{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TT3W72SZNDTLM4BIDS3JAVOTYN","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":"d34cf99fbdfc6c9b093de0f71aad272bd1a676aba03d98ba0be8beaa5948478f","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-25T14:43:58Z","title_canon_sha256":"0a3ec475e0f1f8f7bd1d9901c27f86a82c29db4be4f652ff330f414a40eb90e4"},"schema_version":"1.0","source":{"id":"2410.19596","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.19596","created_at":"2026-07-05T11:27:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.19596v2","created_at":"2026-07-05T11:27:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.19596","created_at":"2026-07-05T11:27:21Z"},{"alias_kind":"pith_short_12","alias_value":"TT3W72SZNDTL","created_at":"2026-07-05T11:27:21Z"},{"alias_kind":"pith_short_16","alias_value":"TT3W72SZNDTLM4BI","created_at":"2026-07-05T11:27:21Z"},{"alias_kind":"pith_short_8","alias_value":"TT3W72SZ","created_at":"2026-07-05T11:27:21Z"}],"graph_snapshots":[{"event_id":"sha256:b544d9f095058b0afe9a32fd1af9e0293440a02008e77bb26a33cd74be4b7cf3","target":"graph","created_at":"2026-07-05T11:27:21Z","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/2410.19596/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive the breakdown point for solutions of semi-discrete optimal transport problems, which characterizes the robustness of the multivariate quantiles based on optimal transport proposed in \\cite{GS}. We do so under very mild assumptions: the absolutely continuous reference measure is only assumed to have a support that is \\textcolor{mygreen}{convex}, whereas the target measure is a general discrete measure on a finite number, $n$ say, of atoms. The breakdown point depends on the target measure only through its probability weights (hence not on the location of the atoms) and involves the ge","authors_text":"Davy Paindaveine, Riccardo Passeggeri","cross_cats":["math.ST","stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-25T14:43:58Z","title":"On the robustness of semi-discrete optimal transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.19596","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":"sha256:0c747576dc117c81207a74892352607c516bcce0d4e840bf403b4891fb25d10c","target":"record","created_at":"2026-07-05T11:27:21Z","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":"d34cf99fbdfc6c9b093de0f71aad272bd1a676aba03d98ba0be8beaa5948478f","cross_cats_sorted":["math.ST","stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-10-25T14:43:58Z","title_canon_sha256":"0a3ec475e0f1f8f7bd1d9901c27f86a82c29db4be4f652ff330f414a40eb90e4"},"schema_version":"1.0","source":{"id":"2410.19596","kind":"arxiv","version":2}},"canonical_sha256":"9cf76fea5968e6b670281cb69055d3c37f091d69309ec884a3b8ae82982eb4c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cf76fea5968e6b670281cb69055d3c37f091d69309ec884a3b8ae82982eb4c5","first_computed_at":"2026-07-05T11:27:21.071300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:21.071300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j7uePSQHjsdbvhnumdySMVd+vNFyCmKA3ogLfhhfEwZ3sHl/N7SAJuX21C2BnQ4bmdkZS8MlhWqxhahZK2/tDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:21.072389Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.19596","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c747576dc117c81207a74892352607c516bcce0d4e840bf403b4891fb25d10c","sha256:b544d9f095058b0afe9a32fd1af9e0293440a02008e77bb26a33cd74be4b7cf3"],"state_sha256":"1c69a9d5d361839ad767cf8c862ea2f4f18373fca42da1651e2f4d748a1880b7"}