{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:TRMBEYEJ3XUPGUFPW2XL67VV5U","short_pith_number":"pith:TRMBEYEJ","canonical_record":{"source":{"id":"2205.00362","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-30T22:49:01Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"4c4ee82e9fb74a68b38c6effcdce465646c542d35dcf571cb1561bc0a1ed193a","abstract_canon_sha256":"27c0083d11e22797db838a4290a92f86b157d2dce7c5468c79d477afda28035e"},"schema_version":"1.0"},"canonical_sha256":"9c58126089dde8f350afb6aebf7eb5ed179bc4f186e98250468a7e10d0cfc698","source":{"kind":"arxiv","id":"2205.00362","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.00362","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"2205.00362v4","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.00362","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"TRMBEYEJ3XUP","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"pith_short_16","alias_value":"TRMBEYEJ3XUPGUFP","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"pith_short_8","alias_value":"TRMBEYEJ","created_at":"2026-07-05T09:39:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:TRMBEYEJ3XUPGUFPW2XL67VV5U","target":"record","payload":{"canonical_record":{"source":{"id":"2205.00362","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-30T22:49:01Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"4c4ee82e9fb74a68b38c6effcdce465646c542d35dcf571cb1561bc0a1ed193a","abstract_canon_sha256":"27c0083d11e22797db838a4290a92f86b157d2dce7c5468c79d477afda28035e"},"schema_version":"1.0"},"canonical_sha256":"9c58126089dde8f350afb6aebf7eb5ed179bc4f186e98250468a7e10d0cfc698","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:49.739217Z","signature_b64":"irpnQy3URLLbg13ZROwtR4RO38ecFOIm8nh7mfj6WURcUyCApFpH2O069zH7H6CnTKk3aX+Ru5Z2xQwDb5/LBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c58126089dde8f350afb6aebf7eb5ed179bc4f186e98250468a7e10d0cfc698","last_reissued_at":"2026-07-05T09:39:49.738776Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:49.738776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.00362","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LmCa7UkjJtpu2qkleUrXloKC7XIBTRJz7130B5k06ZoRXa+8ENizbEjZq7CYB4VrkRwWQMyop8AVpwqHSj8zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:48:06.876843Z"},"content_sha256":"3a57187539679a1b62843b2eaba7fcb285f1ed45a0dc05a1af3b5f8adc99d113","schema_version":"1.0","event_id":"sha256:3a57187539679a1b62843b2eaba7fcb285f1ed45a0dc05a1af3b5f8adc99d113"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:TRMBEYEJ3XUPGUFPW2XL67VV5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Jincheng Yang, Luhao Zhang, Rui Gao","submitted_at":"2022-04-30T22:49:01Z","abstract_excerpt":"We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle inherent in existing duality results, our proof only uses one-dimensional convex analysis. Furthermore, we demonstrate that the interchangeability principle holds if and only if certain measurable projection and weak measurable selection conditions are satisfied. To illustrate the broader applicability of our approach, we provide a rigorous treatment of dua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.00362","kind":"arxiv","version":4},"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/2205.00362/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":"2026-07-05T09:39:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtPKq0VGWixUl+2kRw2eXFGAOn1p966WEN7+lRXIblLPUGz+WFOtelWMBTIJDENG3pXdC+jQb6fej/f1R1GNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T22:48:06.877346Z"},"content_sha256":"0a173dcf021ba1e7e2a60a48655ae173a6be65136cc48819a4d18aed4960418a","schema_version":"1.0","event_id":"sha256:0a173dcf021ba1e7e2a60a48655ae173a6be65136cc48819a4d18aed4960418a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U/bundle.json","state_url":"https://pith.science/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U/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":"2026-08-16T22:48:06Z","links":{"resolver":"https://pith.science/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U","bundle":"https://pith.science/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U/bundle.json","state":"https://pith.science/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRMBEYEJ3XUPGUFPW2XL67VV5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:TRMBEYEJ3XUPGUFPW2XL67VV5U","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":"27c0083d11e22797db838a4290a92f86b157d2dce7c5468c79d477afda28035e","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-30T22:49:01Z","title_canon_sha256":"4c4ee82e9fb74a68b38c6effcdce465646c542d35dcf571cb1561bc0a1ed193a"},"schema_version":"1.0","source":{"id":"2205.00362","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.00362","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"arxiv_version","alias_value":"2205.00362v4","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.00362","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"pith_short_12","alias_value":"TRMBEYEJ3XUP","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"pith_short_16","alias_value":"TRMBEYEJ3XUPGUFP","created_at":"2026-07-05T09:39:49Z"},{"alias_kind":"pith_short_8","alias_value":"TRMBEYEJ","created_at":"2026-07-05T09:39:49Z"}],"graph_snapshots":[{"event_id":"sha256:0a173dcf021ba1e7e2a60a48655ae173a6be65136cc48819a4d18aed4960418a","target":"graph","created_at":"2026-07-05T09:39:49Z","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/2205.00362/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle inherent in existing duality results, our proof only uses one-dimensional convex analysis. Furthermore, we demonstrate that the interchangeability principle holds if and only if certain measurable projection and weak measurable selection conditions are satisfied. To illustrate the broader applicability of our approach, we provide a rigorous treatment of dua","authors_text":"Jincheng Yang, Luhao Zhang, Rui Gao","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-30T22:49:01Z","title":"A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.00362","kind":"arxiv","version":4},"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":"sha256:3a57187539679a1b62843b2eaba7fcb285f1ed45a0dc05a1af3b5f8adc99d113","target":"record","created_at":"2026-07-05T09:39:49Z","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":"27c0083d11e22797db838a4290a92f86b157d2dce7c5468c79d477afda28035e","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-30T22:49:01Z","title_canon_sha256":"4c4ee82e9fb74a68b38c6effcdce465646c542d35dcf571cb1561bc0a1ed193a"},"schema_version":"1.0","source":{"id":"2205.00362","kind":"arxiv","version":4}},"canonical_sha256":"9c58126089dde8f350afb6aebf7eb5ed179bc4f186e98250468a7e10d0cfc698","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c58126089dde8f350afb6aebf7eb5ed179bc4f186e98250468a7e10d0cfc698","first_computed_at":"2026-07-05T09:39:49.738776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:49.738776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"irpnQy3URLLbg13ZROwtR4RO38ecFOIm8nh7mfj6WURcUyCApFpH2O069zH7H6CnTKk3aX+Ru5Z2xQwDb5/LBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:49.739217Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.00362","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a57187539679a1b62843b2eaba7fcb285f1ed45a0dc05a1af3b5f8adc99d113","sha256:0a173dcf021ba1e7e2a60a48655ae173a6be65136cc48819a4d18aed4960418a"],"state_sha256":"cac368ccf7f3bedb0605aa693ff808c156b95d2544e0e13b7244e105c2df8bbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+o38X1AM6fT4qRHs69slmw4o3s5FLiP2M+mloTVfBoIhd89VUoYWbp5Z8d6US4qS7pXCRfXcRPVp+tYH5rRQBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T22:48:06.882306Z","bundle_sha256":"c81c2ed40b568df6306b40dc4ff8e78b66c1eef51862b8ce542b9bb72db30bd1"}}