{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:5MX7ZFMJOJDLJZWREETKSGA3D2","short_pith_number":"pith:5MX7ZFMJ","canonical_record":{"source":{"id":"2606.22579","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-21T16:29:25Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"265bb0e3a5991240f60efd086fb7e55c3ab5fb3e24a18e0c8a16c82e1535c9ee","abstract_canon_sha256":"9ea876d12272b5c9344633e015165d178f19d6a801d48a57f52b578513f70efc"},"schema_version":"1.0"},"canonical_sha256":"eb2ffc95897246b4e6d12126a9181b1ebd2cc43aa37f749fea80b7a7ad79ec2a","source":{"kind":"arxiv","id":"2606.22579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22579","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22579v1","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22579","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"pith_short_12","alias_value":"5MX7ZFMJOJDL","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"pith_short_16","alias_value":"5MX7ZFMJOJDLJZWR","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"pith_short_8","alias_value":"5MX7ZFMJ","created_at":"2026-06-23T02:13:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:5MX7ZFMJOJDLJZWREETKSGA3D2","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22579","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-21T16:29:25Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"265bb0e3a5991240f60efd086fb7e55c3ab5fb3e24a18e0c8a16c82e1535c9ee","abstract_canon_sha256":"9ea876d12272b5c9344633e015165d178f19d6a801d48a57f52b578513f70efc"},"schema_version":"1.0"},"canonical_sha256":"eb2ffc95897246b4e6d12126a9181b1ebd2cc43aa37f749fea80b7a7ad79ec2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:42.108348Z","signature_b64":"HJaJYV53vz7UNAIchC4Fnw3Y1IKHeme+9pP+qBQCvaRA73czJcx8UrJ6TFN8FUMzGD4WZ+i+t1yp+TYr6lu5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb2ffc95897246b4e6d12126a9181b1ebd2cc43aa37f749fea80b7a7ad79ec2a","last_reissued_at":"2026-06-23T02:13:42.107872Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:42.107872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22579","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T02:13:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VrwIo+UHaxqgVgFpue2/dWW1dFFFau+pMyEOxUa30abKzPf+HyD3C5nEE/UgOUyzM35pdrW/gmW+KBjiVApBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T02:44:45.465066Z"},"content_sha256":"d900546eb76d7ad8a606db4d3b9b19de7d8f267a4b47c8df9c9166c7626f1247","schema_version":"1.0","event_id":"sha256:d900546eb76d7ad8a606db4d3b9b19de7d8f267a4b47c8df9c9166c7626f1247"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:5MX7ZFMJOJDLJZWREETKSGA3D2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary Robust Mean-Field Games under Model Mismatches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"cs.LG","authors_text":"Yue Wang","submitted_at":"2026-06-21T16:29:25Z","abstract_excerpt":"Deploying multi-agent reinforcement learning (MARL) in the real world is often limited by model mismatches between the training simulators and the true environment, which could be further amplified through strategic interactions and result in severe performance degradation upon deployment. Distributional robustness offers a principled response by optimizing policies against worst-case transition models drawn from an uncertainty set, but standard robust MARL frameworks become increasingly intractable as the number of agents grows. This paper develops an infinite-horizon, stationary mean-field g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22579","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/2606.22579/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":"2026-06-23T02:13:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcmOg3uEf/oyzWx99qIsGM4fykpjLJTtFl9WRIVxSQ1xoQKzwGJFBCETld5oaojwN+piR9FOM4oTzjGknDNlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T02:44:45.465468Z"},"content_sha256":"66f5ca4a9e9ebcd8c1e1364208500d4ddbf2bf230e533ed58ebc2419b8b8d211","schema_version":"1.0","event_id":"sha256:66f5ca4a9e9ebcd8c1e1364208500d4ddbf2bf230e533ed58ebc2419b8b8d211"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5MX7ZFMJOJDLJZWREETKSGA3D2/bundle.json","state_url":"https://pith.science/pith/5MX7ZFMJOJDLJZWREETKSGA3D2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5MX7ZFMJOJDLJZWREETKSGA3D2/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":"2026-06-30T02:44:45Z","links":{"resolver":"https://pith.science/pith/5MX7ZFMJOJDLJZWREETKSGA3D2","bundle":"https://pith.science/pith/5MX7ZFMJOJDLJZWREETKSGA3D2/bundle.json","state":"https://pith.science/pith/5MX7ZFMJOJDLJZWREETKSGA3D2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5MX7ZFMJOJDLJZWREETKSGA3D2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:5MX7ZFMJOJDLJZWREETKSGA3D2","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":"9ea876d12272b5c9344633e015165d178f19d6a801d48a57f52b578513f70efc","cross_cats_sorted":["cs.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-21T16:29:25Z","title_canon_sha256":"265bb0e3a5991240f60efd086fb7e55c3ab5fb3e24a18e0c8a16c82e1535c9ee"},"schema_version":"1.0","source":{"id":"2606.22579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22579","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22579v1","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22579","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"pith_short_12","alias_value":"5MX7ZFMJOJDL","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"pith_short_16","alias_value":"5MX7ZFMJOJDLJZWR","created_at":"2026-06-23T02:13:42Z"},{"alias_kind":"pith_short_8","alias_value":"5MX7ZFMJ","created_at":"2026-06-23T02:13:42Z"}],"graph_snapshots":[{"event_id":"sha256:66f5ca4a9e9ebcd8c1e1364208500d4ddbf2bf230e533ed58ebc2419b8b8d211","target":"graph","created_at":"2026-06-23T02:13:42Z","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/2606.22579/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Deploying multi-agent reinforcement learning (MARL) in the real world is often limited by model mismatches between the training simulators and the true environment, which could be further amplified through strategic interactions and result in severe performance degradation upon deployment. Distributional robustness offers a principled response by optimizing policies against worst-case transition models drawn from an uncertainty set, but standard robust MARL frameworks become increasingly intractable as the number of agents grows. This paper develops an infinite-horizon, stationary mean-field g","authors_text":"Yue Wang","cross_cats":["cs.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-21T16:29:25Z","title":"Stationary Robust Mean-Field Games under Model Mismatches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22579","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:d900546eb76d7ad8a606db4d3b9b19de7d8f267a4b47c8df9c9166c7626f1247","target":"record","created_at":"2026-06-23T02:13:42Z","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":"9ea876d12272b5c9344633e015165d178f19d6a801d48a57f52b578513f70efc","cross_cats_sorted":["cs.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-21T16:29:25Z","title_canon_sha256":"265bb0e3a5991240f60efd086fb7e55c3ab5fb3e24a18e0c8a16c82e1535c9ee"},"schema_version":"1.0","source":{"id":"2606.22579","kind":"arxiv","version":1}},"canonical_sha256":"eb2ffc95897246b4e6d12126a9181b1ebd2cc43aa37f749fea80b7a7ad79ec2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb2ffc95897246b4e6d12126a9181b1ebd2cc43aa37f749fea80b7a7ad79ec2a","first_computed_at":"2026-06-23T02:13:42.107872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:42.107872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HJaJYV53vz7UNAIchC4Fnw3Y1IKHeme+9pP+qBQCvaRA73czJcx8UrJ6TFN8FUMzGD4WZ+i+t1yp+TYr6lu5Cw==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:42.108348Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d900546eb76d7ad8a606db4d3b9b19de7d8f267a4b47c8df9c9166c7626f1247","sha256:66f5ca4a9e9ebcd8c1e1364208500d4ddbf2bf230e533ed58ebc2419b8b8d211"],"state_sha256":"c336cf7778957f1b7fd5b2979678daabc310e08b4dee4ee1d3cffc9eb74612e0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+Q2tRteWZoP+j/Ohuu0kcqo0KvxhJHjCj/aP5uo63iLk+pQQVi1TBRpnAtMpP0Pm70fG3xDG2hJwk7vgSdtAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T02:44:45.467715Z","bundle_sha256":"6c6155e7881a610e836af60ce51a718a8bf151711e5506638d004dcee01bc1c0"}}