{"as_of":"2026-08-23T14:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a2eb96f44315e32873a40b586a7025680bd93dcc56640270942b7f77c7f9c910","coverage":[{"denominator":80,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":80,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T16:12:18.504740Z","state":"measured"},{"denominator":80,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":80,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.28981/citation-record","integrity":"/paper/2607.28981/integrity","json":"/paper/2607.28981/citation-record.json","paper":"/paper/2607.28981"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:08.927250Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:08.927250Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:803b134cce29c17937e1f3119833ac7a905809b0fd8b6c0f66de5b6ff995d50f","observation_id":"da001a65-60ef-4b8a-ad09-6e6f06db1472","resolution":{"observed_at":"2026-08-03T16:12:08.927250Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:09.053178Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:09.053178Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:82c951085a10319f2dbdb98800726f4c71a821b87d85d79a293d7d0b5450b9f9","observation_id":"2fd02582-d658-4053-858f-615b4813866a","resolution":{"observed_at":"2026-08-03T16:12:09.053178Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:09.222892Z","title":"1993 , isbn =","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:09.222892Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:792f6daeba9d346d1f9d36389c624367de6b8e1cc1bb71e2cbc42099f75174eb","observation_id":"bd615cee-c40f-413e-874b-836ca985aed5","resolution":{"observed_at":"2026-08-03T16:12:09.222892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:09.434223Z","title":"Canadian Journal of Statistics , year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:09.434223Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:f42104e051c17e9953e151203d9f2eaef6291e4c6dddf5554334f07a5d5c3a07","observation_id":"0b487405-ea7e-443b-a8d1-f0c64d9eb270","resolution":{"observed_at":"2026-08-03T16:12:09.434223Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:09.628674Z","title":"Journal of Nonparametric Statistics , volume=","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:09.628674Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:0322322349e5cc32b963ea6cfcfeb2e151ff604d3ebc126fa26bb1579845fef4","observation_id":"028ca6b9-c58b-497a-b420-ea25c9276298","resolution":{"observed_at":"2026-08-03T16:12:09.628674Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:09.773642Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:09.773642Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:baadb991ae1e0d1d32392b5c36ed6e1be4a75635645a225374f751f1bd8d068b","observation_id":"7231d31b-0868-4432-8a6d-f823cae8c7c3","resolution":{"observed_at":"2026-08-03T16:12:09.773642Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:09.954378Z","title":"Journal of the American Statistical Association , volume=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:09.954378Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:1a2decbc356bea1e26b9cee10e9f01c43acfb69dedbd0e5039f1af02a1174b77","observation_id":"f9ec462d-3646-40d7-8732-23deb12f91f3","resolution":{"observed_at":"2026-08-03T16:12:09.954378Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.119786Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.119786Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:f31b84b258295abcebe796e1d2f9c1de3ef49bf2815c8eb9f0030be059e3774c","observation_id":"29aa71c8-b8c5-488e-9574-d3d0a802062f","resolution":{"observed_at":"2026-08-03T16:12:10.119786Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.250755Z","title":"Demography , volume=","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.250755Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:b1cddef544269a45aae7355dc82014dae8b6b0fe21f61024fb0a5cce763c8fef","observation_id":"783b70fd-238e-4190-9cd6-cecbde218790","resolution":{"observed_at":"2026-08-03T16:12:10.250755Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.337198Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.337198Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:945db6a9a4db270edb6ea59d60959ba7d510e231177eb4ea99d1523bc8bdb6a2","observation_id":"9a58e2ca-3608-479d-a9a4-ab02c336483d","resolution":{"observed_at":"2026-08-03T16:12:10.337198Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.22754","last_updated":"2025-06-28T04:55:12Z","snapshot_observed_at":"2026-08-21T15:34:12.613986Z","submitted_at":"2025-06-28T04:55:12Z","title":"Doubly robust estimation of causal effects for random object outcomes with continuous treatments","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.22754","snapshot_observed_at":"2026-08-03T16:12:10.406254Z","title":"arXiv preprint arXiv:2506.22754 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.406254Z"},"links":{"cited_paper":"/paper/2506.22754","citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:eae47a0f7f1581e0098f5d31722c81c8b1f24d5cc5d103707a0f3f68fb2507e4","observation_id":"4da71af4-9514-4b15-9891-7d29341692da","resolution":{"observed_at":"2026-08-03T16:12:10.406254Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.464065Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.464065Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:7425d0dbae35f1fce11cbe061807b92c00a089f18aa920057c2edf89b430ce2b","observation_id":"7e126148-a65c-410b-9339-bb1936696dc7","resolution":{"observed_at":"2026-08-03T16:12:10.464065Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.530167Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.530167Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:04973f8752f5ceccc1144bab4ce1ce889fb680f5334dff2719e77a1950c975dd","observation_id":"30226089-fa0a-4543-95a9-b3fcb8deb257","resolution":{"observed_at":"2026-08-03T16:12:10.530167Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.607112Z","title":"Lecture Notes, Columbia University , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.607112Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:6fb4decf3dde72ac0e43dbaf14dd4fc23b55f8c460a6f052f4c5c94accf82bec","observation_id":"6490edbc-ee7b-4dd9-93a4-9e5f3c912261","resolution":{"observed_at":"2026-08-03T16:12:10.607112Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.689873Z","title":"2015 , publisher =","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.689873Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:f44f3efdcb358114ee4cd480b06301b8c4fc3eadd410bf11506fdd31f4bda7e8","observation_id":"b2580c9d-5b81-48b8-942d-f33d5cd2ff89","resolution":{"observed_at":"2026-08-03T16:12:10.689873Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.763511Z","title":", author=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.763511Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:ddb1119da714d066a72f1ef49f4780e47c56542e8c5c8e73082309a719dc3d00","observation_id":"a5979653-5dc0-4630-9e5b-67f0cc395d0e","resolution":{"observed_at":"2026-08-03T16:12:10.763511Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.824615Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.824615Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:0b8eadd3ad7241a9fe64b49174e99cefe319ca1c3586e49560570a7e027abd6c","observation_id":"2dc09d4a-a9f7-450e-9a8f-74db31caec6e","resolution":{"observed_at":"2026-08-03T16:12:10.824615Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.939414Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.939414Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:83bb82d0acaafa1193c05b7fc54261093d1f9be07abe685bc4394fdcffc99037","observation_id":"5e80dc49-8fbe-4cce-928d-825a99e1d55b","resolution":{"observed_at":"2026-08-03T16:12:10.939414Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:10.998344Z","title":"2020 , publisher=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:10.998344Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:d12573a68b8283a1a12b7dc4fe611c908d6d665cc6ed1c5df756476d9354b192","observation_id":"266b3d69-1880-4879-acd4-47e49b369e0c","resolution":{"observed_at":"2026-08-03T16:12:10.998344Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.117392Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.117392Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:21420099550497d6c275116fe66be4b295425613bcd28ab18e90200c053fff6d","observation_id":"d230a0ef-9999-4f9c-a50b-3e3f7d9ec7e9","resolution":{"observed_at":"2026-08-03T16:12:11.117392Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.168616Z","title":"2012 , publisher=","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.168616Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:89b69d8d2856949ae091876f2ac23860f44523b9f2c878047fe485a8cc5bafbe","observation_id":"ca501188-1a07-454e-b4df-ef21e9767883","resolution":{"observed_at":"2026-08-03T16:12:11.168616Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0710.2063","last_updated":"2007-10-10T16:42:27Z","snapshot_observed_at":"2026-08-17T21:35:08.104714Z","submitted_at":"2007-10-10T16:42:27Z","title":"Distance matrices and isometric embeddings","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0710.2063","snapshot_observed_at":"2026-08-03T16:12:11.248892Z","title":"arXiv preprint arXiv:0710.2063 , year=","venue":null,"work_id":null,"year":2063},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.248892Z"},"links":{"cited_paper":"/paper/0710.2063","citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:dc8e22dd2ea2fadf8dce1ddaa5b83a8f15e271153b3b820bf25ac02712a38e34","observation_id":"c0e18c74-5e69-40ab-87c0-a7ef85c51e77","resolution":{"observed_at":"2026-08-03T16:12:11.248892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.347826Z","title":"IEEE Trans","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.347826Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:4bbcba4da757cdd1187d9d08395358c428e63201756b21d5860066eefa2d44de","observation_id":"e76f885a-bc17-45ae-a7f2-c81d84fccfeb","resolution":{"observed_at":"2026-08-03T16:12:11.347826Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.441171Z","title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition , pages=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.441171Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:72912d65cea8b45c36abc6874af66d7574e6c4533f42222e14072a6abc0cebd6","observation_id":"fd565c96-9383-44c4-930e-7bd210a53991","resolution":{"observed_at":"2026-08-03T16:12:11.441171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.524743Z","title":"Journal of Machine Learning Research , year =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.524743Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:baba9374e2c93fd4d4dae5350fb557fdd18fd1e71c0e3c7eba5d3e17ddfc26cf","observation_id":"6ef8a00a-5071-4038-815c-5be8e3f866b6","resolution":{"observed_at":"2026-08-03T16:12:11.524743Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.581728Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.581728Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:3cdc4a72cd9d172a1dc2cca2fa58814a6a7de79e13a3d06ceb07b10208360706","observation_id":"8b9c0697-99a8-4594-85d0-27712ed2d85e","resolution":{"observed_at":"2026-08-03T16:12:11.581728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.674735Z","title":"Russian Mathematical Surveys , volume=","venue":null,"work_id":null,"year":1964},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.674735Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:95d3728943754bbcf18fa3e0ce65cfd81b75f053d84394c77d27ddb3cba6c8bc","observation_id":"4bfbff62-e35f-40d2-baff-e50bf0a770bc","resolution":{"observed_at":"2026-08-03T16:12:11.674735Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.794739Z","title":"Advances in Neural Information Processing Systems , pages =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.794739Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:a988e2cc8825497e617992947018a6766a0faa5d9280c87671b588845cd03da6","observation_id":"f9c117c2-112a-4d30-8568-0eabc961cab7","resolution":{"observed_at":"2026-08-03T16:12:11.794739Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:11.960298Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:11.960298Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:878de1a4b2a42cfa88af3a2589b6e7a84c12596d9a34029aa7d01da898eabd6e","observation_id":"b1181baf-d8ac-4a0c-821d-3e176e5cbc5e","resolution":{"observed_at":"2026-08-03T16:12:11.960298Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.019933Z","title":"2018 , publisher =","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.019933Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:794a7649b8e307b79804ec0e15e50de40f730e74d2ff81c16d6b92d8ec9c11fa","observation_id":"ccaf9252-d9e1-4490-8055-d97c7c0f9590","resolution":{"observed_at":"2026-08-03T16:12:12.019933Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.102666Z","title":"Nonlinear global Fr","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.102666Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:413b1fcc2e932af0472f8b32cee141d232a800ec15b0f0632e4e41d2a8956060","observation_id":"23e3623b-2c08-4d21-aff1-29b566f18270","resolution":{"observed_at":"2026-08-03T16:12:12.102666Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.173486Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.173486Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:17e510d910f46bbb0214f549fc7b2e988a841baf1fdf83fae94c3970956ac41d","observation_id":"5961d399-05e5-4566-80b8-dd710aa269e5","resolution":{"observed_at":"2026-08-03T16:12:12.173486Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2603.13704","last_updated":"2026-07-06T05:30:45Z","snapshot_observed_at":"2026-08-14T22:58:58.510908Z","submitted_at":"2026-03-14T02:20:05Z","title":"A Reproducing-Kernel-Based Nonparametric Test for Conditional Independence of Functional Data","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2603.13704","snapshot_observed_at":"2026-08-03T16:12:12.284736Z","title":"arXiv preprint arXiv:2603.13704 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.284736Z"},"links":{"cited_paper":"/paper/2603.13704","citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:1de91e22dd8480a1f35f4dd7b1656693956a9df8d6d581456031e24489783f57","observation_id":"d3eecef8-a636-404f-b3f6-772c95f3aeaa","resolution":{"observed_at":"2026-08-03T16:12:12.284736Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.404735Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.404735Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:87147db6a38713ee5d110d07b3f99aeaae831d902f8a19b9ca8308cdace3585c","observation_id":"7356e8f0-f87d-4f26-97ba-8c7e356ae04b","resolution":{"observed_at":"2026-08-03T16:12:12.404735Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.494738Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.494738Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:326304012aaddee441edcd67f9400859a8e20ba1a47b88b2a89d5102da5548b1","observation_id":"cf8d158e-938b-4c71-99fe-df4539b89811","resolution":{"observed_at":"2026-08-03T16:12:12.494738Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.614860Z","title":"Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence , pages=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.614860Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:20b6a6a152260e879d89b464499fbadca91911b961b18fb9025b1e4474bb98a1","observation_id":"03ec58eb-9cdc-4b2a-8b31-ab58ebef1914","resolution":{"observed_at":"2026-08-03T16:12:12.614860Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.762535Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.762535Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:151cc8ddd5cd8d8fb140bd4f5ceedc10e926c14765adca4c131c23193d979d4b","observation_id":"37bc1d25-3de7-4df7-92e6-54e28d268dd7","resolution":{"observed_at":"2026-08-03T16:12:12.762535Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.826873Z","title":"Dimension reduction for Fr","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.826873Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:2f02dd7745fa8ceea07f1268d736bf03018c5dde0b24bab83c5bdacb674e356b","observation_id":"287c4e4c-a563-44fe-869f-e6c7cb2ff92a","resolution":{"observed_at":"2026-08-03T16:12:12.826873Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:12.924835Z","title":"Journal of Multivariate Analysis , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:12.924835Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:0993e3731676b8b0c4c3049388c13fb03d548579ca9a4b34c371bc34405ae7ae","observation_id":"3f20e869-1f75-4f66-a819-05aea9901675","resolution":{"observed_at":"2026-08-03T16:12:12.924835Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.045190Z","title":"Gates Open Research , volume=","venue":null,"work_id":null,"year":1960},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.045190Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:f0fc63f3cffd5ea7ce500646c5e05135e06323708e17a253541e76d8b7e3c802","observation_id":"21847246-5679-4f66-97ea-8ff8ee33b67f","resolution":{"observed_at":"2026-08-03T16:12:13.045190Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.219496Z","title":"2013 , publisher=","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.219496Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:4c447d5b920acf45a6a8d32b87481678eacf86b8af6afaf05bd927b8167781db","observation_id":"1bb817c0-d161-460c-862a-afb901fce0c3","resolution":{"observed_at":"2026-08-03T16:12:13.219496Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.314731Z","title":"The Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.314731Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:0f277008bcafc9d205293e09f0c9300d25284200a9565b9f2c4aef126cfa6ba8","observation_id":"81631678-eda0-4a75-be52-c6f2e0ebe7b1","resolution":{"observed_at":"2026-08-03T16:12:13.314731Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.434790Z","title":"Advances in Neural Information Processing Systems , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.434790Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:0719766644ea1b0f0744c70194d1e544a716a1022e45f4e2f433f11042d57fc3","observation_id":"07f96d19-31ef-493b-b517-f32ba57a92eb","resolution":{"observed_at":"2026-08-03T16:12:13.434790Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.554735Z","title":"and Jordan, Michael I","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.554735Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:fdee9d71879cee38c5ba5a115bccd0b8ab6ff80b215730e7cc044317c7ccde4a","observation_id":"1f27a0d3-7894-4f97-b87c-4c11983eb760","resolution":{"observed_at":"2026-08-03T16:12:13.554735Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.684736Z","title":"On some measures analogous to Haar measure","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.684736Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:b8555377363ef499525c13316d5b12a1462b18b3650a75b9094291cdd0fc2a5b","observation_id":"b8053b1c-9c63-4ff9-ad60-dc834b6f69b6","resolution":{"observed_at":"2026-08-03T16:12:13.684736Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:13.854736Z","title":"Mathematika , author=","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:13.854736Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:87f87172b01c81bb360646107332afb479332e57c7d32ed37148e34209e90dbf","observation_id":"16b7975b-a4f5-49f3-a635-ae85b3219557","resolution":{"observed_at":"2026-08-03T16:12:13.854736Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.031833Z","title":", journal =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.031833Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:0acae15a63e33a676e960ade32f59bcbbbde74ebb65d57dea5e26fb0a5e72bd9","observation_id":"e483ba66-5401-4372-b9bf-f8befc9ff048","resolution":{"observed_at":"2026-08-03T16:12:14.031833Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.158036Z","title":"International conference on algorithmic learning theory , pages=","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.158036Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:a5ec775df21c04f1acb264c824348feff50260b7f9f147ae60e8c249fe5915c3","observation_id":"d828cba9-5f4d-4930-8ef1-0575c730a6ee","resolution":{"observed_at":"2026-08-03T16:12:14.158036Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.225220Z","title":"Journal of Machine Learning Research , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.225220Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:e556513328dd17656cd857b34cd6e83cf50705f668c811f2e4191bd65d77625d","observation_id":"1ab294db-72ee-44b0-91a5-c85626f98586","resolution":{"observed_at":"2026-08-03T16:12:14.225220Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.404969Z","title":"Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.404969Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:2d4336e595954a45258eb013ef7917a04cffc28018216ec08c909914afd4d204","observation_id":"4ca23d7b-c855-45ac-a5be-9c7a81669ae8","resolution":{"observed_at":"2026-08-03T16:12:14.404969Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.565852Z","title":"Wasserstein F-tests for Fr","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.565852Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:8fbb9e9a5055c77af4c2217ad82196d527ebfe3835276f453fb73658330c80b5","observation_id":"cf8803e0-ac68-4e9a-a0ec-a00ac697e618","resolution":{"observed_at":"2026-08-03T16:12:14.565852Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.664465Z","title":"Székely and Maria L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.664465Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:328dac0e888def5fb8ba258d6eda4d4f04540a43c8ffc447fc28d38a33ababa6","observation_id":"2539722c-6b27-4129-ad3f-8598c2b0ba31","resolution":{"observed_at":"2026-08-03T16:12:14.664465Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.716467Z","title":"Journal of Statistical Software , volume=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.716467Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:7f4495c0ba1484cfae1ce9ced23f5d04b094dbc0851bc47d5b98c9123265c892","observation_id":"94872876-9a85-40a9-8562-7e9f06618530","resolution":{"observed_at":"2026-08-03T16:12:14.716467Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.792279Z","title":"Wu and Jun Chen and Christian Hoffmann and Kyle Bittinger and others , title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.792279Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:465b5a9917217cf0784536185a0901b0fdcf7c009df5dfd0c91f0c3487aef6dc","observation_id":"837c8dea-1813-4b53-b8c0-6ecf231f6a31","resolution":{"observed_at":"2026-08-03T16:12:14.792279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.864382Z","title":"Bioinformatics , volume=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.864382Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:d6a959dce06d6e626972c0594e02f3ccf38a0400d54f63924b5f4036634f330c","observation_id":"fb8e0070-70a1-4ae7-a162-c34a9da7f75a","resolution":{"observed_at":"2026-08-03T16:12:14.864382Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:14.974801Z","title":"Annual Review of Statistics and Its Application , author =","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:14.974801Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:e9b136a15be01ca70afba3c189bf0c4a70c6853bb91599268e1ae0a62337756f","observation_id":"343151d3-a571-4c00-81ba-3a210234b833","resolution":{"observed_at":"2026-08-03T16:12:14.974801Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.124745Z","title":"The Lancet , volume=","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.124745Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:5a11385294411c6f6d1c8a36e5cab9c779f2f93844c95edfd07839d6ec21c7fb","observation_id":"32858524-d825-4337-a63f-dfb364fbe338","resolution":{"observed_at":"2026-08-03T16:12:15.124745Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.254745Z","title":"2019 , institution =","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.254745Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:f534f04d84544599ea9abc184c997a0bfa093316a477d8346180a5771a71e27b","observation_id":"c1d88d62-7f03-4ea7-8122-f9574f7ff642","resolution":{"observed_at":"2026-08-03T16:12:15.254745Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.354815Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.354815Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:2d736b92fafce43002632eeab63c209a7afb99cf737e0424ee976cd721ceb928","observation_id":"c480d45e-d86b-4340-80be-424dda37f39e","resolution":{"observed_at":"2026-08-03T16:12:15.354815Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.494741Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.494741Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:1705ddddba918edc46972f8ce6ed2c5b8f5ed1c4bdf134fc05c13b649a3e3f00","observation_id":"1dad98bc-5a0e-41a5-a6d3-a6f51d740e78","resolution":{"observed_at":"2026-08-03T16:12:15.494741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.674744Z","title":"Biometrika , volume=","venue":null,"work_id":null,"year":1938},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.674744Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:b639e27f23455827fd1b21bd5816ef8666eff096330cb9450ab869d85e4e254b","observation_id":"09d44a07-89c6-4568-bccd-1f01c3775c28","resolution":{"observed_at":"2026-08-03T16:12:15.674744Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.812189Z","title":"Biometrika , volume=","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":62,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.812189Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:18e8a2c296db16c69fbd540630bedf3f46b6fcf9b8d6c79fe6cb6cee4c670222","observation_id":"e310ad52-ca5c-41ee-85c9-9ba1eaaab1a2","resolution":{"observed_at":"2026-08-03T16:12:15.812189Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:15.954744Z","title":"Biometrika , volume=","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":63,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:15.954744Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:b932c2caafa2fb65b0cdb598e14bfadb21f3da04d5f9c0cee974adcb07116ece","observation_id":"55234c01-b4ff-4b05-a92c-87ffec85088d","resolution":{"observed_at":"2026-08-03T16:12:15.954744Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:16.124744Z","title":"Biometrika , volume=","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":64,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:16.124744Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:60cc95a270131771fe8963b107de76aeaa47314cf9cb784a1f8e7d663d863367","observation_id":"53ca0044-b7de-49fc-a487-5535c15d259c","resolution":{"observed_at":"2026-08-03T16:12:16.124744Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:16.214740Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":65,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:16.214740Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:2e0b158ad7c1fadb803bba969d8727b45f1090a3644f6d22a435213e655ab7d2","observation_id":"3a6aea42-b584-4d81-ba4b-1c7a1c3a8c9d","resolution":{"observed_at":"2026-08-03T16:12:16.214740Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:16.394825Z","title":"The American Statistician , volume=","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":66,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:16.394825Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:9675d1cdada4bcccadb32378819e997cf602f4684d3889c804c6c52f0d0826b5","observation_id":"4489159a-4f37-44e8-bd13-e5bd2e560808","resolution":{"observed_at":"2026-08-03T16:12:16.394825Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:16.515129Z","title":"Biometrika , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":67,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:16.515129Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:e128c565d0eeb10c0a8df4f19f379479806a57d0bd72d9e2b0d2abbb902d50b0","observation_id":"cf590dec-4784-406a-9459-f4bab40289af","resolution":{"observed_at":"2026-08-03T16:12:16.515129Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:16.684821Z","title":"Biometrical Journal , volume=","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":68,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:16.684821Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:9a576d1b6327adad6b1ccd04d86d3395c2f8d00645d61c631fa249c366ba904b","observation_id":"06b4b1f3-eb4e-442c-b37c-3b1f4d35064e","resolution":{"observed_at":"2026-08-03T16:12:16.684821Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:16.865074Z","title":"Science Advances , volume=","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":69,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:16.865074Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:3e259a2d6e17463607bb585913ba7eedb11284b640929e24cde32b3594c59f93","observation_id":"9a4653c5-6926-4f4b-a0d0-3e8d85163942","resolution":{"observed_at":"2026-08-03T16:12:16.865074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:17.074806Z","title":"Probability measures , booktitle =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":70,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:17.074806Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:4bf963c20438a0e8dd95a43cbe91567e742f5ad0577dc4f7f7ef8fdc969646d5","observation_id":"023c096a-1cf1-4658-b7ad-1119dc6809dd","resolution":{"observed_at":"2026-08-03T16:12:17.074806Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:17.254815Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":71,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:17.254815Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:6e8e090614ef7cfa6a82f64a702ed23afb1bebc31217a5b581b95b9b4a64ab69","observation_id":"a0fcc4e1-5271-4872-b241-fff7c5472066","resolution":{"observed_at":"2026-08-03T16:12:17.254815Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:17.344746Z","title":"arXiv preprint arXiv:2509.13685 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":72,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:17.344746Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:b1957a23f3186e17b49fb8e4a6c548cc6a853be35d14dcd33cbdfa31abda09ae","observation_id":"8a7a9de5-0d0a-49d5-a35d-178f74cd7a10","resolution":{"observed_at":"2026-08-03T16:12:17.344746Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:17.614743Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":73,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:17.614743Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:bdcf4c4ec51feb78ee95981d7f9f109d2bbeb1a2dac424ac836230539b85eded","observation_id":"851ca2c2-92e5-4cf9-81c2-8c07f9ba658a","resolution":{"observed_at":"2026-08-03T16:12:17.614743Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:17.714998Z","title":"Bernoulli , volume=","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":74,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:17.714998Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:fc44209f0609ed4233034394b1b9e054959b401e99d785962c0fe9c73e84c710","observation_id":"afce7e79-13e8-4df0-bc0c-c916d536fb65","resolution":{"observed_at":"2026-08-03T16:12:17.714998Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:17.924743Z","title":"Statistica Sinica, in press , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":75,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:17.924743Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:649c2065069b6db620122b23841998ddd66596a4cb24007835e02569dc0e7d47","observation_id":"7caf57ab-eff1-444b-94f4-6179d1fd47e1","resolution":{"observed_at":"2026-08-03T16:12:17.924743Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:18.124742Z","title":"arXiv preprint arXiv:2603.29058 , year=","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":76,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:18.124742Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:a087b7414df7dbc86ed513e6c22096bbee01bd961e7eafb32caca165e80778b7","observation_id":"7b624507-8b2b-468a-8af3-bc72d6b05519","resolution":{"observed_at":"2026-08-03T16:12:18.124742Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:18.214875Z","title":"Journal of the Royal Statistical Society Series B , pages=","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":77,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:18.214875Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:45a9ecae4b8fece05ece734b27ac668a7e451a0c3f75367644180e3b5e99367c","observation_id":"473e64a4-1226-487f-9385-f02169553520","resolution":{"observed_at":"2026-08-03T16:12:18.214875Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:18.284769Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":78,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:18.284769Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:c416d94e5a8ecc8002feedcac443eb56b45d52a93638c0f02a3ee326375b2b1c","observation_id":"338c63c6-13f2-4c0c-a46f-cee87b59b857","resolution":{"observed_at":"2026-08-03T16:12:18.284769Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:18.326571Z","title":"Linear algebra and its applications , volume=","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":79,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:18.326571Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:de8c06b8a00d089ae70b0633549580ec4cf779252ed4cf28ec52ea2fb643eec5","observation_id":"649690ce-8b0a-48d6-8281-46fc257cdbd4","resolution":{"observed_at":"2026-08-03T16:12:18.326571Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T16:12:18.504740Z","title":", title =","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects","version":1},"reference_index":80,"source":"arxiv_source","source_observed_at":"2026-08-03T16:12:18.504740Z"},"links":{"citing_paper":"/paper/2607.28981"},"observation_digest":"sha256:2a50db785b914316634c181b13afbc91271c49aa6370fec225621818ce3cb016","observation_id":"76485cb4-bfee-4ac0-8f84-5bded4330ec5","resolution":{"observed_at":"2026-08-03T16:12:18.504740Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.28981","last_updated":"2026-07-31T03:12:47Z","latest_version":1,"primary_category":"stat.ME","snapshot_observed_at":"2026-08-17T23:18:55.421240Z","submitted_at":"2026-07-31T03:12:47Z","title":"Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects"},"reference_resolution":{"displayed":80,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":80,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":80},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 0 inbound Pith citation observations for arXiv:2607.28981."}