{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:64PCNYIRSXS6L66NIBKUXPZN5G","short_pith_number":"pith:64PCNYIR","canonical_record":{"source":{"id":"1805.03588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-09T15:29:54Z","cross_cats_sorted":[],"title_canon_sha256":"4c458a4c1bf987d4afed55a95ba239a89088d3b6da679298303d82c9557dc5a2","abstract_canon_sha256":"79a161360b0a595af5428ee66bfa351f16dbbb8ab220870c7358ab847c39f5b0"},"schema_version":"1.0"},"canonical_sha256":"f71e26e11195e5e5fbcd40554bbf2de99348d6f5f28475eeb3d417832016f204","source":{"kind":"arxiv","id":"1805.03588","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03588","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03588v1","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03588","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"64PCNYIRSXS6","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"64PCNYIRSXS6L66N","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"64PCNYIR","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:64PCNYIRSXS6L66NIBKUXPZN5G","target":"record","payload":{"canonical_record":{"source":{"id":"1805.03588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-09T15:29:54Z","cross_cats_sorted":[],"title_canon_sha256":"4c458a4c1bf987d4afed55a95ba239a89088d3b6da679298303d82c9557dc5a2","abstract_canon_sha256":"79a161360b0a595af5428ee66bfa351f16dbbb8ab220870c7358ab847c39f5b0"},"schema_version":"1.0"},"canonical_sha256":"f71e26e11195e5e5fbcd40554bbf2de99348d6f5f28475eeb3d417832016f204","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:19.778929Z","signature_b64":"yf/YWR80yrSinThgYWQCowBehQlZP8e2KCNjqjHuyGXZZihdYb3nsFGk2WBdNj5KPa3hE4UxnkuBqXiIAtuaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f71e26e11195e5e5fbcd40554bbf2de99348d6f5f28475eeb3d417832016f204","last_reissued_at":"2026-05-18T00:16:19.778435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:19.778435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.03588","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":"2026-05-18T00:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aumJaQn3Rne/NUPtC9VYvpjVTu0fBO4H4fZrjVNNRmz0S3g2uRXDCR413LkKi4MFgzMejhLb5DdJzaYbesELBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:58:15.507325Z"},"content_sha256":"bcb64c55cf1178766d5959126e53f90571210b03f8efc9ac17dd8264676c369d","schema_version":"1.0","event_id":"sha256:bcb64c55cf1178766d5959126e53f90571210b03f8efc9ac17dd8264676c369d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:64PCNYIRSXS6L66NIBKUXPZN5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributionally robust optimization with polynomial densities: theory, models and algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daniel Kuhn, Etienne de Klerk, Krzysztof Postek","submitted_at":"2018-05-09T15:29:54Z","abstract_excerpt":"In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much freedom to inflict damage. We thus introduce a new class of ambiguity sets that contain only distributions with sum-of-squares polynomial density functions of known degrees. We show that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03588","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":""},"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":"2026-05-18T00:16:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OaUtaEtAc4yd6TQ4X2Txwtp48jpFUv4La3o9NEyVsB9VvFbZPWpHJGLAxJPqA0aUTm5/AAnFecbflfso+ZnhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:58:15.507683Z"},"content_sha256":"8a4349cdf9b0c11811fed5c3323ec552b642f0e8a8b20a9765e1f14fafcaf29d","schema_version":"1.0","event_id":"sha256:8a4349cdf9b0c11811fed5c3323ec552b642f0e8a8b20a9765e1f14fafcaf29d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64PCNYIRSXS6L66NIBKUXPZN5G/bundle.json","state_url":"https://pith.science/pith/64PCNYIRSXS6L66NIBKUXPZN5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64PCNYIRSXS6L66NIBKUXPZN5G/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":"2026-06-04T14:58:15Z","links":{"resolver":"https://pith.science/pith/64PCNYIRSXS6L66NIBKUXPZN5G","bundle":"https://pith.science/pith/64PCNYIRSXS6L66NIBKUXPZN5G/bundle.json","state":"https://pith.science/pith/64PCNYIRSXS6L66NIBKUXPZN5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64PCNYIRSXS6L66NIBKUXPZN5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:64PCNYIRSXS6L66NIBKUXPZN5G","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":"79a161360b0a595af5428ee66bfa351f16dbbb8ab220870c7358ab847c39f5b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-09T15:29:54Z","title_canon_sha256":"4c458a4c1bf987d4afed55a95ba239a89088d3b6da679298303d82c9557dc5a2"},"schema_version":"1.0","source":{"id":"1805.03588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.03588","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"arxiv_version","alias_value":"1805.03588v1","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.03588","created_at":"2026-05-18T00:16:19Z"},{"alias_kind":"pith_short_12","alias_value":"64PCNYIRSXS6","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"64PCNYIRSXS6L66N","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"64PCNYIR","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:8a4349cdf9b0c11811fed5c3323ec552b642f0e8a8b20a9765e1f14fafcaf29d","target":"graph","created_at":"2026-05-18T00:16:19Z","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"},"paper":{"abstract_excerpt":"In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much freedom to inflict damage. We thus introduce a new class of ambiguity sets that contain only distributions with sum-of-squares polynomial density functions of known degrees. We show that","authors_text":"Daniel Kuhn, Etienne de Klerk, Krzysztof Postek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-09T15:29:54Z","title":"Distributionally robust optimization with polynomial densities: theory, models and algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03588","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:bcb64c55cf1178766d5959126e53f90571210b03f8efc9ac17dd8264676c369d","target":"record","created_at":"2026-05-18T00:16:19Z","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":"79a161360b0a595af5428ee66bfa351f16dbbb8ab220870c7358ab847c39f5b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-09T15:29:54Z","title_canon_sha256":"4c458a4c1bf987d4afed55a95ba239a89088d3b6da679298303d82c9557dc5a2"},"schema_version":"1.0","source":{"id":"1805.03588","kind":"arxiv","version":1}},"canonical_sha256":"f71e26e11195e5e5fbcd40554bbf2de99348d6f5f28475eeb3d417832016f204","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f71e26e11195e5e5fbcd40554bbf2de99348d6f5f28475eeb3d417832016f204","first_computed_at":"2026-05-18T00:16:19.778435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:19.778435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yf/YWR80yrSinThgYWQCowBehQlZP8e2KCNjqjHuyGXZZihdYb3nsFGk2WBdNj5KPa3hE4UxnkuBqXiIAtuaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:19.778929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.03588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcb64c55cf1178766d5959126e53f90571210b03f8efc9ac17dd8264676c369d","sha256:8a4349cdf9b0c11811fed5c3323ec552b642f0e8a8b20a9765e1f14fafcaf29d"],"state_sha256":"677d6198d7927cedb3f5586fc15daab7473ebe93f5f1a01399ada9b237cf943d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eQtuD2cfaifyHWejCNQLj3HST7F9Cl6rReXi8D5o72ylw2Dtx8xdfgbsrs+IXehdZEY+L0lLB5tdLnDrZ42bAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:58:15.509896Z","bundle_sha256":"03c48b7bdc283fb549ecabb7ac4c59e710dae59163407be85ed08c2562cc60c6"}}