyUwu2sM3rPCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:18:48.017691Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.04495","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47c80efe315a6e49135e18ffb06065f48765107f379b8b51c236d560e77688e3","sha256:0b75accc52cfde2e77fb0737d12a9be502c62599fa7403cd8bcbe71ff09e72bc"],"state_sha256":"69f35678f221dad1feacf00db84b59d1ad6be478e08e58b6a9a52bcd713fb35a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34vRckeLhLCAIXmxiVUapVLFnkv6/tMEF4A74llTFp7viOE2lfUZgH1KCKjX4Agw9WEZNGxpyqbLpqvM4pjaDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T12:48:59.773827Z","bundle_sha256":"8a25d72280cc8ef43d9f060609778c5d4150aa91b6acd5540603a218bfcb5cf9"}}