{"as_of":"2026-08-11T18:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1a95b5fef6bd871d17f73ad824f9b4533ff8e079383c2b31b7f3875aa69fa710","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T11:26:24.045653Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2509.02881/citation-record","integrity":"/paper/2509.02881/integrity","json":"/paper/2509.02881/citation-record.json","paper":"/paper/2509.02881"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T11:26:24.255400Z","title":"Gerasimov, S","venue":null,"work_id":"f0f3c08d-f84b-48a5-9bdd-9c7fe622264a","year":2006},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:23.994964Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:d25b3519a9985461feeed00bbc02d485e3815fb4de0db7aa73db9a577837885b","observation_id":"dab9d4dd-a950-49ee-9e94-c3469639a213","resolution":{"observed_at":"2026-08-05T11:26:24.259307Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.242195Z","title":"”Macdonald processes.” Probability Theory and Related Fields 158.1 (2014): 225-400","venue":null,"work_id":"4ccbb9d7-ff86-4ab2-bb63-7ccbdf9c0d66","year":2014},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.000228Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:6f26b0c967c4c7a256ca00c0a0ddd9942d415dee134d33c7b85de8bf65f0fc8e","observation_id":"2a305acd-cc43-46da-a2e8-174461ff9f1f","resolution":{"observed_at":"2026-08-05T11:26:24.246160Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.227826Z","title":null,"venue":null,"work_id":"8e7947e2-9184-47a7-b01b-56d7027d3eb9","year":2009},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.004693Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:8a49dbab5a66a535c9f7889fed1c8d7cca4241c9a97a6afaf4f285df0184bac0","observation_id":"7de54b25-af1a-4d6e-a140-95bddc981915","resolution":{"observed_at":"2026-08-05T11:26:24.232016Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/9901053","last_updated":"1999-01-13T00:10:20Z","snapshot_observed_at":"2026-08-11T06:37:23.506701Z","submitted_at":"1999-01-13T00:10:20Z","title":"Whittaker functions on quantum groups and q-deformed Toda operators","version":1},"cited_work":{"arxiv_id":"math/9901053","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/9901053","snapshot_observed_at":"2026-08-05T11:26:24.107475Z","title":"Whittaker functions on quantum groups and q-deformed Toda operators","venue":"math.QA","work_id":"7288601c-79ec-4a75-91fe-ffc6f5b6ee14","year":1999},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.009760Z"},"links":{"cited_paper":"/paper/math/9901053","citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:1946179994e4a3fe3fe4274e5b5838f6d0d8659b588541a9fc7b2d895ad1b0b2","observation_id":"d26e4aa9-ea8e-4699-a972-ee32b4df6c95","resolution":{"observed_at":"2026-08-05T11:26:24.113741Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.213109Z","title":"”Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian.” Letters in Mathematical Physics 88 (2009): 39-77","venue":null,"work_id":"779f19cc-f3cf-4633-a1f6-919155c4ee32","year":2009},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.014623Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:d6ced44276a4ecd97dca63ab9095b78bf76e4244d4b65a1d2c9ddee5c7e64008","observation_id":"2840b981-9996-4aae-95cf-6f47abe10517","resolution":{"observed_at":"2026-08-05T11:26:24.217746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.198577Z","title":null,"venue":null,"work_id":"70fff7b8-6b08-46ec-a8f5-0b9d1e912a2b","year":2011},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.019231Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:c9595319a96556039df18d89b2570b4c21fbde9ee86aaebe362d028dfaa9422c","observation_id":"bbf1d673-c645-4e99-9ce9-14d6aeb0b3b5","resolution":{"observed_at":"2026-08-05T11:26:24.202890Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.182741Z","title":"”On q-Deformed-Whittaker Function I.” Communications in Mathematical Physics 294.1 (2010): 97-119","venue":null,"work_id":"cc41ff87-fff3-41be-8b36-bf360e4ef68f","year":2010},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.023955Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:a9cc2263c098d3f3bde8ccaa66dcec7e8b4d4f700413e390622f88228c412e77","observation_id":"8c517be5-4a75-4f29-9b52-49a0fb597e5d","resolution":{"observed_at":"2026-08-05T11:26:24.187836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.167637Z","title":"”Quantum K-theory on flag manifolds, finite-difference Toda lattices and quantum groups.”","venue":null,"work_id":"1f518f50-1369-493d-93a1-ee25a52a00f3","year":null},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.028145Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:3a508bf0092134e572176782a0b8cf5515829892991e207b9ce47a7ffa435d90","observation_id":"ed1e7549-09f2-4eb4-bb7a-a7855e47c9dd","resolution":{"observed_at":"2026-08-05T11:26:24.171915Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2502.10655","last_updated":"2026-07-28T14:00:36Z","snapshot_observed_at":"2026-08-07T18:16:26.375796Z","submitted_at":"2025-02-15T03:40:26Z","title":"On a specialization of Toda eigenfunctions","version":3},"cited_work":{"arxiv_id":"2502.10655","doi":null,"metadata_source":"pith","pith_arxiv_id":"2502.10655","snapshot_observed_at":"2026-08-05T11:26:24.083740Z","title":"On a specialization of Toda eigenfunctions","venue":"math.RT","work_id":"17b5fea8-45d9-4c9d-868c-983f58fb14e0","year":2025},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.032595Z"},"links":{"cited_paper":"/paper/2502.10655","citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:7c76346acae47d5e6d9b4b1d2c4c9a1bec48b4c971f794a4aafcfba66e573603","observation_id":"9a73d2e6-6d39-407b-895e-b6fa6b8f6734","resolution":{"observed_at":"2026-08-05T11:26:24.089763Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.153839Z","title":"”Directed polymers and the quantum Toda lattice.” (2012): 437-458","venue":null,"work_id":"9e094753-3137-4cc1-8602-7397788cad56","year":2012},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.037244Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:f6d6f335442428392b3ac11f0ad87706ba882aa9d3ad2847fd2598c5bbdf8a1b","observation_id":"71919425-fb15-4ac9-9efe-1b33f9414b47","resolution":{"observed_at":"2026-08-05T11:26:24.158147Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.139974Z","title":"”Discrete Whittaker processes.” Probability and Mathematical Physics 4.4 (2023): 965- 1002","venue":null,"work_id":"d474c697-3a22-4547-a9fd-faacc3f0f286","year":2023},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.041417Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:1ae87ac15ad24b83171f2a0b3ec4138d10269c728cce43f4e7c51f7bb8ff0290","observation_id":"e9343723-1882-4e85-b7e2-03313c8b2ddd","resolution":{"observed_at":"2026-08-05T11:26:24.144287Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-05T11:26:24.125153Z","title":"Chris G., and J","venue":null,"work_id":"6124f5f6-6c41-44f8-af16-431e79df4c55","year":1981},"citing_paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T11:26:24.045653Z"},"links":{"citing_paper":"/paper/2509.02881"},"observation_digest":"sha256:7323a996a3f8a2e97308d8986a0cd9f638008b029dcb8b413c1fbf4d036ce2f4","observation_id":"0ebc0742-171c-4412-ada7-c7ff35014283","resolution":{"observed_at":"2026-08-05T11:26:24.129767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2509.02881","last_updated":"2026-06-02T21:58:39Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-11T10:57:14.572604Z","submitted_at":"2025-09-02T23:03:50Z","title":"$q$-Deformed Discrete Whittaker Processes"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":8},"total_outbound_references":12},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2509.02881."}