{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:NO6CYLEPZ5VDQPZIIOX4RMPKCG","short_pith_number":"pith:NO6CYLEP","canonical_record":{"source":{"id":"2102.05573","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-10T17:13:21Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"04ede079b086ee175a5a288a65f381ae83c89f35683405ebae3fbb475831060a","abstract_canon_sha256":"6a5b7551d0553c2c6d78f2cb8a6e98573107c9f44d774df1e67e754d74b0e572"},"schema_version":"1.0"},"canonical_sha256":"6bbc2c2c8fcf6a383f2843afc8b1ea11a985e218127c538e7fe85614f4f850b3","source":{"kind":"arxiv","id":"2102.05573","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05573","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05573v3","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05573","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"NO6CYLEPZ5VD","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"pith_short_16","alias_value":"NO6CYLEPZ5VDQPZI","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"pith_short_8","alias_value":"NO6CYLEP","created_at":"2026-07-05T03:56:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:NO6CYLEPZ5VDQPZIIOX4RMPKCG","target":"record","payload":{"canonical_record":{"source":{"id":"2102.05573","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-10T17:13:21Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"04ede079b086ee175a5a288a65f381ae83c89f35683405ebae3fbb475831060a","abstract_canon_sha256":"6a5b7551d0553c2c6d78f2cb8a6e98573107c9f44d774df1e67e754d74b0e572"},"schema_version":"1.0"},"canonical_sha256":"6bbc2c2c8fcf6a383f2843afc8b1ea11a985e218127c538e7fe85614f4f850b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:56:00.697479Z","signature_b64":"XW7e1JeMSJSUuohfG87TAoNL2msInP+IPElUfJbg6gnDSAnPTeokmbLq0s3Ox4x6UeQWmU+K8rSdjFZ7uKWGDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bbc2c2c8fcf6a383f2843afc8b1ea11a985e218127c538e7fe85614f4f850b3","last_reissued_at":"2026-07-05T03:56:00.696974Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:56:00.696974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.05573","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":"2026-07-05T03:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2UUsvLzxLVP5bFuzTpD2F0LQr1pz+WnuaRVGdrBaPzUPv4ukdRwx+EUiEvxdYC0Mezq5Zr12m1DVkWWGXHaRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:26:21.869424Z"},"content_sha256":"ad5f996d059d504c5dbe0acf4113035b6d02e0382947bf0b8e07a4c73e998902","schema_version":"1.0","event_id":"sha256:ad5f996d059d504c5dbe0acf4113035b6d02e0382947bf0b8e07a4c73e998902"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:NO6CYLEPZ5VDQPZIIOX4RMPKCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Witness Two-Sample Test","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Bernhard Sch\\\"olkopf, Jonas M. K\\\"ubler, Krikamol Muandet, Wittawat Jitkrittum","submitted_at":"2021-02-10T17:13:21Z","abstract_excerpt":"The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a weighted sum of kernel evaluations on a set of basis points. Typically the kernel is optimized on a training set, and hypothesis testing is performed on a separate test set to avoid overfitting (i.e., control type-I error). That is, the test set is used to simultaneously estimate the expectations and define the basis points, while the training set only serves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05573","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/2102.05573/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":"2026-07-05T03:56:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fDWeo9E2qpFwkVSOBj59hVZpY6eOcT5842DKen1uRiwtze4YLlApzUDwf8KQxPIjG4yDwfjY7/ZzyLlqu6/rAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:26:21.869924Z"},"content_sha256":"c3d6ccc67eb94014d5c4f1614894747385c0cd01397c3e021ab53c2481539033","schema_version":"1.0","event_id":"sha256:c3d6ccc67eb94014d5c4f1614894747385c0cd01397c3e021ab53c2481539033"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG/bundle.json","state_url":"https://pith.science/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG/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":"2026-08-18T15:26:21Z","links":{"resolver":"https://pith.science/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG","bundle":"https://pith.science/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG/bundle.json","state":"https://pith.science/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NO6CYLEPZ5VDQPZIIOX4RMPKCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:NO6CYLEPZ5VDQPZIIOX4RMPKCG","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":"6a5b7551d0553c2c6d78f2cb8a6e98573107c9f44d774df1e67e754d74b0e572","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-10T17:13:21Z","title_canon_sha256":"04ede079b086ee175a5a288a65f381ae83c89f35683405ebae3fbb475831060a"},"schema_version":"1.0","source":{"id":"2102.05573","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05573","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05573v3","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05573","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"pith_short_12","alias_value":"NO6CYLEPZ5VD","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"pith_short_16","alias_value":"NO6CYLEPZ5VDQPZI","created_at":"2026-07-05T03:56:00Z"},{"alias_kind":"pith_short_8","alias_value":"NO6CYLEP","created_at":"2026-07-05T03:56:00Z"}],"graph_snapshots":[{"event_id":"sha256:c3d6ccc67eb94014d5c4f1614894747385c0cd01397c3e021ab53c2481539033","target":"graph","created_at":"2026-07-05T03:56:00Z","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/2102.05573/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Maximum Mean Discrepancy (MMD) has been the state-of-the-art nonparametric test for tackling the two-sample problem. Its statistic is given by the difference in expectations of the witness function, a real-valued function defined as a weighted sum of kernel evaluations on a set of basis points. Typically the kernel is optimized on a training set, and hypothesis testing is performed on a separate test set to avoid overfitting (i.e., control type-I error). That is, the test set is used to simultaneously estimate the expectations and define the basis points, while the training set only serves","authors_text":"Bernhard Sch\\\"olkopf, Jonas M. K\\\"ubler, Krikamol Muandet, Wittawat Jitkrittum","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-10T17:13:21Z","title":"A Witness Two-Sample Test"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05573","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:ad5f996d059d504c5dbe0acf4113035b6d02e0382947bf0b8e07a4c73e998902","target":"record","created_at":"2026-07-05T03:56:00Z","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":"6a5b7551d0553c2c6d78f2cb8a6e98573107c9f44d774df1e67e754d74b0e572","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2021-02-10T17:13:21Z","title_canon_sha256":"04ede079b086ee175a5a288a65f381ae83c89f35683405ebae3fbb475831060a"},"schema_version":"1.0","source":{"id":"2102.05573","kind":"arxiv","version":3}},"canonical_sha256":"6bbc2c2c8fcf6a383f2843afc8b1ea11a985e218127c538e7fe85614f4f850b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bbc2c2c8fcf6a383f2843afc8b1ea11a985e218127c538e7fe85614f4f850b3","first_computed_at":"2026-07-05T03:56:00.696974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:56:00.696974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XW7e1JeMSJSUuohfG87TAoNL2msInP+IPElUfJbg6gnDSAnPTeokmbLq0s3Ox4x6UeQWmU+K8rSdjFZ7uKWGDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:56:00.697479Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.05573","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad5f996d059d504c5dbe0acf4113035b6d02e0382947bf0b8e07a4c73e998902","sha256:c3d6ccc67eb94014d5c4f1614894747385c0cd01397c3e021ab53c2481539033"],"state_sha256":"e619254aabeddcff977ccf8c436b944c899b5acbcd5e2d64bd99a6a0546e2f85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2lnHC/cbjehAWpy+uoVSp5Q+3kEMTEOqQh7hTwYgQQf3s2E9ahR0VDaE2vvnraq2yQTa7ZSKefLGOUz5BA1Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T15:26:21.874109Z","bundle_sha256":"70675a93f4808cf5e7da5258291bfa22b630cb8451f3c558b661ae6ec0bedadc"}}