{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2TFBAY6J63UH6HCFWUS5MXQ7EF","short_pith_number":"pith:2TFBAY6J","canonical_record":{"source":{"id":"2405.03664","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-06T17:41:13Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c5bf64a98f0eae51360bb6fcbc4baa081a8a3b299f2bc24ba6625b9d96f2f4b1","abstract_canon_sha256":"cdbc22cf7376d54776cc5e4a76a2842302f23e6727f6c18dae11f6e4486b282d"},"schema_version":"1.0"},"canonical_sha256":"d4ca1063c9f6e87f1c45b525d65e1f216fd27fdaf6beb58562c7f5060d3e5633","source":{"kind":"arxiv","id":"2405.03664","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03664","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03664v2","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03664","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"2TFBAY6J63UH","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"2TFBAY6J63UH6HCF","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"2TFBAY6J","created_at":"2026-07-05T08:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2TFBAY6J63UH6HCFWUS5MXQ7EF","target":"record","payload":{"canonical_record":{"source":{"id":"2405.03664","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-06T17:41:13Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"c5bf64a98f0eae51360bb6fcbc4baa081a8a3b299f2bc24ba6625b9d96f2f4b1","abstract_canon_sha256":"cdbc22cf7376d54776cc5e4a76a2842302f23e6727f6c18dae11f6e4486b282d"},"schema_version":"1.0"},"canonical_sha256":"d4ca1063c9f6e87f1c45b525d65e1f216fd27fdaf6beb58562c7f5060d3e5633","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:26:24.364057Z","signature_b64":"eE0pr6gqD7fkKqxlLsvLu49KhulqNoaI7odQa9NZ+a/brL2WhvpuBXfUyo9PwGWQPipBbwy6Lz9j0iN/jYgTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4ca1063c9f6e87f1c45b525d65e1f216fd27fdaf6beb58562c7f5060d3e5633","last_reissued_at":"2026-07-05T08:26:24.363533Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:26:24.363533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.03664","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":"2026-07-05T08:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c28gWSsSy61DtY24ehZHRXHgPTkxc9sfNSmUhYascsIPRgCPxkmVNh0nHksC5MSunh9fOCK9qqbaV5pyUg1rAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T20:35:08.919989Z"},"content_sha256":"87b56bc974da07124b33bbd10afffcf8fcefcdc6a7102645f97fac837edef4d9","schema_version":"1.0","event_id":"sha256:87b56bc974da07124b33bbd10afffcf8fcefcdc6a7102645f97fac837edef4d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2TFBAY6J63UH6HCFWUS5MXQ7EF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Robust Partial $p$-Wasserstein-Based Metric for Comparing Distributions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Kaiyi Zhang, Pouyan Shirzadian, Sharath Raghvendra","submitted_at":"2024-05-06T17:41:13Z","abstract_excerpt":"The $2$-Wasserstein distance is sensitive to minor geometric differences between distributions, making it a very powerful dissimilarity metric. However, due to this sensitivity, a small outlier mass can also cause a significant increase in the $2$-Wasserstein distance between two similar distributions. Similarly, sampling discrepancy can cause the empirical $2$-Wasserstein distance on $n$ samples in $\\mathbb{R}^2$ to converge to the true distance at a rate of $n^{-1/4}$, which is significantly slower than the rate of $n^{-1/2}$ for $1$-Wasserstein distance. We introduce a new family of distanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03664","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.03664/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":"2026-07-05T08:26:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yz325M4CRiQ7AuTvMZUR5FTzCkdONQ1TYf44iDVg8hWpGMcN4ZGdFR7BonXR7nGh42Xvg4P8IBdmLNp2Y+IYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T20:35:08.920980Z"},"content_sha256":"6ae66be0de1454d071eb0030c9c589be8aa2e774ef015869dc4abee9dcc8b8e8","schema_version":"1.0","event_id":"sha256:6ae66be0de1454d071eb0030c9c589be8aa2e774ef015869dc4abee9dcc8b8e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF/bundle.json","state_url":"https://pith.science/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF/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":"2026-08-14T20:35:08Z","links":{"resolver":"https://pith.science/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF","bundle":"https://pith.science/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF/bundle.json","state":"https://pith.science/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2TFBAY6J63UH6HCFWUS5MXQ7EF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2TFBAY6J63UH6HCFWUS5MXQ7EF","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":"cdbc22cf7376d54776cc5e4a76a2842302f23e6727f6c18dae11f6e4486b282d","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-06T17:41:13Z","title_canon_sha256":"c5bf64a98f0eae51360bb6fcbc4baa081a8a3b299f2bc24ba6625b9d96f2f4b1"},"schema_version":"1.0","source":{"id":"2405.03664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03664","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03664v2","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03664","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"pith_short_12","alias_value":"2TFBAY6J63UH","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"2TFBAY6J63UH6HCF","created_at":"2026-07-05T08:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"2TFBAY6J","created_at":"2026-07-05T08:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:6ae66be0de1454d071eb0030c9c589be8aa2e774ef015869dc4abee9dcc8b8e8","target":"graph","created_at":"2026-07-05T08:26:24Z","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/2405.03664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The $2$-Wasserstein distance is sensitive to minor geometric differences between distributions, making it a very powerful dissimilarity metric. However, due to this sensitivity, a small outlier mass can also cause a significant increase in the $2$-Wasserstein distance between two similar distributions. Similarly, sampling discrepancy can cause the empirical $2$-Wasserstein distance on $n$ samples in $\\mathbb{R}^2$ to converge to the true distance at a rate of $n^{-1/4}$, which is significantly slower than the rate of $n^{-1/2}$ for $1$-Wasserstein distance. We introduce a new family of distanc","authors_text":"Kaiyi Zhang, Pouyan Shirzadian, Sharath Raghvendra","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-06T17:41:13Z","title":"A New Robust Partial $p$-Wasserstein-Based Metric for Comparing Distributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03664","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":"sha256:87b56bc974da07124b33bbd10afffcf8fcefcdc6a7102645f97fac837edef4d9","target":"record","created_at":"2026-07-05T08:26:24Z","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":"cdbc22cf7376d54776cc5e4a76a2842302f23e6727f6c18dae11f6e4486b282d","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-06T17:41:13Z","title_canon_sha256":"c5bf64a98f0eae51360bb6fcbc4baa081a8a3b299f2bc24ba6625b9d96f2f4b1"},"schema_version":"1.0","source":{"id":"2405.03664","kind":"arxiv","version":2}},"canonical_sha256":"d4ca1063c9f6e87f1c45b525d65e1f216fd27fdaf6beb58562c7f5060d3e5633","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d4ca1063c9f6e87f1c45b525d65e1f216fd27fdaf6beb58562c7f5060d3e5633","first_computed_at":"2026-07-05T08:26:24.363533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:26:24.363533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eE0pr6gqD7fkKqxlLsvLu49KhulqNoaI7odQa9NZ+a/brL2WhvpuBXfUyo9PwGWQPipBbwy6Lz9j0iN/jYgTAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:26:24.364057Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.03664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87b56bc974da07124b33bbd10afffcf8fcefcdc6a7102645f97fac837edef4d9","sha256:6ae66be0de1454d071eb0030c9c589be8aa2e774ef015869dc4abee9dcc8b8e8"],"state_sha256":"c69b07a0daef9a404dfb6e6c1e8b99e5edcf6de13132d34996f8c23fe67ba27e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBnHAq9+oddgfB746G/G/UQQzbX+ILxB22MTmp+LVPn/dCC4xXNXnkSDmvKGbamqBrgYj0hRMAZ9cfMajPEyDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T20:35:08.928287Z","bundle_sha256":"7fd2cab2a45d50b40303229597ebc5d908e2d604a65ce86fa2ee1d5bd2aacfcd"}}