{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:K3GIQTL47DONEQ2WDPJ3P6QGGK","short_pith_number":"pith:K3GIQTL4","canonical_record":{"source":{"id":"2602.22047","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-02-25T15:56:14Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"1744970c04ea658c4280de4cb6dc79a5a79df421ea5e91f8d37ddd364d0d7f6e","abstract_canon_sha256":"dd1eef55c3dade3878d7a47297198bbc909b50564cf748240c5964dc2d85c8cd"},"schema_version":"1.0"},"canonical_sha256":"56cc884d7cf8dcd243561bd3b7fa063294095adf51ddd446085a9810ed3262b6","source":{"kind":"arxiv","id":"2602.22047","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.22047","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"2602.22047v2","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.22047","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"K3GIQTL47DON","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"pith_short_16","alias_value":"K3GIQTL47DONEQ2W","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"pith_short_8","alias_value":"K3GIQTL4","created_at":"2026-07-22T00:22:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:K3GIQTL47DONEQ2WDPJ3P6QGGK","target":"record","payload":{"canonical_record":{"source":{"id":"2602.22047","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-02-25T15:56:14Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"1744970c04ea658c4280de4cb6dc79a5a79df421ea5e91f8d37ddd364d0d7f6e","abstract_canon_sha256":"dd1eef55c3dade3878d7a47297198bbc909b50564cf748240c5964dc2d85c8cd"},"schema_version":"1.0"},"canonical_sha256":"56cc884d7cf8dcd243561bd3b7fa063294095adf51ddd446085a9810ed3262b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:16.748859Z","signature_b64":"1d7YUxryz703QRP2V4y23qkzGYbr6VBfSRvnVDwW8N4Dr853O+NtSt5nYSQ1g6vqvhxMQSGJp6f2qW38/GtACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56cc884d7cf8dcd243561bd3b7fa063294095adf51ddd446085a9810ed3262b6","last_reissued_at":"2026-07-22T00:22:16.747977Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:16.747977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.22047","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":"2026-07-22T00:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JM2tJtwZURHZiVEInEHm+4p3nMzr971Yp1/KJ4uZ6DJUxAqTK4oYwtAGLvU2OYFTWad/q7OMOISs/WkB+35NCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:25:50.762688Z"},"content_sha256":"ea3884759de1d8b48d4932b61e02d4a3726b8f057cd560e50baf0c831a200643","schema_version":"1.0","event_id":"sha256:ea3884759de1d8b48d4932b61e02d4a3726b8f057cd560e50baf0c831a200643"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:K3GIQTL47DONEQ2WDPJ3P6QGGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Optimal Control with Side Information and Bayesian Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.OC","authors_text":"Alexander Shapiro, Enlu Zhou, Johannes Milz","submitted_at":"2026-02-25T15:56:14Z","abstract_excerpt":"We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian reformulation based on a parametric density model and posterior predictive dynamics, which yields a Bayesian Bellman equation. We prove posterior consistency under Markov samples and, under correct specification and identifiability, uniform convergence of the Bayesian value function. Finally, we establish Bernstein--von Mises-type asymptotic normality for th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.22047","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/2602.22047/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":"2026-07-22T00:22:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zccTTWViiGqE8XjhkDleYvK+CackfPTJIjbbtHmfUHnZEqT/Dq7MQVNKdJtlTlNPLK1pVsd66rPA/rJcOADlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:25:50.763604Z"},"content_sha256":"8a814aba2706750f52e0ed6999adefb832c77d363ea470e80800e5ec56154d56","schema_version":"1.0","event_id":"sha256:8a814aba2706750f52e0ed6999adefb832c77d363ea470e80800e5ec56154d56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK/bundle.json","state_url":"https://pith.science/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK/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":"2026-08-04T06:25:50Z","links":{"resolver":"https://pith.science/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK","bundle":"https://pith.science/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK/bundle.json","state":"https://pith.science/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K3GIQTL47DONEQ2WDPJ3P6QGGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K3GIQTL47DONEQ2WDPJ3P6QGGK","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":"dd1eef55c3dade3878d7a47297198bbc909b50564cf748240c5964dc2d85c8cd","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-02-25T15:56:14Z","title_canon_sha256":"1744970c04ea658c4280de4cb6dc79a5a79df421ea5e91f8d37ddd364d0d7f6e"},"schema_version":"1.0","source":{"id":"2602.22047","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.22047","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"arxiv_version","alias_value":"2602.22047v2","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.22047","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"pith_short_12","alias_value":"K3GIQTL47DON","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"pith_short_16","alias_value":"K3GIQTL47DONEQ2W","created_at":"2026-07-22T00:22:16Z"},{"alias_kind":"pith_short_8","alias_value":"K3GIQTL4","created_at":"2026-07-22T00:22:16Z"}],"graph_snapshots":[{"event_id":"sha256:8a814aba2706750f52e0ed6999adefb832c77d363ea470e80800e5ec56154d56","target":"graph","created_at":"2026-07-22T00:22:16Z","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/2602.22047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study infinite-horizon stochastic optimal control problems with observable side information: a Markov chain that modulates an unknown context-conditional randomness distribution. Since this distribution is unknown, we propose a Bayesian reformulation based on a parametric density model and posterior predictive dynamics, which yields a Bayesian Bellman equation. We prove posterior consistency under Markov samples and, under correct specification and identifiability, uniform convergence of the Bayesian value function. Finally, we establish Bernstein--von Mises-type asymptotic normality for th","authors_text":"Alexander Shapiro, Enlu Zhou, Johannes Milz","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-02-25T15:56:14Z","title":"Stochastic Optimal Control with Side Information and Bayesian Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.22047","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:ea3884759de1d8b48d4932b61e02d4a3726b8f057cd560e50baf0c831a200643","target":"record","created_at":"2026-07-22T00:22:16Z","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":"dd1eef55c3dade3878d7a47297198bbc909b50564cf748240c5964dc2d85c8cd","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-02-25T15:56:14Z","title_canon_sha256":"1744970c04ea658c4280de4cb6dc79a5a79df421ea5e91f8d37ddd364d0d7f6e"},"schema_version":"1.0","source":{"id":"2602.22047","kind":"arxiv","version":2}},"canonical_sha256":"56cc884d7cf8dcd243561bd3b7fa063294095adf51ddd446085a9810ed3262b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56cc884d7cf8dcd243561bd3b7fa063294095adf51ddd446085a9810ed3262b6","first_computed_at":"2026-07-22T00:22:16.747977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:16.747977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1d7YUxryz703QRP2V4y23qkzGYbr6VBfSRvnVDwW8N4Dr853O+NtSt5nYSQ1g6vqvhxMQSGJp6f2qW38/GtACA==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:16.748859Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.22047","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea3884759de1d8b48d4932b61e02d4a3726b8f057cd560e50baf0c831a200643","sha256:8a814aba2706750f52e0ed6999adefb832c77d363ea470e80800e5ec56154d56"],"state_sha256":"50516bc600ec8cf0d1d7e85b4b0a66110d075bd5134615fa6ff3ae00a60090bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JRefxfu0mELQyQIxjGkgS00olF0xKccSpZGAy/TI5611ZwBnn5leiJFuQk9U8VnY1NXfNiYhH3osFAQmrfcpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:25:50.770431Z","bundle_sha256":"e6ed5abe6827f911bb386f7bc44610c7f8f1c3ab30dfc28ee8663f8326dc0035"}}