{"as_of":"2026-08-13T00:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:585279bc0f57188866faf51328a7762296323420ea4a0cb1f8804d4b85cd0387","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T05:38:10.083382Z","state":"measured"},{"denominator":35,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":35,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T17:05:04.538471Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-10T17:05:04.601576Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"cited_work":{"arxiv_id":"2509.05487","doi":null,"metadata_source":"pith","pith_arxiv_id":"2509.05487","snapshot_observed_at":"2026-08-10T17:05:04.601576Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","venue":"math-ph","work_id":"2aa34b1f-51c6-4e0f-ad6c-84bb0fb6d72a","year":2025},"citing_paper":{"arxiv_id":"2608.06995","last_updated":"2026-08-07T09:12:41Z","snapshot_observed_at":"2026-08-12T23:11:39.529162Z","submitted_at":"2026-08-07T09:12:41Z","title":"Fugacity-Resolved Stabilizer Entropy in Critical Quantum Chains: Discrete Selberg Sums and Exactly Solvable R\\'enyi Indices","version":1},"reference_index":126,"source":"pdf_text","source_observed_at":"2026-08-10T17:05:04.538471Z"},"links":{"cited_paper":"/paper/2509.05487","citing_paper":"/paper/2608.06995"},"observation_digest":"sha256:b610b12301acc582f1bdd0087ef79f527ebcca7ce9edec291863aab9e1c24bd9","observation_id":"339967d9-4ba7-420b-a059-4d5c1d6cb947","resolution":{"observed_at":"2026-08-10T17:05:04.610233Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2509.05487/citation-record","integrity":"/paper/2509.05487/integrity","json":"/paper/2509.05487/citation-record.json","paper":"/paper/2509.05487"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T05:38:16.394361Z","title":"Adler, P","venue":null,"work_id":"59047331-22b5-408c-84d8-bc37d3b46347","year":2000},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.153913Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:e551ec22b6ab8dbbef97956ae04d42f7f92de27de0e71c65cd7ab038cefe6278","observation_id":"1790b7a4-f3e6-4da5-bfef-bd7b07c12213","resolution":{"observed_at":"2026-08-05T05:38:16.468774Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:16.291894Z","title":null,"venue":null,"work_id":"76fd5b2e-5ca1-4865-b1aa-2be195514b9d","year":1966},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.202986Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:213325f27d895aef26ae47217c791b467129b7a0344549a85243b0822e3fd8ba","observation_id":"6544b882-4da1-469d-a7ba-4f4ca2add7c6","resolution":{"observed_at":"2026-08-05T05:38:16.338093Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:16.144863Z","title":"Coefficients of Wronskian Hermite polynomials","venue":null,"work_id":"3ba43785-6b54-448c-8894-91ec00bd3f19","year":2020},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.269878Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:dc7a5583119cf4cf260db94ab4c968a4df7727913e81cd93279f2f0598d72ad5","observation_id":"76f91f30-b6c2-473c-a5ce-46769afb0a79","resolution":{"observed_at":"2026-08-05T05:38:16.195887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.959095Z","title":"Wronskian Appell polynomials and symmetric functions.Adv","venue":null,"work_id":"afd0389c-6e8d-496f-93f9-54809b03edaf","year":2019},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.330131Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:2f069a24cdd0f8fc4f7e2d128462162d714dde54247ad69862e723d207dd7b91","observation_id":"231d7668-0712-481a-9768-f5e199085459","resolution":{"observed_at":"2026-08-05T05:38:16.033103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.843747Z","title":"Janossy densities","venue":null,"work_id":"afde481f-aee8-4511-aea7-7c402fb97941","year":2003},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.424405Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:8ce552e0dca09ea52b45f1eb0aad28de43530479c2cf440e6243412fdb4dd0b0","observation_id":"7d27d4ed-bbdb-48ef-af98-00639f25e6fa","resolution":{"observed_at":"2026-08-05T05:38:15.898739Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.705959Z","title":"Iterated integrals and exponential homomorphisms.Proc","venue":null,"work_id":"1d9397f3-7b2b-4275-a71f-7a3b95d7d212","year":1954},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.503085Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:99545da2bc986fbc87196ed78ee3dbfee954b4c98b2f4bedda1ea85a6b917d98","observation_id":"741b2aee-2d4b-42c1-9645-6dbeb3394539","resolution":{"observed_at":"2026-08-05T05:38:15.777790Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.545681Z","title":"Matrix models for beta ensembles.J","venue":null,"work_id":"a03d8cf4-a74c-4f61-9ac3-c47e87bdd6b0","year":2002},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.534773Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:f8df9ba333852f02ffa3f5e583ba54676fe44494fa768f18b3c5483a3bab04cd","observation_id":"f2b4e6ae-7044-4b00-b585-baa63ddf8f15","resolution":{"observed_at":"2026-08-05T05:38:15.624495Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.378035Z","title":null,"venue":null,"work_id":"bce6c7d0-46e1-415d-9b3a-e969d5f79fec","year":1962},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.631535Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:dc012511210d3c8e7b1c2feca0686187de2adf4473328eb5fcf775790fbe5e14","observation_id":"575e518d-a76c-4093-b7c4-a8463308f9a2","resolution":{"observed_at":"2026-08-05T05:38:15.463448Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.256810Z","title":null,"venue":null,"work_id":"8279e1ba-d32e-4087-870e-c0060e1660ec","year":1962},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.698771Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:bf0b056c382f107e180cc19c582378e2dcccb34e7f9572c5cb16c4f963545ba2","observation_id":"af0ffe6c-d65a-4f21-96f0-fb0bef02d3a0","resolution":{"observed_at":"2026-08-05T05:38:15.310089Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:15.086714Z","title":null,"venue":null,"work_id":"3fff2ca0-9e8f-42c5-8ae0-dc4c63348aa2","year":1962},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.788901Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:0cf2a5ea9e61e1b275f00ca5cd3e9745d8974e233eb6b43e5476c4a7bdef31ae","observation_id":"6db348a8-d378-4ae1-8faf-accb8506b903","resolution":{"observed_at":"2026-08-05T05:38:15.165765Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:14.931936Z","title":null,"venue":null,"work_id":"61f80f8e-0e68-4ac1-a524-cdfa24b348fa","year":1962},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:07.910341Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:e24c91a3e33e45cec0ba8cae1a42aeb1335995c690dfafa82efadd36e7c4cbbc","observation_id":"0def699c-aa84-42d5-b97d-4a279617b034","resolution":{"observed_at":"2026-08-05T05:38:14.991286Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T05:38:08.041763Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.041763Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:550dea82ed3b2027b9b09587b7e04d2eff0527008aa82d685ac0d52e88853ba5","observation_id":"26b7b834-8944-4b40-93b5-9a9cba04e1a8","resolution":{"observed_at":"2026-08-05T05:38:08.041763Z","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":"2026-08-05T05:38:14.769428Z","title":"Felder, A","venue":null,"work_id":"f7df1f75-e43f-4295-b293-28a1f87643dc","year":2012},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.106574Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:c0c21a26c929c49ffa9cc2664ad3c4156d33e9866926ed8a2a199db29fe47811","observation_id":"ae86132c-3246-46f4-a789-c9d007ec1b00","resolution":{"observed_at":"2026-08-05T05:38:14.845327Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:14.589579Z","title":"Forrester and S","venue":null,"work_id":"bd8a5165-56b5-41b3-b873-1cb86cd55a0c","year":2008},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.205835Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:f28f319012b105ebc34890704b345593e035a27b4267197dd8dfa72924dc20ec","observation_id":"488c7627-c7d6-458b-93b5-e83f26f96674","resolution":{"observed_at":"2026-08-05T05:38:14.687258Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:14.400076Z","title":"The expansion of Wronskian Hermite polynomials in the Hermite basis.SIGMA Symmetry Integrability Geom","venue":null,"work_id":"f17a6a37-46bd-497e-a114-d5d7106ba551","year":2021},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.356837Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:eb1e14cc04b2eea8c41a1aa3e5426fbc3ed07cc98cec6d37465666f6d52f112f","observation_id":"59a885f9-e4ba-4ed5-a2fc-9aa42ab931d6","resolution":{"observed_at":"2026-08-05T05:38:14.504305Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:14.168592Z","title":null,"venue":null,"work_id":"b8dd997b-9b05-4bbd-9c01-e60016429a5b","year":1962},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.428265Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:6b6ea1c77c531857b593b39725de797c53fdef52ace4e8b2cf0fbb00f6884e6a","observation_id":"d750d0df-13e4-43c3-8f7b-917ce839e370","resolution":{"observed_at":"2026-08-05T05:38:14.279318Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2008.09776","last_updated":"2022-10-20T13:37:43Z","snapshot_observed_at":"2026-07-06T09:49:17.164814Z","submitted_at":"2020-08-22T08:12:51Z","title":"Minor summation formula of hyperpfaffians and Selberg integrals","version":3},"cited_work":{"arxiv_id":"2008.09776","doi":null,"metadata_source":"pith","pith_arxiv_id":"2008.09776","snapshot_observed_at":"2026-08-05T05:38:10.445102Z","title":"Minor summation formula of hyperpfaffians and Selberg integrals","venue":"math.CO","work_id":"0adc73a0-4702-46f6-aeb5-f5bd6125ac30","year":2020},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.530355Z"},"links":{"cited_paper":"/paper/2008.09776","citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:795004646e1e973e2971748fc04ad93d40cd88fba74655c7e233e2411eedfa4b","observation_id":"060763ec-824b-4948-a717-111cd332b642","resolution":{"observed_at":"2026-08-05T05:38:10.555446Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:13.924451Z","title":"Density matrix of an impenetrable Bose gas and the fifth Painlev´ e transcendent.Phys","venue":null,"work_id":"a0243ba8-7576-4e49-b1ab-6389fb44a365","year":1980},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.629119Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:c9b00b9ddf108cbe3681f1d2f7696d27e981588e72206efaf3d4f5f538d8943c","observation_id":"b8813870-b40d-4107-bd90-644d873479f7","resolution":{"observed_at":"2026-08-05T05:38:14.039512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:13.739866Z","title":"Karlin and G","venue":null,"work_id":"8d4b8ab8-58b8-4f18-9715-b5320dab60e7","year":1960},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.703817Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:b49384942d3df601c3ec877fb365846c88d9365e8163ed6a815d0dbfe0070a18","observation_id":"8d371851-1cb2-4c0e-ba09-cf9b965c8671","resolution":{"observed_at":"2026-08-05T05:38:13.815392Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:13.549743Z","title":"Pfaffian and Hafnian identities in shuffle algebras.Adv","venue":null,"work_id":"e1bf05dd-5398-4466-bcce-6493ab198b1e","year":2002},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.826071Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:93a65b716f778b4414b3a223269816d82a17c75c794d4dfce3f83a0dd8dfac3f","observation_id":"af7c4299-3520-4b79-b7d7-f7bce7a1f841","resolution":{"observed_at":"2026-08-05T05:38:13.647700Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:13.326633Z","title":"Hankel hyperdeterminants and Selberg integrals.J","venue":null,"work_id":"f59c6d4d-9630-4a2c-843a-df5af1cfe5e6","year":2003},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:08.930122Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:fe1ffd66e29a54da435e8f3db9be3455a1f2588751776a1220341a9072d9e1e7","observation_id":"22762eef-f2ba-427a-9843-7bb82dc6176d","resolution":{"observed_at":"2026-08-05T05:38:13.440497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:13.104373Z","title":"Elsevier/Academic Press, Amsterdam, third edition, 2004","venue":null,"work_id":"89bb6ce8-6f7f-424e-a294-536b9d0d000a","year":2004},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.035249Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:b8397108ba9800ff8a524537cb846e1876fb86bfb294ea4018b605d16d4ca9f9","observation_id":"1221c21e-6651-450d-9c35-c3502c6a59c5","resolution":{"observed_at":"2026-08-05T05:38:13.219550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:12.933096Z","title":"Ram ´ ırez, Brian Rider, and B´ alint Vir´ ag","venue":null,"work_id":"2a5a88fa-3edf-4e37-8438-1db5708aac47","year":2011},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.139027Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:76fab0becfbe8c0521a5b29d0ca2b8dc110f7fe353e9de55e1d2d6792c5cab78","observation_id":"3d589075-b6d7-41eb-9ca6-a6b7145e6fd3","resolution":{"observed_at":"2026-08-05T05:38:13.045842Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00605-011-0371-8","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T06:12:12.796739Z","title":"Ensemble averages whenβis a square integer.Monatshefte f¨ ur Mathematik, 166:121–144, 2012","venue":"Monatshefte für Mathematik","work_id":"88b314f1-1c2d-4b15-a090-5fe9649ca53e","year":2012},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.236487Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:d201fc5285fba048a5b80e45cc956642937ef29accdddc7a744cef301ddaebd1","observation_id":"cf757c3e-f2ce-4c11-94ad-51ffaac273e8","resolution":{"observed_at":"2026-08-05T05:38:10.327291Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:12.683091Z","title":"The partition function of multicomponent log-gases.Journal of Physics A: Mathematical and Theoretical, 45(16):165002, 2012","venue":null,"work_id":"39e793ce-4a48-41d0-87b5-930b026a10e9","year":2012},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.331840Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:038b9dc001b60f246c33b7bc986e88cf6dd01de0b4408c06701a8238966cd7c1","observation_id":"0ab190f0-2ce2-4f78-8e6d-af5fb36171f6","resolution":{"observed_at":"2026-08-05T05:38:12.837526Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:12.433467Z","title":"Soshnikov","venue":null,"work_id":"17eacec9-f1c1-423c-bbfa-f5bfeacf6b2f","year":2000},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.441389Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:f8c3b002ec0790a6017b24fa537c6fd22386779c34c929b663d1edfb632cb953","observation_id":"4f4bfc43-e3b8-4ab8-854c-180b1c1b7581","resolution":{"observed_at":"2026-08-05T05:38:12.551691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:12.202736Z","title":"Janossy densities","venue":null,"work_id":"69f2997c-a5a5-46e4-9775-53a7ae02ad43","year":2003},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.506521Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:9d54a3452906985f441e8ced0ab1212cc9d80f51c3cd1b7f7d7938da9e1d99a5","observation_id":"350f2281-49e8-493b-9a1c-2a769512234e","resolution":{"observed_at":"2026-08-05T05:38:12.347298Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:11.967821Z","title":"Tracy and Harold Widom","venue":null,"work_id":"7d912c8f-db1a-4dba-8aac-b67634758572","year":1996},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.620858Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:60da45ebceafba4b0baeeaa8009364583c4a681f806c9a9d83720db0fa12ec2f","observation_id":"0ea0791f-119f-46f4-9758-19335dc3d672","resolution":{"observed_at":"2026-08-05T05:38:12.090016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:11.775117Z","title":"Tracy and Harold Widom","venue":null,"work_id":"31a17b8c-5149-421a-8c60-9e39f0747e61","year":1998},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.692691Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:3184b966072bb67075fe3a9d63232fd18f46000937719bb86e210edcab28c923","observation_id":"4580aa76-922d-44d2-865e-a2e44c7ec097","resolution":{"observed_at":"2026-08-05T05:38:11.861207Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:11.563378Z","title":"Tracy and Harold Widom","venue":null,"work_id":"8f837168-8a4a-4892-a257-81cca3c9c1e1","year":1997},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.822132Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:dedc05a728d4ec181503e001f4b70d13eaa7bcaefd6fa00430ea1b58e45d2666","observation_id":"f6957d0f-fa72-4fdf-b61a-6c17456f3a03","resolution":{"observed_at":"2026-08-05T05:38:11.677307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:11.340820Z","title":null,"venue":null,"work_id":"af1184c3-42f5-4d33-9295-a2b4f973be0d","year":1960},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.885286Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:176fa8249ec2f26883e55fe40815131980c396a23df35d5b7575ef4e86e03627","observation_id":"d72ccbeb-e807-42dc-9343-285fa9b19897","resolution":{"observed_at":"2026-08-05T05:38:11.453930Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:11.058201Z","title":"Wells.On the Solvability of Beta-ensembles when Beta Is a Square Integer","venue":null,"work_id":"7bdf3b04-7019-442e-9a3b-88c5d5ebb73b","year":2019},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:09.957161Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:a5dedf0299399c586db70e45d4268892349e166159031c06d3c495d932b201d2","observation_id":"32bb3cb7-7332-4aff-8d4c-d8fff3999680","resolution":{"observed_at":"2026-08-05T05:38:11.216555Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:10.860599Z","title":"On the relation between orthogonal, symplectic and unitary matrix ensembles.J","venue":null,"work_id":"13f90faa-de22-4d9f-a4e3-a2d72303f61a","year":1999},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:10.013013Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:c5a271ad58e3b97e783e6d8e214c632d5d36c5cfee4d642b4d5c12ee4bbc1d3c","observation_id":"5e0daf00-50be-40fe-83f2-b3197408da0a","resolution":{"observed_at":"2026-08-05T05:38:10.936934Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-08-05T05:38:10.632700Z","title":"Wolff and Jonathan M","venue":null,"work_id":"255654af-97e5-431d-8e4b-5426bc39b8d1","year":2022},"citing_paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T05:38:10.083382Z"},"links":{"citing_paper":"/paper/2509.05487"},"observation_digest":"sha256:610973a1f63e4cfffa6b1a6c69f65a78ca1f9a6ceef69a94f963ad7630e8cf0c","observation_id":"1f350b72-4819-4aa5-aa1f-82a9d667384a","resolution":{"observed_at":"2026-08-05T05:38:10.749439Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.05487","last_updated":"2026-07-24T19:56:17Z","latest_version":2,"primary_category":"math-ph","snapshot_observed_at":"2026-08-10T02:40:09.607463Z","submitted_at":"2025-09-05T20:28:29Z","title":"Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":2,"verified_fuzzy":24},"total_outbound_references":34},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2509.05487."}