{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6VNGSR5OJ6QBY7YJADNVYXE7JU","short_pith_number":"pith:6VNGSR5O","canonical_record":{"source":{"id":"2605.31172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T11:37:07Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"8db602a2d1fdedfc698d8ce7d3eca83185977e68de235ea3f3c6b1439b9b7aff","abstract_canon_sha256":"6fa7fe8269a9b44d0974700cc4674d75a3dae2b0b3adad814a891df36b5368e0"},"schema_version":"1.0"},"canonical_sha256":"f55a6947ae4fa01c7f0900db5c5c9f4d22fd078a31203d9901c5a2bd403fa134","source":{"kind":"arxiv","id":"2605.31172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31172","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31172v1","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31172","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"6VNGSR5OJ6QB","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"pith_short_16","alias_value":"6VNGSR5OJ6QBY7YJ","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"pith_short_8","alias_value":"6VNGSR5O","created_at":"2026-06-01T01:04:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6VNGSR5OJ6QBY7YJADNVYXE7JU","target":"record","payload":{"canonical_record":{"source":{"id":"2605.31172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T11:37:07Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"8db602a2d1fdedfc698d8ce7d3eca83185977e68de235ea3f3c6b1439b9b7aff","abstract_canon_sha256":"6fa7fe8269a9b44d0974700cc4674d75a3dae2b0b3adad814a891df36b5368e0"},"schema_version":"1.0"},"canonical_sha256":"f55a6947ae4fa01c7f0900db5c5c9f4d22fd078a31203d9901c5a2bd403fa134","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:04:02.392381Z","signature_b64":"mBtONJHntLsamuC5uejU3LghKR+iyn+R/d/rUg47FdFMvMPfC88u3WAWO1AVwdXO/eMNTA4rgxvM5/SR/PPQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f55a6947ae4fa01c7f0900db5c5c9f4d22fd078a31203d9901c5a2bd403fa134","last_reissued_at":"2026-06-01T01:04:02.391613Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:04:02.391613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.31172","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":"2026-06-01T01:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"is4aHh775ajbXymBm7LL+G5hRQAfeVtwVkF7h4CMPDdR5nmGTuvxfBUS5752eDRpdEPFMSWqz6Y6FK/KTlChAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:16:38.191124Z"},"content_sha256":"21b6302666f69ec10f334e6414f27e3c23b733a09a53cdfb200a16c6dd1089df","schema_version":"1.0","event_id":"sha256:21b6302666f69ec10f334e6414f27e3c23b733a09a53cdfb200a16c6dd1089df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6VNGSR5OJ6QBY7YJADNVYXE7JU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of Two-Timescale Markovian Stochastic Approximations with Applications in Reinforcement Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Claire Chen, Shangtong Zhang, Shuze Daniel Liu, Vagul Mahadevan","submitted_at":"2026-05-29T11:37:07Z","abstract_excerpt":"This work studies the convergence of two-timescale stochastic approximations (SA), a class of iterative algorithms that update two sets of parameters in fast and slow timescales respectively. Notable examples of two-timescale SA in reinforcement learning (RL) include temporal difference learning with gradient correction (TDC) and actor-critic methods. Previously, the stability (i.e., boundedness) and convergence of two-timescale SA were only established under i.i.d. noise. This work instead establishes the stability and convergence of two-timescale SA under Markovian noise, a setup that is mor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31172","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/2605.31172/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":"2026-06-01T01:04:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNQKMHnT7IU0XeysxvVozowzS4Z03vO/fFKmq/uQhfqM1+nqUMAzY6ESrKvXEDF/7HXy43JiKLRaLkVJYQNUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T22:16:38.191521Z"},"content_sha256":"6d1b35fadf3bff2ac21854f5dd62b2ee1d9f59b67ce3f839eac1ed86ce7f7f4e","schema_version":"1.0","event_id":"sha256:6d1b35fadf3bff2ac21854f5dd62b2ee1d9f59b67ce3f839eac1ed86ce7f7f4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU/bundle.json","state_url":"https://pith.science/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU/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":"2026-06-23T22:16:38Z","links":{"resolver":"https://pith.science/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU","bundle":"https://pith.science/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU/bundle.json","state":"https://pith.science/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6VNGSR5OJ6QBY7YJADNVYXE7JU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6VNGSR5OJ6QBY7YJADNVYXE7JU","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":"6fa7fe8269a9b44d0974700cc4674d75a3dae2b0b3adad814a891df36b5368e0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T11:37:07Z","title_canon_sha256":"8db602a2d1fdedfc698d8ce7d3eca83185977e68de235ea3f3c6b1439b9b7aff"},"schema_version":"1.0","source":{"id":"2605.31172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.31172","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"arxiv_version","alias_value":"2605.31172v1","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.31172","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"pith_short_12","alias_value":"6VNGSR5OJ6QB","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"pith_short_16","alias_value":"6VNGSR5OJ6QBY7YJ","created_at":"2026-06-01T01:04:02Z"},{"alias_kind":"pith_short_8","alias_value":"6VNGSR5O","created_at":"2026-06-01T01:04:02Z"}],"graph_snapshots":[{"event_id":"sha256:6d1b35fadf3bff2ac21854f5dd62b2ee1d9f59b67ce3f839eac1ed86ce7f7f4e","target":"graph","created_at":"2026-06-01T01:04:02Z","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/2605.31172/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work studies the convergence of two-timescale stochastic approximations (SA), a class of iterative algorithms that update two sets of parameters in fast and slow timescales respectively. Notable examples of two-timescale SA in reinforcement learning (RL) include temporal difference learning with gradient correction (TDC) and actor-critic methods. Previously, the stability (i.e., boundedness) and convergence of two-timescale SA were only established under i.i.d. noise. This work instead establishes the stability and convergence of two-timescale SA under Markovian noise, a setup that is mor","authors_text":"Claire Chen, Shangtong Zhang, Shuze Daniel Liu, Vagul Mahadevan","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T11:37:07Z","title":"Convergence of Two-Timescale Markovian Stochastic Approximations with Applications in Reinforcement Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31172","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":"sha256:21b6302666f69ec10f334e6414f27e3c23b733a09a53cdfb200a16c6dd1089df","target":"record","created_at":"2026-06-01T01:04:02Z","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":"6fa7fe8269a9b44d0974700cc4674d75a3dae2b0b3adad814a891df36b5368e0","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T11:37:07Z","title_canon_sha256":"8db602a2d1fdedfc698d8ce7d3eca83185977e68de235ea3f3c6b1439b9b7aff"},"schema_version":"1.0","source":{"id":"2605.31172","kind":"arxiv","version":1}},"canonical_sha256":"f55a6947ae4fa01c7f0900db5c5c9f4d22fd078a31203d9901c5a2bd403fa134","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f55a6947ae4fa01c7f0900db5c5c9f4d22fd078a31203d9901c5a2bd403fa134","first_computed_at":"2026-06-01T01:04:02.391613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:04:02.391613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mBtONJHntLsamuC5uejU3LghKR+iyn+R/d/rUg47FdFMvMPfC88u3WAWO1AVwdXO/eMNTA4rgxvM5/SR/PPQBQ==","signature_status":"signed_v1","signed_at":"2026-06-01T01:04:02.392381Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.31172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21b6302666f69ec10f334e6414f27e3c23b733a09a53cdfb200a16c6dd1089df","sha256:6d1b35fadf3bff2ac21854f5dd62b2ee1d9f59b67ce3f839eac1ed86ce7f7f4e"],"state_sha256":"f4c580bc25b8795854a61847dc0d201a0c4df8b53e3416611bb770b56fe413fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+IgqRufszl5OFoIu2jH/eRBidFh/LLcTil/otTbMiSQ06zTYDSuc1ZBNMOikjN+fIs+9f6n6smX+UXMZKADDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T22:16:38.193893Z","bundle_sha256":"6f47706fa7816779a8cecfda76c824af8bb12e54f6f691ab47d3f606dc2a03d4"}}