{"as_of":"2026-08-23T15:41:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0bf30bf029e33205cd7916ce9637eb97364fb8806dc28c3df9677523dc76d980","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T15:31:17.623227Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"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/2608.00445/citation-record","integrity":"/paper/2608.00445/integrity","json":"/paper/2608.00445/citation-record.json","paper":"/paper/2608.00445"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.785020Z","title":"Hereκ∈R + is the concentration parameter,µis the unknown location (nuisance) parameter, andc FvML p,κ ,c Wat p,κ are normalizing constants","venue":null,"work_id":"2923a745-ea14-4c44-89c4-a23991bd3341","year":2017},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.571919Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:74907b0d1db624b0cf293d639d1dbb37dd8eb88c6d72dd638d692eacb4031a92","observation_id":"3eb7a2cc-c807-42af-9cbd-69d8df73a0aa","resolution":{"observed_at":"2026-08-15T15:31:17.789068Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.751048Z","title":"This scaling is also the same as under the null (uniformity)","venue":null,"work_id":"bf44dfd1-fae8-462f-bede-5403daf5d4d2","year":2017},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.584790Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:7c2cf23afc066951e6f8d9a5e7d8458dd9916cdbaae0be4da1267865d4dc5d75","observation_id":"f6ec7d3b-0da3-41c1-97b2-214b3bad4d23","resolution":{"observed_at":"2026-08-15T15:31:17.755090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.727790Z","title":"Indeed, conditionally on eT1, eT2, the event n X⊤ 1 X2 >t◦ n o is equivalent to √ d·Z> √ d· t◦ n− eT1eT2 q 1− eT 2 1 q 1− eT 2 2","venue":null,"work_id":"cd3c3fe8-ccba-4ebd-a973-213fd8b5b2b4","year":2003},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.593307Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:35336d796ba0000050120286e2f090e23cc26571f908bc01d5a471771e933af7","observation_id":"60d48c49-ced9-4e63-96d4-05ccefbaa87c","resolution":{"observed_at":"2026-08-15T15:31:17.731677Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.716840Z","title":"u2 2 +v 2 + u4 8 + v4 4 # + 1 2 (2−uv−ε )2 + ≥(1−3ε)","venue":null,"work_id":"a06b3617-8782-4502-bae1-299ed4f3b88a","year":2003},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.597500Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:039911c618b653d55eed0c85bbff9f0ff8dcfe8608752afe1d00494ffd15cafe","observation_id":"8856daf8-e401-4ec0-bd21-a01deceebe07","resolution":{"observed_at":"2026-08-15T15:31:17.720559Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.705693Z","title":"√ 2q+ q2 2 √ 2 # + 1 2 (2−q−ε )2 + ) > 3+c 2 . Proof of Lemma 6.Fixε∈[0,1/10]. Consider the caseq≥2−ε. Then inf q≥0 ( (1−2ε )","venue":null,"work_id":"b0072734-5215-466b-b0a8-389f85e3093b","year":1989},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.601810Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:1b4a4c8a5fb0636798fc49274d729e0c125d27fb1a773bb30f70e98a2bda5ebb","observation_id":"074139f4-4da3-4a84-aba0-8893eb41c40c","resolution":{"observed_at":"2026-08-15T15:31:17.709528Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.762743Z","title":"[2026]; Jammalamadaka and Janson","venue":null,"work_id":"f942e155-b438-4a67-b232-d5e4aa78b113","year":2026},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.581094Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:6290a0971f81950296db94f2c2513467a45821f665bbdae5702f61691aab5300","observation_id":"bd49a128-5af9-4c7d-97f1-93695ccaefc8","resolution":{"observed_at":"2026-08-15T15:31:17.766429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2110.09348","last_updated":"2022-04-23T16:44:20Z","snapshot_observed_at":"2026-08-16T17:48:26.312603Z","submitted_at":"2021-10-18T14:22:19Z","title":"Understanding Dimensional Collapse in Contrastive Self-supervised Learning","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2110.09348","snapshot_observed_at":"2026-08-15T15:31:17.614516Z","title":"Understanding dimensional collapse in contrastive self-supervised learning.arXiv preprint arXiv:2110.09348,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2003,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.614516Z"},"links":{"cited_paper":"/paper/2110.09348","citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:536a520fa9ecfa4d6432c1af285c340de07bbf03f6bd6cb5f47a460e0726a40f","observation_id":"959b90a1-8c60-4fbd-802b-b102adcd4652","resolution":{"observed_at":"2026-08-15T15:31:17.614516Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.739066Z","title":"This proves the second claim in (17)","venue":null,"work_id":"4b3f2895-905d-48b6-a6c4-7117c283b20f","year":2020},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2014,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.589309Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:7e0125d0104de3d846f453a2c9b914a418b031a02ea29112c693e594b5bd05ca","observation_id":"d0886d71-cf79-4444-90ef-364eaba83f67","resolution":{"observed_at":"2026-08-15T15:31:17.743063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.00393","last_updated":"2025-05-31T05:18:22Z","snapshot_observed_at":"2026-08-13T12:28:02.616202Z","submitted_at":"2025-05-31T05:18:22Z","title":"Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.00393","snapshot_observed_at":"2026-08-15T15:31:17.610094Z","title":"Asymptotic analysis of high-dimensional uniformity tests under heavy-tailed alternatives.arXiv preprint arXiv:2506.00393, 2025a","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.610094Z"},"links":{"cited_paper":"/paper/2506.00393","citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:6fa9f943f574d714aff821c37b06493641638274fdbd21694721758510b8499c","observation_id":"49786e32-50f7-4291-a922-081dfeca91a3","resolution":{"observed_at":"2026-08-15T15:31:17.610094Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.692108Z","title":"Learning with hyperspherical uniformity","venue":null,"work_id":"b55febc9-5e39-443a-b1b8-7585a8387082","year":2021},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.619022Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:dc86610b995ed86d1317140ceb50bf091d76f72b9eb4c520c29ce3f5501e5a91","observation_id":"a6b0a9bf-0064-461a-9e5d-b10081f4e70c","resolution":{"observed_at":"2026-08-15T15:31:17.697837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.00286","last_updated":"2018-04-03T07:37:00Z","snapshot_observed_at":"2026-08-20T08:02:44.680420Z","submitted_at":"2018-04-01T11:52:36Z","title":"An overview of uniformity tests on the hypersphere","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1804.00286","snapshot_observed_at":"2026-08-15T15:31:17.623227Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.623227Z"},"links":{"cited_paper":"/paper/1804.00286","citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:f1452c07b17f83257146744524cd52582b7f030389f0f0a3db54d3a622439262","observation_id":"a5c73ef1-d958-40a7-836d-a7e0509937c9","resolution":{"observed_at":"2026-08-15T15:31:17.623227Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.10898","last_updated":"2026-07-15T15:36:02Z","snapshot_observed_at":"2026-08-20T08:04:24.692415Z","submitted_at":"2025-01-18T23:15:09Z","title":"High-dimensional Sobolev tests on hyperspheres","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.10898","snapshot_observed_at":"2026-08-15T15:31:17.605647Z","title":"High-dimensional sobolev tests on hyperspheres.arXiv preprint arXiv:2501.10898,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.605647Z"},"links":{"cited_paper":"/paper/2501.10898","citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:9b4362f29b1b031b7a0ebc7b5c6c41067f197414303515fe01ad93234ac41ec0","observation_id":"b2cb7bd0-8bc4-4490-8c41-200832842e2d","resolution":{"observed_at":"2026-08-15T15:31:17.605647Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:31:17.773525Z","title":"In particular, any linear combination ofR n andB n in (2) and (3), respectively, that is not proportional toR n fails to achieve the optimal detection rate","venue":null,"work_id":"a6e6a6c5-f8f2-41d4-8c51-deb7ea15b034","year":2017},"citing_paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-15T15:31:17.576880Z"},"links":{"citing_paper":"/paper/2608.00445"},"observation_digest":"sha256:9193c28efd3169b740b3c34d6b010c5e4483eeff8b3108dda7dbaf0c0ef555f2","observation_id":"68c9bfb5-8fb7-438c-90e8-30837803398b","resolution":{"observed_at":"2026-08-15T15:31:17.777710Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.00445","last_updated":"2026-08-01T05:02:15Z","latest_version":1,"primary_category":"math.ST","snapshot_observed_at":"2026-08-20T08:03:04.778658Z","submitted_at":"2026-08-01T05:02:15Z","title":"Exact detection threshold of the packing test"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":0,"verified_fuzzy":9},"total_outbound_references":13},"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 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2608.00445."}