{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:OUVCBNIQAWI2OIEIOZQDRXEAWD","short_pith_number":"pith:OUVCBNIQ","canonical_record":{"source":{"id":"2503.02825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:49:24Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"e96efa26ff507e8a6822f914f775b398c0b6dda66141844bc4337cc751e94f56","abstract_canon_sha256":"f74d06667c94ddab8a4810fd519fc21b48525e1ad8f2e6628771e63a5c1e1f0c"},"schema_version":"1.0"},"canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","source":{"kind":"arxiv","id":"2503.02825","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02825","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02825v1","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02825","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"OUVCBNIQAWI2","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_16","alias_value":"OUVCBNIQAWI2OIEI","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_8","alias_value":"OUVCBNIQ","created_at":"2026-07-05T10:24:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:OUVCBNIQAWI2OIEIOZQDRXEAWD","target":"record","payload":{"canonical_record":{"source":{"id":"2503.02825","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:49:24Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"e96efa26ff507e8a6822f914f775b398c0b6dda66141844bc4337cc751e94f56","abstract_canon_sha256":"f74d06667c94ddab8a4810fd519fc21b48525e1ad8f2e6628771e63a5c1e1f0c"},"schema_version":"1.0"},"canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:24:14.676846Z","signature_b64":"ZQCubs18aDXFhjWhbL7Y0ahzTkkhe+yYY/Z3r25wH3uQLQsOL68fwvmI8eTpkMsFH8TI2RY/f4LpuoNf/e78Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","last_reissued_at":"2026-07-05T10:24:14.676300Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:24:14.676300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.02825","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":"2026-07-05T10:24:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8iNrGHgAzLNzujkQ0iWvBbShpzAZWWSfn1DdNBEUkkD20Vu3cLr7QUfDH+H1NXjvGpmyhKmdlaxx1VrqlZ8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:10:45.706352Z"},"content_sha256":"5db8c847aa4a2bcf04c6abfef753dc7071b90454b0fe09cbf9b6743da0d62eb6","schema_version":"1.0","event_id":"sha256:5db8c847aa4a2bcf04c6abfef753dc7071b90454b0fe09cbf9b6743da0d62eb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:OUVCBNIQAWI2OIEIOZQDRXEAWD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate Convergence of Learning in Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","math.OC"],"primary_cat":"cs.LG","authors_text":"Christian Kroer, Chung-Wei Lee, Gabriele Farina, Haipeng Luo, Julien Grand-Cl\\'ement, Weiqiang Zheng, Yang Cai","submitted_at":"2025-03-04T17:49:24Z","abstract_excerpt":"Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic Multiplicative Weights Update (OMWU), can exhibit arbitrarily slow last-iterate convergence even in simple $2 \\times 2$ matrix games, despite many of these dynamics being known to converge asymptotically in the last iterate. It remains unclear, however, whether these algorithms achieve fast non-ergodic convergence under weaker criteria, such as best-iterate conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02825","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/2503.02825/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":"2026-07-05T10:24:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9T54v1LXE6KYMEdFnnYaK+u4Eyzr+wwImCvAfUa27Wncr66n65RoCItahEpJgjrPveKjcswsP2zDQnzznGYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T20:10:45.706986Z"},"content_sha256":"67e72b670423fbc97f590920d9b563ac7ff8a3cd6ce079d8c37bd77f3c315d48","schema_version":"1.0","event_id":"sha256:67e72b670423fbc97f590920d9b563ac7ff8a3cd6ce079d8c37bd77f3c315d48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/bundle.json","state_url":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/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":"2026-08-17T20:10:45Z","links":{"resolver":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD","bundle":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/bundle.json","state":"https://pith.science/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUVCBNIQAWI2OIEIOZQDRXEAWD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:OUVCBNIQAWI2OIEIOZQDRXEAWD","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":"f74d06667c94ddab8a4810fd519fc21b48525e1ad8f2e6628771e63a5c1e1f0c","cross_cats_sorted":["cs.GT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:49:24Z","title_canon_sha256":"e96efa26ff507e8a6822f914f775b398c0b6dda66141844bc4337cc751e94f56"},"schema_version":"1.0","source":{"id":"2503.02825","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02825","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02825v1","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02825","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_12","alias_value":"OUVCBNIQAWI2","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_16","alias_value":"OUVCBNIQAWI2OIEI","created_at":"2026-07-05T10:24:14Z"},{"alias_kind":"pith_short_8","alias_value":"OUVCBNIQ","created_at":"2026-07-05T10:24:14Z"}],"graph_snapshots":[{"event_id":"sha256:67e72b670423fbc97f590920d9b563ac7ff8a3cd6ce079d8c37bd77f3c315d48","target":"graph","created_at":"2026-07-05T10:24:14Z","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/2503.02825/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Non-ergodic convergence of learning dynamics in games is widely studied recently because of its importance in both theory and practice. Recent work (Cai et al., 2024) showed that a broad class of learning dynamics, including Optimistic Multiplicative Weights Update (OMWU), can exhibit arbitrarily slow last-iterate convergence even in simple $2 \\times 2$ matrix games, despite many of these dynamics being known to converge asymptotically in the last iterate. It remains unclear, however, whether these algorithms achieve fast non-ergodic convergence under weaker criteria, such as best-iterate conv","authors_text":"Christian Kroer, Chung-Wei Lee, Gabriele Farina, Haipeng Luo, Julien Grand-Cl\\'ement, Weiqiang Zheng, Yang Cai","cross_cats":["cs.GT","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:49:24Z","title":"On Separation Between Best-Iterate, Random-Iterate, and Last-Iterate Convergence of Learning in Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02825","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":"sha256:5db8c847aa4a2bcf04c6abfef753dc7071b90454b0fe09cbf9b6743da0d62eb6","target":"record","created_at":"2026-07-05T10:24:14Z","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":"f74d06667c94ddab8a4810fd519fc21b48525e1ad8f2e6628771e63a5c1e1f0c","cross_cats_sorted":["cs.GT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-03-04T17:49:24Z","title_canon_sha256":"e96efa26ff507e8a6822f914f775b398c0b6dda66141844bc4337cc751e94f56"},"schema_version":"1.0","source":{"id":"2503.02825","kind":"arxiv","version":1}},"canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"752a20b5100591a72088766038dc80b0fc1d7f4634966033e78a13bca737bf59","first_computed_at":"2026-07-05T10:24:14.676300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:14.676300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZQCubs18aDXFhjWhbL7Y0ahzTkkhe+yYY/Z3r25wH3uQLQsOL68fwvmI8eTpkMsFH8TI2RY/f4LpuoNf/e78Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:14.676846Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.02825","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5db8c847aa4a2bcf04c6abfef753dc7071b90454b0fe09cbf9b6743da0d62eb6","sha256:67e72b670423fbc97f590920d9b563ac7ff8a3cd6ce079d8c37bd77f3c315d48"],"state_sha256":"369dbac732425714d290d75ce7ee2cedea9eda9d9fe605aa1b914e86df87df7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nR6qt8NmlMFHmehFi9PQ4bLimTZp95MUwd09i4DLoCMHdP0GJ6CJmse67xZCE3px9OfCsXRttfYbmdap33WuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T20:10:45.714111Z","bundle_sha256":"2d2fe65d7595c157eb1d4a06e7abfeb984b82f74aa97fe05e67a9fd752e3e884"}}