{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:JYFHYZYRJ72UHQDLD7V4QWGREJ","short_pith_number":"pith:JYFHYZYR","canonical_record":{"source":{"id":"2105.02073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-05-05T14:19:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5e7f643e28e78f9dd9b23c20e6952935ca87d12a953649dc5f30301bbee40e2d","abstract_canon_sha256":"4b334435bef06bd5fb624387b582ed4f4a89371a7b1618a5d0d01f6cdf2f12ed"},"schema_version":"1.0"},"canonical_sha256":"4e0a7c67114ff543c06b1febc858d1225d966f27e2c4ea8d95bcfe4a5acdf3e1","source":{"kind":"arxiv","id":"2105.02073","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.02073","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"arxiv_version","alias_value":"2105.02073v3","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.02073","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"pith_short_12","alias_value":"JYFHYZYRJ72U","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"pith_short_16","alias_value":"JYFHYZYRJ72UHQDL","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"pith_short_8","alias_value":"JYFHYZYR","created_at":"2026-07-05T05:52:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:JYFHYZYRJ72UHQDLD7V4QWGREJ","target":"record","payload":{"canonical_record":{"source":{"id":"2105.02073","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-05-05T14:19:28Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5e7f643e28e78f9dd9b23c20e6952935ca87d12a953649dc5f30301bbee40e2d","abstract_canon_sha256":"4b334435bef06bd5fb624387b582ed4f4a89371a7b1618a5d0d01f6cdf2f12ed"},"schema_version":"1.0"},"canonical_sha256":"4e0a7c67114ff543c06b1febc858d1225d966f27e2c4ea8d95bcfe4a5acdf3e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:52:16.493654Z","signature_b64":"TT6LPgnK/RRejOvElXTjJu+m7wV9Z4+8jSvnd60frVjFMfESA+k4cESMq+01dbT0aA4YOG/1hibKaCLOGX32CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e0a7c67114ff543c06b1febc858d1225d966f27e2c4ea8d95bcfe4a5acdf3e1","last_reissued_at":"2026-07-05T05:52:16.493218Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:52:16.493218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.02073","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":"2026-07-05T05:52:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gd1vVXyUeAIjd2h+PEysMJyDQZBp0LJ5/ZAvO4PU2GGY27LYlUtdxG746OImV8Wk1zZ1r4gQ7MalSs59HEB+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:21:10.162818Z"},"content_sha256":"c48d9311864a0429c65f99ba12b7a6ce2985a4b48fc3f4a02d91666085956cf5","schema_version":"1.0","event_id":"sha256:c48d9311864a0429c65f99ba12b7a6ce2985a4b48fc3f4a02d91666085956cf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:JYFHYZYRJ72UHQDLD7V4QWGREJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transport Dependency: Optimal Transport Based Dependency Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Axel Munk, Thomas Giacomo Nies, Thomas Staudt","submitted_at":"2021-05-05T14:19:28Z","abstract_excerpt":"Finding meaningful ways to measure the statistical dependency between random variables $\\xi$ and $\\zeta$ is a timeless statistical endeavor. In recent years, several novel concepts, like the distance covariance, have extended classical notions of dependency to more general settings. In this article, we propose and study an alternative framework that is based on optimal transport. The transport dependency $\\tau \\ge 0$ applies to general Polish spaces and intrinsically respects metric properties. For suitable ground costs, independence is fully characterized by $\\tau = 0$. Via proper normalizati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.02073","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/2105.02073/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":"2026-07-05T05:52:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O9jfMOeAp4Vy45V46O7vgVZF78lnIO/IkuF6V6AHvUVMDYH54qUTXD7lY1wG8yvpq00kSsM55yL9A7XcEkkLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T05:21:10.163320Z"},"content_sha256":"21419d96dc5a20ac296966c89b11f71ce2072c073d91f2521f47db679daa8f7a","schema_version":"1.0","event_id":"sha256:21419d96dc5a20ac296966c89b11f71ce2072c073d91f2521f47db679daa8f7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ/bundle.json","state_url":"https://pith.science/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ/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":"2026-08-19T05:21:10Z","links":{"resolver":"https://pith.science/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ","bundle":"https://pith.science/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ/bundle.json","state":"https://pith.science/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JYFHYZYRJ72UHQDLD7V4QWGREJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JYFHYZYRJ72UHQDLD7V4QWGREJ","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":"4b334435bef06bd5fb624387b582ed4f4a89371a7b1618a5d0d01f6cdf2f12ed","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-05-05T14:19:28Z","title_canon_sha256":"5e7f643e28e78f9dd9b23c20e6952935ca87d12a953649dc5f30301bbee40e2d"},"schema_version":"1.0","source":{"id":"2105.02073","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.02073","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"arxiv_version","alias_value":"2105.02073v3","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.02073","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"pith_short_12","alias_value":"JYFHYZYRJ72U","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"pith_short_16","alias_value":"JYFHYZYRJ72UHQDL","created_at":"2026-07-05T05:52:16Z"},{"alias_kind":"pith_short_8","alias_value":"JYFHYZYR","created_at":"2026-07-05T05:52:16Z"}],"graph_snapshots":[{"event_id":"sha256:21419d96dc5a20ac296966c89b11f71ce2072c073d91f2521f47db679daa8f7a","target":"graph","created_at":"2026-07-05T05:52:16Z","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/2105.02073/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Finding meaningful ways to measure the statistical dependency between random variables $\\xi$ and $\\zeta$ is a timeless statistical endeavor. In recent years, several novel concepts, like the distance covariance, have extended classical notions of dependency to more general settings. In this article, we propose and study an alternative framework that is based on optimal transport. The transport dependency $\\tau \\ge 0$ applies to general Polish spaces and intrinsically respects metric properties. For suitable ground costs, independence is fully characterized by $\\tau = 0$. Via proper normalizati","authors_text":"Axel Munk, Thomas Giacomo Nies, Thomas Staudt","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-05-05T14:19:28Z","title":"Transport Dependency: Optimal Transport Based Dependency Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.02073","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:c48d9311864a0429c65f99ba12b7a6ce2985a4b48fc3f4a02d91666085956cf5","target":"record","created_at":"2026-07-05T05:52:16Z","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":"4b334435bef06bd5fb624387b582ed4f4a89371a7b1618a5d0d01f6cdf2f12ed","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-05-05T14:19:28Z","title_canon_sha256":"5e7f643e28e78f9dd9b23c20e6952935ca87d12a953649dc5f30301bbee40e2d"},"schema_version":"1.0","source":{"id":"2105.02073","kind":"arxiv","version":3}},"canonical_sha256":"4e0a7c67114ff543c06b1febc858d1225d966f27e2c4ea8d95bcfe4a5acdf3e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e0a7c67114ff543c06b1febc858d1225d966f27e2c4ea8d95bcfe4a5acdf3e1","first_computed_at":"2026-07-05T05:52:16.493218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:52:16.493218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TT6LPgnK/RRejOvElXTjJu+m7wV9Z4+8jSvnd60frVjFMfESA+k4cESMq+01dbT0aA4YOG/1hibKaCLOGX32CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:52:16.493654Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.02073","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c48d9311864a0429c65f99ba12b7a6ce2985a4b48fc3f4a02d91666085956cf5","sha256:21419d96dc5a20ac296966c89b11f71ce2072c073d91f2521f47db679daa8f7a"],"state_sha256":"9c11d98cd020256f5b1d92c3830e3eefd208ba3102b88285031894bf2c7cf6b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5ougO9L4iWz3o5E0TCLEq+Iwd5aC6mX+6LJPN65iPbeZCbjrKYUmV6u5hNXGA0bTzX5U4+fhamDq7h59imHBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T05:21:10.169012Z","bundle_sha256":"f7eb503e30cd4ce1b46e8d28c477767bfe14398e638e7ff995b9c9cc11df0df1"}}