{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:U76FNIFQWGTXMB6ZKTNFHPOPH4","short_pith_number":"pith:U76FNIFQ","canonical_record":{"source":{"id":"2207.14779","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-07-29T16:44:37Z","cross_cats_sorted":[],"title_canon_sha256":"04e3b7f36642961af5e754981bbd70b17e0705f6e0e97e04b6245821f93fa77b","abstract_canon_sha256":"8fe1caaa23e89c096f86ee48e503cab8587bf50abf1288fb5d5047a91ea38c33"},"schema_version":"1.0"},"canonical_sha256":"a7fc56a0b0b1a77607d954da53bdcf3f28496d9cd456f02d569590db4c2a1647","source":{"kind":"arxiv","id":"2207.14779","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.14779","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"2207.14779v2","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.14779","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"U76FNIFQWGTX","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"pith_short_16","alias_value":"U76FNIFQWGTXMB6Z","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"pith_short_8","alias_value":"U76FNIFQ","created_at":"2026-07-05T06:08:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:U76FNIFQWGTXMB6ZKTNFHPOPH4","target":"record","payload":{"canonical_record":{"source":{"id":"2207.14779","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-07-29T16:44:37Z","cross_cats_sorted":[],"title_canon_sha256":"04e3b7f36642961af5e754981bbd70b17e0705f6e0e97e04b6245821f93fa77b","abstract_canon_sha256":"8fe1caaa23e89c096f86ee48e503cab8587bf50abf1288fb5d5047a91ea38c33"},"schema_version":"1.0"},"canonical_sha256":"a7fc56a0b0b1a77607d954da53bdcf3f28496d9cd456f02d569590db4c2a1647","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:08:51.682692Z","signature_b64":"7CboiBYolta3iuzH6X6jSZw/ER+SKMgDvSbUO+bbzdotQSM3FBIoqhOABOAtrrkeUCKnJ7O7rFu22wyX1dL/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7fc56a0b0b1a77607d954da53bdcf3f28496d9cd456f02d569590db4c2a1647","last_reissued_at":"2026-07-05T06:08:51.682330Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:08:51.682330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.14779","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":"2026-07-05T06:08:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNv6MHUHb2t+gZPkJufIsKDwDh7KZopjwsTlsi6kBcORWlBggbS2M2nEQswgN45xQpvx87aeh0JH7JZyRYGnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:28:11.341095Z"},"content_sha256":"a61597333efe7815e359f00e1ed67bdc89e77c0b03e0b8e10c767df0b5ad2544","schema_version":"1.0","event_id":"sha256:a61597333efe7815e359f00e1ed67bdc89e77c0b03e0b8e10c767df0b5ad2544"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:U76FNIFQWGTXMB6ZKTNFHPOPH4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Margarita P. Castro, Merve Bodur, Yongjia Song","submitted_at":"2022-07-29T16:44:37Z","abstract_excerpt":"We introduce an aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We demonstrate that the aggregated MSILP can be solved exactly via a branch-and-cut algorithm integrated with a variant of stochastic dual dynamic programming. To improve tractability, we propose to use this approach to obtain dual bounds. Moreover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.14779","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/2207.14779/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":"2026-07-05T06:08:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"37ugXxpTateyPDIq5rj4DAn4zmIaN5mzPKAPS07IIqcUF9lt4DYKAvq2LMEEpPSL5bjkTRhM53czh8/JTH4GBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T20:28:11.341976Z"},"content_sha256":"d41bf135c5a363e1d99fdefb6caf5270e3f11cbf539707319befd28bdc4159ad","schema_version":"1.0","event_id":"sha256:d41bf135c5a363e1d99fdefb6caf5270e3f11cbf539707319befd28bdc4159ad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4/bundle.json","state_url":"https://pith.science/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4/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":"2026-08-05T20:28:11Z","links":{"resolver":"https://pith.science/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4","bundle":"https://pith.science/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4/bundle.json","state":"https://pith.science/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U76FNIFQWGTXMB6ZKTNFHPOPH4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:U76FNIFQWGTXMB6ZKTNFHPOPH4","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":"8fe1caaa23e89c096f86ee48e503cab8587bf50abf1288fb5d5047a91ea38c33","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-07-29T16:44:37Z","title_canon_sha256":"04e3b7f36642961af5e754981bbd70b17e0705f6e0e97e04b6245821f93fa77b"},"schema_version":"1.0","source":{"id":"2207.14779","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.14779","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"2207.14779v2","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.14779","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"U76FNIFQWGTX","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"pith_short_16","alias_value":"U76FNIFQWGTXMB6Z","created_at":"2026-07-05T06:08:51Z"},{"alias_kind":"pith_short_8","alias_value":"U76FNIFQ","created_at":"2026-07-05T06:08:51Z"}],"graph_snapshots":[{"event_id":"sha256:d41bf135c5a363e1d99fdefb6caf5270e3f11cbf539707319befd28bdc4159ad","target":"graph","created_at":"2026-07-05T06:08:51Z","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/2207.14779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce an aggregation framework to address multi-stage stochastic programs with mixed-integer state variables and continuous local variables (MSILPs). Our aggregation framework imposes additional structure to the integer state variables by leveraging the information of the underlying stochastic process, which is modeled as a Markov chain (MC). We demonstrate that the aggregated MSILP can be solved exactly via a branch-and-cut algorithm integrated with a variant of stochastic dual dynamic programming. To improve tractability, we propose to use this approach to obtain dual bounds. Moreover","authors_text":"Margarita P. Castro, Merve Bodur, Yongjia Song","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-07-29T16:44:37Z","title":"Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.14779","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:a61597333efe7815e359f00e1ed67bdc89e77c0b03e0b8e10c767df0b5ad2544","target":"record","created_at":"2026-07-05T06:08:51Z","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":"8fe1caaa23e89c096f86ee48e503cab8587bf50abf1288fb5d5047a91ea38c33","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2022-07-29T16:44:37Z","title_canon_sha256":"04e3b7f36642961af5e754981bbd70b17e0705f6e0e97e04b6245821f93fa77b"},"schema_version":"1.0","source":{"id":"2207.14779","kind":"arxiv","version":2}},"canonical_sha256":"a7fc56a0b0b1a77607d954da53bdcf3f28496d9cd456f02d569590db4c2a1647","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a7fc56a0b0b1a77607d954da53bdcf3f28496d9cd456f02d569590db4c2a1647","first_computed_at":"2026-07-05T06:08:51.682330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:08:51.682330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7CboiBYolta3iuzH6X6jSZw/ER+SKMgDvSbUO+bbzdotQSM3FBIoqhOABOAtrrkeUCKnJ7O7rFu22wyX1dL/Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:08:51.682692Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.14779","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a61597333efe7815e359f00e1ed67bdc89e77c0b03e0b8e10c767df0b5ad2544","sha256:d41bf135c5a363e1d99fdefb6caf5270e3f11cbf539707319befd28bdc4159ad"],"state_sha256":"9e5702bd1e31f3bc177c1aac47441d10439538f16f11bc453e2573f68f7b7866"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Alu8m1K5982bC+YH8lxoKooQ/GW4JhpqidaFbJraJCor+3Fr5ikX37hdS92NUY5+gvo5qPUih7oV0+QcBaFLDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T20:28:11.349510Z","bundle_sha256":"5661f8d2d048735d1904fabd70a0152263642e8d65b22494b18d90c798012db8"}}