{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ZDTHQIIGTMQIJ3QNEPF4674DEW","short_pith_number":"pith:ZDTHQIIG","canonical_record":{"source":{"id":"2601.07144","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-01-12T02:26:32Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"f70be8eba644a359b9514c2b89bdd224f6c7f352611737eea15b225b88840a81","abstract_canon_sha256":"270f66d95c9e440361529b2702ef95aad7e387803b3c0564727de2871e5bfe26"},"schema_version":"1.0"},"canonical_sha256":"c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf","source":{"kind":"arxiv","id":"2601.07144","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.07144","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"arxiv_version","alias_value":"2601.07144v3","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.07144","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZDTHQIIGTMQI","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"pith_short_16","alias_value":"ZDTHQIIGTMQIJ3QN","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"pith_short_8","alias_value":"ZDTHQIIG","created_at":"2026-06-04T01:08:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ZDTHQIIGTMQIJ3QNEPF4674DEW","target":"record","payload":{"canonical_record":{"source":{"id":"2601.07144","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-01-12T02:26:32Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"f70be8eba644a359b9514c2b89bdd224f6c7f352611737eea15b225b88840a81","abstract_canon_sha256":"270f66d95c9e440361529b2702ef95aad7e387803b3c0564727de2871e5bfe26"},"schema_version":"1.0"},"canonical_sha256":"c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:39.648066Z","signature_b64":"2SsV63SSM6GgY8VwgvJFy79hV5m3kEpE0PTmCYmKqZM/n/USxYPA6BbKLzdiRZI+GGkM8yAdV6R0aomhmBr6Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf","last_reissued_at":"2026-06-04T01:08:39.647011Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:39.647011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.07144","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T01:08:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dF47dZn56B1Xe54GAoSOZm494FmQqmiPmvJ1JKPrXQtg1i7MhZGlEyA4qKnNGprJCZwGWDnf3ILDV+qPqTllCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:03:27.093522Z"},"content_sha256":"e732370da58f80dab2119f28e5deab1c20e428c51304442b20e1a4381a8782cf","schema_version":"1.0","event_id":"sha256:e732370da58f80dab2119f28e5deab1c20e428c51304442b20e1a4381a8782cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ZDTHQIIGTMQIJ3QNEPF4674DEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Transport under Group Fairness Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Aur\\'elien Bellet, Francisco Andrade, Linus Bleistein, Mathieu Dagr\\'eou, Thomas Boudou","submitted_at":"2026-01-12T02:26:32Z","abstract_excerpt":"Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalized OT problem, for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07144","kind":"arxiv","version":3},"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/2601.07144/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":"2026-06-04T01:08:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QXRnqebD/uBKtcSkz0XAnTzuLklPRMy0HUCN4iGW/mlxZZJL8MB5dikDC6x6EGnxshOiJ3PTrvGxrf1OGPTJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T08:03:27.093901Z"},"content_sha256":"33ccb61f6966d14e36542131561d33532bab0ae09398d96cc89e2fd09950ac30","schema_version":"1.0","event_id":"sha256:33ccb61f6966d14e36542131561d33532bab0ae09398d96cc89e2fd09950ac30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW/bundle.json","state_url":"https://pith.science/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW/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":"2026-06-28T08:03:27Z","links":{"resolver":"https://pith.science/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW","bundle":"https://pith.science/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW/bundle.json","state":"https://pith.science/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDTHQIIGTMQIJ3QNEPF4674DEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZDTHQIIGTMQIJ3QNEPF4674DEW","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":"270f66d95c9e440361529b2702ef95aad7e387803b3c0564727de2871e5bfe26","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-01-12T02:26:32Z","title_canon_sha256":"f70be8eba644a359b9514c2b89bdd224f6c7f352611737eea15b225b88840a81"},"schema_version":"1.0","source":{"id":"2601.07144","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.07144","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"arxiv_version","alias_value":"2601.07144v3","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.07144","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZDTHQIIGTMQI","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"pith_short_16","alias_value":"ZDTHQIIGTMQIJ3QN","created_at":"2026-06-04T01:08:39Z"},{"alias_kind":"pith_short_8","alias_value":"ZDTHQIIG","created_at":"2026-06-04T01:08:39Z"}],"graph_snapshots":[{"event_id":"sha256:33ccb61f6966d14e36542131561d33532bab0ae09398d96cc89e2fd09950ac30","target":"graph","created_at":"2026-06-04T01:08:39Z","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/2601.07144/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two individuals from any two given groups in the OT plan satisfies a predefined target. We first propose a modified Sinkhorn algorithm to compute perfectly fair transport plans efficiently. Since exact fairness can significantly degrade matching quality in practice, we then develop two relaxation strategies. The first one involves solving a penalized OT problem, for ","authors_text":"Aur\\'elien Bellet, Francisco Andrade, Linus Bleistein, Mathieu Dagr\\'eou, Thomas Boudou","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-01-12T02:26:32Z","title":"Optimal Transport under Group Fairness Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.07144","kind":"arxiv","version":3},"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:e732370da58f80dab2119f28e5deab1c20e428c51304442b20e1a4381a8782cf","target":"record","created_at":"2026-06-04T01:08:39Z","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":"270f66d95c9e440361529b2702ef95aad7e387803b3c0564727de2871e5bfe26","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-01-12T02:26:32Z","title_canon_sha256":"f70be8eba644a359b9514c2b89bdd224f6c7f352611737eea15b225b88840a81"},"schema_version":"1.0","source":{"id":"2601.07144","kind":"arxiv","version":3}},"canonical_sha256":"c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8e67821069b2084ee0d23cbcf7f8325acebf25dffd3fea38ede4397e3a382bf","first_computed_at":"2026-06-04T01:08:39.647011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:08:39.647011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2SsV63SSM6GgY8VwgvJFy79hV5m3kEpE0PTmCYmKqZM/n/USxYPA6BbKLzdiRZI+GGkM8yAdV6R0aomhmBr6Ag==","signature_status":"signed_v1","signed_at":"2026-06-04T01:08:39.648066Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.07144","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e732370da58f80dab2119f28e5deab1c20e428c51304442b20e1a4381a8782cf","sha256:33ccb61f6966d14e36542131561d33532bab0ae09398d96cc89e2fd09950ac30"],"state_sha256":"452cd783800b7530f7e9dc380acadb7ac88f918734ffd4462e64866a59f7c482"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbcp8xSBAMk6ZlWCKTJRZ+PVEAbmhIJ56jTerE1KlMtt0XemGX2vQGBJDPYew8dES2PVktG+BhxdcW0Jw233Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T08:03:27.095935Z","bundle_sha256":"f8832e9c7c77ea53455f114fea5b928a147b8f5c935b61f66b75493e4a22596f"}}