{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:CZ2S5PPH6HVZKS5XIRZ4PJ7GOA","short_pith_number":"pith:CZ2S5PPH","canonical_record":{"source":{"id":"2412.19299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-26T17:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"a496706d2bc430aea55d45df9d162d9cda5a9edc1944394df9eb51e7a7371e22","abstract_canon_sha256":"3531f387f63cb3a2eaa14007cde678c85ced345bcae798ed469d7a7466b7bf50"},"schema_version":"1.0"},"canonical_sha256":"16752ebde7f1eb954bb74473c7a7e67014563750a24390808d9247d91a45c31f","source":{"kind":"arxiv","id":"2412.19299","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19299","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19299v1","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19299","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"pith_short_12","alias_value":"CZ2S5PPH6HVZ","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"pith_short_16","alias_value":"CZ2S5PPH6HVZKS5X","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"pith_short_8","alias_value":"CZ2S5PPH","created_at":"2026-07-05T09:54:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:CZ2S5PPH6HVZKS5XIRZ4PJ7GOA","target":"record","payload":{"canonical_record":{"source":{"id":"2412.19299","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-26T17:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"a496706d2bc430aea55d45df9d162d9cda5a9edc1944394df9eb51e7a7371e22","abstract_canon_sha256":"3531f387f63cb3a2eaa14007cde678c85ced345bcae798ed469d7a7466b7bf50"},"schema_version":"1.0"},"canonical_sha256":"16752ebde7f1eb954bb74473c7a7e67014563750a24390808d9247d91a45c31f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:33.631522Z","signature_b64":"hP/KZfwIRbe9NmxEMEpyND01+aSSoGuOtl7ENh8DIFt6GGMK7fhUMRqzAmmFxRT9+glFLAWAol67iCvOapLmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16752ebde7f1eb954bb74473c7a7e67014563750a24390808d9247d91a45c31f","last_reissued_at":"2026-07-05T09:54:33.631091Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:33.631091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.19299","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":"2026-07-05T09:54:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaqYrP7itzMsI2gEaNAHUIwjxQd0AQNSY8Sr7bPTgnQRZZPgyLUOn2OaJ/iu7hFYy59z0y9+eeuEeBRe2GGDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:40:51.584927Z"},"content_sha256":"a0cdb06fc92fa0446b73db4734e62c1793d05b1382a7748c4847eea8d1393f11","schema_version":"1.0","event_id":"sha256:a0cdb06fc92fa0446b73db4734e62c1793d05b1382a7748c4847eea8d1393f11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:CZ2S5PPH6HVZKS5XIRZ4PJ7GOA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sample Complexity of Data-driven Multistage Stochastic Programming under Markovian Uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Grani A. Hanasusanto, Hyuk Park","submitted_at":"2024-12-26T17:46:27Z","abstract_excerpt":"This work is motivated by the challenges of applying the sample average approximation (SAA) method to multistage stochastic programming with an unknown continuous-state Markov process. While SAA is widely used in static and two-stage stochastic optimization, it becomes computationally intractable in general multistage settings as the time horizon $T$ increases. Indeed, the number of samples required to obtain a reasonably accurate solution grows exponentially$\\text{ -- }$a phenomenon known as the curse of dimensionality with respect to the time horizon. To overcome this limitation, we propose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19299","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/2412.19299/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":"2026-07-05T09:54:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FnlszkkjUHGdcoz0NfAMzhiLiygJZP7LO7dePQTLiCNjXO9hafdnBBoG/pBuKVnmlTyzieLdlj2jbJYbbAnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:40:51.585827Z"},"content_sha256":"dfaf1aac097d284f2fa05d8d1ea0f9005064e3e7dccb60b112c8d05bee441a90","schema_version":"1.0","event_id":"sha256:dfaf1aac097d284f2fa05d8d1ea0f9005064e3e7dccb60b112c8d05bee441a90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA/bundle.json","state_url":"https://pith.science/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA/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":"2026-08-13T05:40:51Z","links":{"resolver":"https://pith.science/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA","bundle":"https://pith.science/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA/bundle.json","state":"https://pith.science/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZ2S5PPH6HVZKS5XIRZ4PJ7GOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:CZ2S5PPH6HVZKS5XIRZ4PJ7GOA","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":"3531f387f63cb3a2eaa14007cde678c85ced345bcae798ed469d7a7466b7bf50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-26T17:46:27Z","title_canon_sha256":"a496706d2bc430aea55d45df9d162d9cda5a9edc1944394df9eb51e7a7371e22"},"schema_version":"1.0","source":{"id":"2412.19299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19299","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19299v1","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19299","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"pith_short_12","alias_value":"CZ2S5PPH6HVZ","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"pith_short_16","alias_value":"CZ2S5PPH6HVZKS5X","created_at":"2026-07-05T09:54:33Z"},{"alias_kind":"pith_short_8","alias_value":"CZ2S5PPH","created_at":"2026-07-05T09:54:33Z"}],"graph_snapshots":[{"event_id":"sha256:dfaf1aac097d284f2fa05d8d1ea0f9005064e3e7dccb60b112c8d05bee441a90","target":"graph","created_at":"2026-07-05T09:54:33Z","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/2412.19299/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work is motivated by the challenges of applying the sample average approximation (SAA) method to multistage stochastic programming with an unknown continuous-state Markov process. While SAA is widely used in static and two-stage stochastic optimization, it becomes computationally intractable in general multistage settings as the time horizon $T$ increases. Indeed, the number of samples required to obtain a reasonably accurate solution grows exponentially$\\text{ -- }$a phenomenon known as the curse of dimensionality with respect to the time horizon. To overcome this limitation, we propose ","authors_text":"Grani A. Hanasusanto, Hyuk Park","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-26T17:46:27Z","title":"Sample Complexity of Data-driven Multistage Stochastic Programming under Markovian Uncertainty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19299","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:a0cdb06fc92fa0446b73db4734e62c1793d05b1382a7748c4847eea8d1393f11","target":"record","created_at":"2026-07-05T09:54:33Z","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":"3531f387f63cb3a2eaa14007cde678c85ced345bcae798ed469d7a7466b7bf50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-12-26T17:46:27Z","title_canon_sha256":"a496706d2bc430aea55d45df9d162d9cda5a9edc1944394df9eb51e7a7371e22"},"schema_version":"1.0","source":{"id":"2412.19299","kind":"arxiv","version":1}},"canonical_sha256":"16752ebde7f1eb954bb74473c7a7e67014563750a24390808d9247d91a45c31f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16752ebde7f1eb954bb74473c7a7e67014563750a24390808d9247d91a45c31f","first_computed_at":"2026-07-05T09:54:33.631091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:33.631091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hP/KZfwIRbe9NmxEMEpyND01+aSSoGuOtl7ENh8DIFt6GGMK7fhUMRqzAmmFxRT9+glFLAWAol67iCvOapLmCA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:33.631522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0cdb06fc92fa0446b73db4734e62c1793d05b1382a7748c4847eea8d1393f11","sha256:dfaf1aac097d284f2fa05d8d1ea0f9005064e3e7dccb60b112c8d05bee441a90"],"state_sha256":"87a08c012052c2c5be3f4d416e7848f994ced6ddcd8dc5bf734627f52a66da61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zaya+NlN3cyffQKQ2pW5mRZn8n7pRUk6OMy2FoeoXYpgV9TSa7nvvy36rfAzthDKTtGH7Ub8BqogeO83/+vqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:40:51.628067Z","bundle_sha256":"783b661ba93cff939094894f4d7f94e6fe84d5bdeb65e30ba94d278d76c60fa9"}}