{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:WECQAESYIX35YJ5JQGBLCMNYVH","short_pith_number":"pith:WECQAESY","canonical_record":{"source":{"id":"2502.02623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-04T14:03:49Z","cross_cats_sorted":["cs.AI","math.ST","stat.TH"],"title_canon_sha256":"96962bc0f606570ce13cca77b0ca527200aa71d84b04d1f35287edf0a2dcc30f","abstract_canon_sha256":"2f38d42cd1089c31dfcd00579d9ee3e8bafe1f1c203b53dbe8c0100fb6275752"},"schema_version":"1.0"},"canonical_sha256":"b10500125845f7dc27a98182b131b8a9e6de26f48001f94f4bec111e2fd3ea89","source":{"kind":"arxiv","id":"2502.02623","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.02623","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"2502.02623v1","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02623","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"WECQAESYIX35","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"WECQAESYIX35YJ5J","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"WECQAESY","created_at":"2026-07-05T10:09:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:WECQAESYIX35YJ5JQGBLCMNYVH","target":"record","payload":{"canonical_record":{"source":{"id":"2502.02623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-04T14:03:49Z","cross_cats_sorted":["cs.AI","math.ST","stat.TH"],"title_canon_sha256":"96962bc0f606570ce13cca77b0ca527200aa71d84b04d1f35287edf0a2dcc30f","abstract_canon_sha256":"2f38d42cd1089c31dfcd00579d9ee3e8bafe1f1c203b53dbe8c0100fb6275752"},"schema_version":"1.0"},"canonical_sha256":"b10500125845f7dc27a98182b131b8a9e6de26f48001f94f4bec111e2fd3ea89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:09:31.888816Z","signature_b64":"Hwp1zUJ8TvXIBldeh/ZzJMiYI1IGwW0W3H5cr+ksl7WH0w/uO0hSIpcyDtGJee4JFWuWjuVnUi3s9fxsAxgIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b10500125845f7dc27a98182b131b8a9e6de26f48001f94f4bec111e2fd3ea89","last_reissued_at":"2026-07-05T10:09:31.888394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:09:31.888394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.02623","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":"2026-07-05T10:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXnwoHbnCozJvYwQonlfk3yzPczjGt5M5w2Zo3VcHFlUuGVitIbDzXSKE530lxKy36qEz24puzLIwq4dFyRlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:46:49.289186Z"},"content_sha256":"acafd47836ad91c68f350c4abc35778e9b5805274661658f4778b954063cecd3","schema_version":"1.0","event_id":"sha256:acafd47836ad91c68f350c4abc35778e9b5805274661658f4778b954063cecd3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:WECQAESYIX35YJ5JQGBLCMNYVH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sample Complexity of Bias Detection with Subsampled Point-to-Subspace Distances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"German Martinez Matilla, Jakub Marecek","submitted_at":"2025-02-04T14:03:49Z","abstract_excerpt":"Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected attributes. Unless one wishes to run a bias detection with a doubly-exponential run-time, one should like to have polynomial complexity of bias detection for a single subgroup. At the same time, the reference data may be based on surveys, and thus come with non-trivial uncertainty.\n  Here, we reformulate bias detection as a point-to-subspace problem on the spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02623","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.02623/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":"2026-07-05T10:09:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E56PYBdM/HpSESlVWUlUPaZq28i2j4otVC/DfxUT6MappTpP5ebk/xWPleXLiVjODreGOH9GXsDra1WYnkX6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T20:46:49.289828Z"},"content_sha256":"f8914691329825a35849b38367e574a4ac64be9117a2c734d35325a067c4d7da","schema_version":"1.0","event_id":"sha256:f8914691329825a35849b38367e574a4ac64be9117a2c734d35325a067c4d7da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WECQAESYIX35YJ5JQGBLCMNYVH/bundle.json","state_url":"https://pith.science/pith/WECQAESYIX35YJ5JQGBLCMNYVH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WECQAESYIX35YJ5JQGBLCMNYVH/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":"2026-08-13T20:46:49Z","links":{"resolver":"https://pith.science/pith/WECQAESYIX35YJ5JQGBLCMNYVH","bundle":"https://pith.science/pith/WECQAESYIX35YJ5JQGBLCMNYVH/bundle.json","state":"https://pith.science/pith/WECQAESYIX35YJ5JQGBLCMNYVH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WECQAESYIX35YJ5JQGBLCMNYVH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WECQAESYIX35YJ5JQGBLCMNYVH","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":"2f38d42cd1089c31dfcd00579d9ee3e8bafe1f1c203b53dbe8c0100fb6275752","cross_cats_sorted":["cs.AI","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-04T14:03:49Z","title_canon_sha256":"96962bc0f606570ce13cca77b0ca527200aa71d84b04d1f35287edf0a2dcc30f"},"schema_version":"1.0","source":{"id":"2502.02623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.02623","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"arxiv_version","alias_value":"2502.02623v1","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.02623","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"pith_short_12","alias_value":"WECQAESYIX35","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"pith_short_16","alias_value":"WECQAESYIX35YJ5J","created_at":"2026-07-05T10:09:31Z"},{"alias_kind":"pith_short_8","alias_value":"WECQAESY","created_at":"2026-07-05T10:09:31Z"}],"graph_snapshots":[{"event_id":"sha256:f8914691329825a35849b38367e574a4ac64be9117a2c734d35325a067c4d7da","target":"graph","created_at":"2026-07-05T10:09:31Z","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/2502.02623/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected attributes. Unless one wishes to run a bias detection with a doubly-exponential run-time, one should like to have polynomial complexity of bias detection for a single subgroup. At the same time, the reference data may be based on surveys, and thus come with non-trivial uncertainty.\n  Here, we reformulate bias detection as a point-to-subspace problem on the spac","authors_text":"German Martinez Matilla, Jakub Marecek","cross_cats":["cs.AI","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-04T14:03:49Z","title":"Sample Complexity of Bias Detection with Subsampled Point-to-Subspace Distances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.02623","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:acafd47836ad91c68f350c4abc35778e9b5805274661658f4778b954063cecd3","target":"record","created_at":"2026-07-05T10:09:31Z","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":"2f38d42cd1089c31dfcd00579d9ee3e8bafe1f1c203b53dbe8c0100fb6275752","cross_cats_sorted":["cs.AI","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-04T14:03:49Z","title_canon_sha256":"96962bc0f606570ce13cca77b0ca527200aa71d84b04d1f35287edf0a2dcc30f"},"schema_version":"1.0","source":{"id":"2502.02623","kind":"arxiv","version":1}},"canonical_sha256":"b10500125845f7dc27a98182b131b8a9e6de26f48001f94f4bec111e2fd3ea89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b10500125845f7dc27a98182b131b8a9e6de26f48001f94f4bec111e2fd3ea89","first_computed_at":"2026-07-05T10:09:31.888394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:09:31.888394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hwp1zUJ8TvXIBldeh/ZzJMiYI1IGwW0W3H5cr+ksl7WH0w/uO0hSIpcyDtGJee4JFWuWjuVnUi3s9fxsAxgIBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:09:31.888816Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.02623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:acafd47836ad91c68f350c4abc35778e9b5805274661658f4778b954063cecd3","sha256:f8914691329825a35849b38367e574a4ac64be9117a2c734d35325a067c4d7da"],"state_sha256":"3844e30ec2bc267c48c1205cb52427f0b0031649a39efc6652cba114c7818294"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KgJzauENM2mwv5QUyRJTqZTDJhpcWER9sqtWZg1FTNZY3XdufZM8xts8IGkr27qQL7DF4tzh4RF+ioCPfagiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T20:46:49.299060Z","bundle_sha256":"bdc71adcb5fdf621694d3e981143e912fca3a7e45690ac0c9d5497a3ee12c7ed"}}