{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FSGPDUZQ6MPMFFFLMHKWBTDP3A","short_pith_number":"pith:FSGPDUZQ","canonical_record":{"source":{"id":"1810.08278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-10-18T21:13:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b9612573aba144008b7e71fc0d7aaeda5dd3d55dca4a6209630c5f51bc5043b8","abstract_canon_sha256":"87964a3de5fedb3d4709761f6e08cc8068f2d7744039190989174f62d9feb034"},"schema_version":"1.0"},"canonical_sha256":"2c8cf1d330f31ec294ab61d560cc6fd800abaf935ad0e68d5303de2ec092fa39","source":{"kind":"arxiv","id":"1810.08278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08278","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08278v1","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08278","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"FSGPDUZQ6MPM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FSGPDUZQ6MPMFFFL","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FSGPDUZQ","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FSGPDUZQ6MPMFFFLMHKWBTDP3A","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-10-18T21:13:45Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b9612573aba144008b7e71fc0d7aaeda5dd3d55dca4a6209630c5f51bc5043b8","abstract_canon_sha256":"87964a3de5fedb3d4709761f6e08cc8068f2d7744039190989174f62d9feb034"},"schema_version":"1.0"},"canonical_sha256":"2c8cf1d330f31ec294ab61d560cc6fd800abaf935ad0e68d5303de2ec092fa39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:48.617804Z","signature_b64":"dAHolu68KhGYpaa+pHu0SNpT8an42FU48+iYyqh8dDFzLe7Jqwz6jqhUJxwR0F1hfR/HYlT67s0PzaF33Y7wBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c8cf1d330f31ec294ab61d560cc6fd800abaf935ad0e68d5303de2ec092fa39","last_reissued_at":"2026-05-18T00:02:48.617268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:48.617268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08278","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":"2026-05-18T00:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4qIs09eZbRQsl0Vc1IhdQMyqI9R8fDdCyJ0OYhF4+nRaC3QCq2yv6pHwa/4Peb/XA2h8VjYXuzZBjJORoMBlCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T12:56:07.025043Z"},"content_sha256":"0ce02f24589b2b4e7507ed8e3e6e170d48ba88947e1f3acbc23498747b068c42","schema_version":"1.0","event_id":"sha256:0ce02f24589b2b4e7507ed8e3e6e170d48ba88947e1f3acbc23498747b068c42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FSGPDUZQ6MPMFFFLMHKWBTDP3A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interpolating between Optimal Transport and MMD using Sinkhorn Divergences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alain Trouv\\'e, Fran\\c{c}ois-Xavier Vialard, Gabriel Peyr\\'e, Jean Feydy, Shun-ichi Amari, Thibault S\\'ejourn\\'e","submitted_at":"2018-10-18T21:13:45Z","abstract_excerpt":"Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric nature of the problem. In sharp contrast, Maximum Mean Discrepancies (MMD) and Optimal Transport distances (OT) are two classes of distances between measures that take into account the geometry of the underlying space and metrize the convergence in law.\n  This paper studies the Sinkhorn divergences, a family of geometric divergences that interpolates betwee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08278","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":""},"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":"2026-05-18T00:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PNVuA2f6zfHw29BFspn9nMXSLDWG75kmRo2XN6FPSL5OkrRsrg7+HppRsIvD9vkRGsbalEFjgbPBjWlOVBeBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T12:56:07.025431Z"},"content_sha256":"4c2645bbb96784b4a7e0e8175242a5ed70591a49ab1315bca8554493c7c860fc","schema_version":"1.0","event_id":"sha256:4c2645bbb96784b4a7e0e8175242a5ed70591a49ab1315bca8554493c7c860fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A/bundle.json","state_url":"https://pith.science/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A/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":"2026-05-19T12:56:07Z","links":{"resolver":"https://pith.science/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A","bundle":"https://pith.science/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A/bundle.json","state":"https://pith.science/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSGPDUZQ6MPMFFFLMHKWBTDP3A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FSGPDUZQ6MPMFFFLMHKWBTDP3A","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":"87964a3de5fedb3d4709761f6e08cc8068f2d7744039190989174f62d9feb034","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-10-18T21:13:45Z","title_canon_sha256":"b9612573aba144008b7e71fc0d7aaeda5dd3d55dca4a6209630c5f51bc5043b8"},"schema_version":"1.0","source":{"id":"1810.08278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08278","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08278v1","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08278","created_at":"2026-05-18T00:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"FSGPDUZQ6MPM","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FSGPDUZQ6MPMFFFL","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FSGPDUZQ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:4c2645bbb96784b4a7e0e8175242a5ed70591a49ab1315bca8554493c7c860fc","target":"graph","created_at":"2026-05-18T00:02:48Z","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":"Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric nature of the problem. In sharp contrast, Maximum Mean Discrepancies (MMD) and Optimal Transport distances (OT) are two classes of distances between measures that take into account the geometry of the underlying space and metrize the convergence in law.\n  This paper studies the Sinkhorn divergences, a family of geometric divergences that interpolates betwee","authors_text":"Alain Trouv\\'e, Fran\\c{c}ois-Xavier Vialard, Gabriel Peyr\\'e, Jean Feydy, Shun-ichi Amari, Thibault S\\'ejourn\\'e","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-10-18T21:13:45Z","title":"Interpolating between Optimal Transport and MMD using Sinkhorn Divergences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08278","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":"sha256:0ce02f24589b2b4e7507ed8e3e6e170d48ba88947e1f3acbc23498747b068c42","target":"record","created_at":"2026-05-18T00:02:48Z","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":"87964a3de5fedb3d4709761f6e08cc8068f2d7744039190989174f62d9feb034","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-10-18T21:13:45Z","title_canon_sha256":"b9612573aba144008b7e71fc0d7aaeda5dd3d55dca4a6209630c5f51bc5043b8"},"schema_version":"1.0","source":{"id":"1810.08278","kind":"arxiv","version":1}},"canonical_sha256":"2c8cf1d330f31ec294ab61d560cc6fd800abaf935ad0e68d5303de2ec092fa39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c8cf1d330f31ec294ab61d560cc6fd800abaf935ad0e68d5303de2ec092fa39","first_computed_at":"2026-05-18T00:02:48.617268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:48.617268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dAHolu68KhGYpaa+pHu0SNpT8an42FU48+iYyqh8dDFzLe7Jqwz6jqhUJxwR0F1hfR/HYlT67s0PzaF33Y7wBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:48.617804Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ce02f24589b2b4e7507ed8e3e6e170d48ba88947e1f3acbc23498747b068c42","sha256:4c2645bbb96784b4a7e0e8175242a5ed70591a49ab1315bca8554493c7c860fc"],"state_sha256":"da277fbf05b6b0ed3a3c4bfac1ee4c25181f40458a0302c373d0c3a212ed2b41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4bT70O4gjXE3U00L3NLAAfvrmhVCBpzZFarzloLDNaagXjASsZgGcLcvjrQq8a+bYa46cx5vAnymvqHyrOvADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T12:56:07.027427Z","bundle_sha256":"7e0fbb3df5a035b62fcdfddf0b1126758ff750c82d8dbd470df0f0aef879035d"}}