{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OHZCK2MIWXK2J5L6X3JYYUGGHS","short_pith_number":"pith:OHZCK2MI","canonical_record":{"source":{"id":"1509.02237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-08T01:08:04Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"29854569d7acf90700fe586c04afd32ea6bb8f65d4628fce1b172d4c8e50d5e7","abstract_canon_sha256":"efa4bb6c938b4707e722b7f7a28386b351b1203f0df99cf7dbea7794217751dc"},"schema_version":"1.0"},"canonical_sha256":"71f2256988b5d5a4f57ebed38c50c63c81042e42837021343da5b3986534f76e","source":{"kind":"arxiv","id":"1509.02237","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02237","created_at":"2026-05-18T01:30:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02237v2","created_at":"2026-05-18T01:30:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02237","created_at":"2026-05-18T01:30:17Z"},{"alias_kind":"pith_short_12","alias_value":"OHZCK2MIWXK2","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHZCK2MIWXK2J5L6","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHZCK2MI","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OHZCK2MIWXK2J5L6X3JYYUGGHS","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02237","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-08T01:08:04Z","cross_cats_sorted":["stat.ML","stat.TH"],"title_canon_sha256":"29854569d7acf90700fe586c04afd32ea6bb8f65d4628fce1b172d4c8e50d5e7","abstract_canon_sha256":"efa4bb6c938b4707e722b7f7a28386b351b1203f0df99cf7dbea7794217751dc"},"schema_version":"1.0"},"canonical_sha256":"71f2256988b5d5a4f57ebed38c50c63c81042e42837021343da5b3986534f76e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:17.903836Z","signature_b64":"QoF+En35uN02381QBaOaFNSMp1GtHM35eOUpmJ0283jWRjkfDWvAMw7p1se2jil1zhXVF6/jGOHqJ1UKOytrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71f2256988b5d5a4f57ebed38c50c63c81042e42837021343da5b3986534f76e","last_reissued_at":"2026-05-18T01:30:17.903151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:17.903151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02237","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvZpm4YEua3DwOlaL6pk8AeUZ6Z+zwBp2Sb2BwspGlN9WzJNsCYsqId8Tx/tXdxMymkcNg2znxVbuxY+Dlp5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:09:50.138830Z"},"content_sha256":"1e08bf2abc58047a055d026c67dc51776ea7111f211a0472b1700c5a1dbfdbf9","schema_version":"1.0","event_id":"sha256:1e08bf2abc58047a055d026c67dc51776ea7111f211a0472b1700c5a1dbfdbf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OHZCK2MIWXK2J5L6X3JYYUGGHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML","stat.TH"],"primary_cat":"math.ST","authors_text":"Aaditya Ramdas, Marco Cuturi, Nicolas Garcia","submitted_at":"2015-09-08T01:08:04Z","abstract_excerpt":"Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being intelligently designed and analyzed, both for the unidimensional and the multivariate setting. Our contribution is to tie together many of these tests, drawing connections between seemingly very different statistics. In this work, our central object is the Wasserstein distance, as we form a chain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02237","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:30:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e1rUIREecXsFR5z7dPgkhY/X48XSQrPT1KMueRaesSEy6IjOv3ad0n+6tdkh8WNT8fLjCmvPWnWQ5SRH6qzmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:09:50.139372Z"},"content_sha256":"033ce07373fde9f7576a43e38ea526359b5c2a53aaf6ba8cd41dede6e62f1ac2","schema_version":"1.0","event_id":"sha256:033ce07373fde9f7576a43e38ea526359b5c2a53aaf6ba8cd41dede6e62f1ac2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS/bundle.json","state_url":"https://pith.science/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS/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":"2026-05-26T00:09:50Z","links":{"resolver":"https://pith.science/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS","bundle":"https://pith.science/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS/bundle.json","state":"https://pith.science/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OHZCK2MIWXK2J5L6X3JYYUGGHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OHZCK2MIWXK2J5L6X3JYYUGGHS","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":"efa4bb6c938b4707e722b7f7a28386b351b1203f0df99cf7dbea7794217751dc","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-08T01:08:04Z","title_canon_sha256":"29854569d7acf90700fe586c04afd32ea6bb8f65d4628fce1b172d4c8e50d5e7"},"schema_version":"1.0","source":{"id":"1509.02237","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02237","created_at":"2026-05-18T01:30:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02237v2","created_at":"2026-05-18T01:30:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02237","created_at":"2026-05-18T01:30:17Z"},{"alias_kind":"pith_short_12","alias_value":"OHZCK2MIWXK2","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OHZCK2MIWXK2J5L6","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OHZCK2MI","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:033ce07373fde9f7576a43e38ea526359b5c2a53aaf6ba8cd41dede6e62f1ac2","target":"graph","created_at":"2026-05-18T01:30:17Z","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"},"paper":{"abstract_excerpt":"Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is old and rich, with a wide variety of statistics having being intelligently designed and analyzed, both for the unidimensional and the multivariate setting. Our contribution is to tie together many of these tests, drawing connections between seemingly very different statistics. In this work, our central object is the Wasserstein distance, as we form a chain ","authors_text":"Aaditya Ramdas, Marco Cuturi, Nicolas Garcia","cross_cats":["stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-08T01:08:04Z","title":"On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02237","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":"sha256:1e08bf2abc58047a055d026c67dc51776ea7111f211a0472b1700c5a1dbfdbf9","target":"record","created_at":"2026-05-18T01:30:17Z","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":"efa4bb6c938b4707e722b7f7a28386b351b1203f0df99cf7dbea7794217751dc","cross_cats_sorted":["stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2015-09-08T01:08:04Z","title_canon_sha256":"29854569d7acf90700fe586c04afd32ea6bb8f65d4628fce1b172d4c8e50d5e7"},"schema_version":"1.0","source":{"id":"1509.02237","kind":"arxiv","version":2}},"canonical_sha256":"71f2256988b5d5a4f57ebed38c50c63c81042e42837021343da5b3986534f76e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71f2256988b5d5a4f57ebed38c50c63c81042e42837021343da5b3986534f76e","first_computed_at":"2026-05-18T01:30:17.903151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:17.903151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QoF+En35uN02381QBaOaFNSMp1GtHM35eOUpmJ0283jWRjkfDWvAMw7p1se2jil1zhXVF6/jGOHqJ1UKOytrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:17.903836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02237","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e08bf2abc58047a055d026c67dc51776ea7111f211a0472b1700c5a1dbfdbf9","sha256:033ce07373fde9f7576a43e38ea526359b5c2a53aaf6ba8cd41dede6e62f1ac2"],"state_sha256":"60bcdadb2dab26e0d48795c645ca683a2e61d627aaeda6b81f590b5b35764e34"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G7L45GU/Jfpj1i7FBZMWpI9aDArgLF5C7dHgxiADmyOx/cJYFeoIH5QiJhDfPCnCEl0Dv1ajV3Bi6j+oC5oTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:09:50.142759Z","bundle_sha256":"6057402d1e678f862e4ab587272dfc9f1143e4ba767c6c1be27789a82e21c26a"}}