{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BZR3RTAFRTQI5CNFZO77SLNT56","short_pith_number":"pith:BZR3RTAF","schema_version":"1.0","canonical_sha256":"0e63b8cc058ce08e89a5cbbff92db3efa1f6739e79cf93cb1f8f6d749c85157c","source":{"kind":"arxiv","id":"1803.11500","version":2},"attestation_state":"computed","paper":{"title":"Distributionally robust polynomial chance-constraints under mixture ambiguity sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean Lasserre (LAAS-MAC), Tillmann Weisser (LAAS-MAC)","submitted_at":"2018-03-30T15:08:10Z","abstract_excerpt":"Given $X \\subset R^n$, $\\varepsilon \\in (0,1)$, a parametrized family of probability distributions $(\\mu\\_{a})\\_{a\\in A}$ on $\\Omega\\subset R^p$, we consider the feasible set $X^*\\_\\varepsilon\\subset X$ associated with  the {\\em distributionally robust} chance-constraint \\[X^*\\_\\varepsilon\\,=\\,\\{x \\in X :\\:{\\rm Prob}\\_\\mu[f(x,\\omega)\\,>\\,0]> 1-\\varepsilon,\\,\\forall\\mu\\in M\\_a\\},\\]where $M\\_a$ is the set of all possibles mixtures of distributions $\\mu\\_a$, $a\\in A$.For instance and typically, the family$M\\_a$ is the set of all mixtures ofGaussian distributions on $R$ with mean and standard devi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.11500","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-30T15:08:10Z","cross_cats_sorted":[],"title_canon_sha256":"7d64f80a711469f1796a02f004e4b83e58bf28c034f244d030624db60dcace13","abstract_canon_sha256":"b57e2e87bd1c27d9c2089a7f833e0638fd4969f45b4aa33aa0b169e5550ffc92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:08.674979Z","signature_b64":"5Yevky2yKx/X1eZ3vWT74w4Z01s6QLY3mf8qHFRHSkOZn1Wt4limwkf3rWSUNPhwkWgnaxPORxoz1gY7RBQ1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e63b8cc058ce08e89a5cbbff92db3efa1f6739e79cf93cb1f8f6d749c85157c","last_reissued_at":"2026-05-18T00:00:08.674438Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:08.674438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Distributionally robust polynomial chance-constraints under mixture ambiguity sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jean Lasserre (LAAS-MAC), Tillmann Weisser (LAAS-MAC)","submitted_at":"2018-03-30T15:08:10Z","abstract_excerpt":"Given $X \\subset R^n$, $\\varepsilon \\in (0,1)$, a parametrized family of probability distributions $(\\mu\\_{a})\\_{a\\in A}$ on $\\Omega\\subset R^p$, we consider the feasible set $X^*\\_\\varepsilon\\subset X$ associated with  the {\\em distributionally robust} chance-constraint \\[X^*\\_\\varepsilon\\,=\\,\\{x \\in X :\\:{\\rm Prob}\\_\\mu[f(x,\\omega)\\,>\\,0]> 1-\\varepsilon,\\,\\forall\\mu\\in M\\_a\\},\\]where $M\\_a$ is the set of all possibles mixtures of distributions $\\mu\\_a$, $a\\in A$.For instance and typically, the family$M\\_a$ is the set of all mixtures ofGaussian distributions on $R$ with mean and standard devi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11500","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.11500","created_at":"2026-05-18T00:00:08.674523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.11500v2","created_at":"2026-05-18T00:00:08.674523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.11500","created_at":"2026-05-18T00:00:08.674523+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZR3RTAFRTQI","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZR3RTAFRTQI5CNF","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZR3RTAF","created_at":"2026-05-18T12:32:16.446611+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56","json":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56.json","graph_json":"https://pith.science/api/pith-number/BZR3RTAFRTQI5CNFZO77SLNT56/graph.json","events_json":"https://pith.science/api/pith-number/BZR3RTAFRTQI5CNFZO77SLNT56/events.json","paper":"https://pith.science/paper/BZR3RTAF"},"agent_actions":{"view_html":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56","download_json":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56.json","view_paper":"https://pith.science/paper/BZR3RTAF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.11500&json=true","fetch_graph":"https://pith.science/api/pith-number/BZR3RTAFRTQI5CNFZO77SLNT56/graph.json","fetch_events":"https://pith.science/api/pith-number/BZR3RTAFRTQI5CNFZO77SLNT56/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56/action/storage_attestation","attest_author":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56/action/author_attestation","sign_citation":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56/action/citation_signature","submit_replication":"https://pith.science/pith/BZR3RTAFRTQI5CNFZO77SLNT56/action/replication_record"}},"created_at":"2026-05-18T00:00:08.674523+00:00","updated_at":"2026-05-18T00:00:08.674523+00:00"}