{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2D4QS2G4RBMJYJSS2OSV7TD5UB","short_pith_number":"pith:2D4QS2G4","canonical_record":{"source":{"id":"2407.01718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-07-01T18:48:55Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"1078c43b5fefd9657d1d6a2b133911dc84618a6105565658308201240f674791","abstract_canon_sha256":"bb1f4c339d5887cb2d9cb776cadb62c548dbc4f50a4ce715200bd931d374d16f"},"schema_version":"1.0"},"canonical_sha256":"d0f90968dc88589c2652d3a55fcc7da07fe7631892d411afd081ac9c58846e16","source":{"kind":"arxiv","id":"2407.01718","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.01718","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"arxiv_version","alias_value":"2407.01718v2","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01718","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"pith_short_12","alias_value":"2D4QS2G4RBMJ","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"pith_short_16","alias_value":"2D4QS2G4RBMJYJSS","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"pith_short_8","alias_value":"2D4QS2G4","created_at":"2026-06-09T02:06:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2D4QS2G4RBMJYJSS2OSV7TD5UB","target":"record","payload":{"canonical_record":{"source":{"id":"2407.01718","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-07-01T18:48:55Z","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"title_canon_sha256":"1078c43b5fefd9657d1d6a2b133911dc84618a6105565658308201240f674791","abstract_canon_sha256":"bb1f4c339d5887cb2d9cb776cadb62c548dbc4f50a4ce715200bd931d374d16f"},"schema_version":"1.0"},"canonical_sha256":"d0f90968dc88589c2652d3a55fcc7da07fe7631892d411afd081ac9c58846e16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:06:59.720847Z","signature_b64":"AC2ZGIIED1wBK4665jq06isuGjUo7PZjWN6mBwqA5yOBmXcJN4FrLcFfz96NQ7KSL9GLALXFZQl5P4ZHppZ3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0f90968dc88589c2652d3a55fcc7da07fe7631892d411afd081ac9c58846e16","last_reissued_at":"2026-06-09T02:06:59.719881Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:06:59.719881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.01718","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":"2026-06-09T02:06:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j97oZv4XrHRhHBwVpI5PfZZ2WEq3T5O+fAG37i3FmUl0FiZfNDjqfJ19IBRAJRDk2PPBX5U0YkpU0dIS2jszCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:48:22.589948Z"},"content_sha256":"d94312529941f882bab39a4c906cea20c98eded27795e27df79bd24a4ad29577","schema_version":"1.0","event_id":"sha256:d94312529941f882bab39a4c906cea20c98eded27795e27df79bd24a4ad29577"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2D4QS2G4RBMJYJSS2OSV7TD5UB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Boris Landa, Rong Ma, Yuval Kluger","submitted_at":"2024-07-01T18:48:55Z","abstract_excerpt":"Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose Entropic Optimal Transport (EOT) eigenmaps, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverag"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01718","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/2407.01718/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":"2026-06-09T02:06:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKQRnRg/q0UjHcpT6lm0dqo6NestgTWDJ9JJ5QGDjLRsD+nStZNsb6UJGk3H9Uhk9JoGj7OKipfv/1Yl11dgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T06:48:22.590655Z"},"content_sha256":"a9f2a76c1872f2838654096f2e98536b8f2f41e53cbdd1cc55fe652a0fea6697","schema_version":"1.0","event_id":"sha256:a9f2a76c1872f2838654096f2e98536b8f2f41e53cbdd1cc55fe652a0fea6697"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB/bundle.json","state_url":"https://pith.science/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB/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":"2026-06-12T06:48:22Z","links":{"resolver":"https://pith.science/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB","bundle":"https://pith.science/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB/bundle.json","state":"https://pith.science/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2D4QS2G4RBMJYJSS2OSV7TD5UB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2D4QS2G4RBMJYJSS2OSV7TD5UB","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":"bb1f4c339d5887cb2d9cb776cadb62c548dbc4f50a4ce715200bd931d374d16f","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-07-01T18:48:55Z","title_canon_sha256":"1078c43b5fefd9657d1d6a2b133911dc84618a6105565658308201240f674791"},"schema_version":"1.0","source":{"id":"2407.01718","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.01718","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"arxiv_version","alias_value":"2407.01718v2","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.01718","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"pith_short_12","alias_value":"2D4QS2G4RBMJ","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"pith_short_16","alias_value":"2D4QS2G4RBMJYJSS","created_at":"2026-06-09T02:06:59Z"},{"alias_kind":"pith_short_8","alias_value":"2D4QS2G4","created_at":"2026-06-09T02:06:59Z"}],"graph_snapshots":[{"event_id":"sha256:a9f2a76c1872f2838654096f2e98536b8f2f41e53cbdd1cc55fe652a0fea6697","target":"graph","created_at":"2026-06-09T02:06:59Z","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/2407.01718/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis. In numerous applications, it is necessary to align and jointly embed multiple datasets from different studies or experimental conditions. Such datasets may share underlying structures of interest but exhibit individual distortions, resulting in misaligned embeddings using traditional techniques. In this work, we propose Entropic Optimal Transport (EOT) eigenmaps, a principled approach for aligning and jointly embedding a pair of datasets with theoretical guarantees. Our approach leverag","authors_text":"Boris Landa, Rong Ma, Yuval Kluger","cross_cats":["cs.LG","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-07-01T18:48:55Z","title":"Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.01718","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:d94312529941f882bab39a4c906cea20c98eded27795e27df79bd24a4ad29577","target":"record","created_at":"2026-06-09T02:06:59Z","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":"bb1f4c339d5887cb2d9cb776cadb62c548dbc4f50a4ce715200bd931d374d16f","cross_cats_sorted":["cs.LG","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-07-01T18:48:55Z","title_canon_sha256":"1078c43b5fefd9657d1d6a2b133911dc84618a6105565658308201240f674791"},"schema_version":"1.0","source":{"id":"2407.01718","kind":"arxiv","version":2}},"canonical_sha256":"d0f90968dc88589c2652d3a55fcc7da07fe7631892d411afd081ac9c58846e16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0f90968dc88589c2652d3a55fcc7da07fe7631892d411afd081ac9c58846e16","first_computed_at":"2026-06-09T02:06:59.719881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:06:59.719881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AC2ZGIIED1wBK4665jq06isuGjUo7PZjWN6mBwqA5yOBmXcJN4FrLcFfz96NQ7KSL9GLALXFZQl5P4ZHppZ3CA==","signature_status":"signed_v1","signed_at":"2026-06-09T02:06:59.720847Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.01718","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d94312529941f882bab39a4c906cea20c98eded27795e27df79bd24a4ad29577","sha256:a9f2a76c1872f2838654096f2e98536b8f2f41e53cbdd1cc55fe652a0fea6697"],"state_sha256":"5cd4a494aa3d7687e6a7aead0214421e57346e3a12c79cfe7c250876f7dd860c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pI7ZKT+uTrgTLWhsL38IUxsK/S2AOjZ5bT1jIBuQATsJQfx7P8QWhFDV/eBEgEZM4S14J725jcSU0wm/rlRGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T06:48:22.593941Z","bundle_sha256":"2200db9cd8e9e11b11ad572866e6e5b6f315e8cdaf6dd6d85d0c4a14a97a7d7f"}}