{"as_of":"2026-08-12T20:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a14999371fa230a68c0b0803fc8a7fd1b6b70ae6611be5bf6c4da33a54e5daf4","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-16T14:21:39.057368Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"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":"2026-08-07T12:06:41.416780Z","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":"2026-08-07T12:06:43.426256Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"cited_work":{"arxiv_id":"2601.09485","doi":null,"metadata_source":"pith","pith_arxiv_id":"2601.09485","snapshot_observed_at":"2026-08-07T12:06:43.426256Z","title":"On lower bounds for hypergeometric tails","venue":"math.PR","work_id":"be5463cc-db92-40a8-8ec3-f522444f9320","year":2026},"citing_paper":{"arxiv_id":"2608.06232","last_updated":"2026-08-06T16:20:28Z","snapshot_observed_at":"2026-08-12T19:40:31.727472Z","submitted_at":"2026-08-06T16:20:28Z","title":"The mean absolute deviation of the classical discrete distributions: collapse identities, complete asymptotic expansions, and enveloping series","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:41.416780Z"},"links":{"cited_paper":"/paper/2601.09485","citing_paper":"/paper/2608.06232"},"observation_digest":"sha256:48300d0f3ce6682391d6ecc080a8f5d8076172c6c5abe33c14cb9fa0b01ce579","observation_id":"64d88cbc-0eb4-4fb8-b59c-f78893d143d8","resolution":{"observed_at":"2026-08-07T12:06:43.488195Z","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/2601.09485/citation-record","integrity":"/paper/2601.09485/integrity","json":"/paper/2601.09485/citation-record.json","paper":"/paper/2601.09485"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Aydinian, V","venue":null,"work_id":"1de6b2b9-08aa-470a-a2f2-1b5965a45983","year":2012},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:84eecd591a97470b85a0a5eb47dbba9c67099fcfcbceff26ef529bf0f989b64f","observation_id":"65110253-3ad7-4a5b-abe8-417b1c4c63cd","resolution":{"observed_at":"2026-05-16T14:22:59.430602Z","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":"2026-06-05T21:23:00.469572Z","title":"Berend, A","venue":null,"work_id":"7a8a5a7a-9707-4dd8-abe9-f28baa6e3455","year":2013},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:30e70acbaa9c052c608884195f3949fe456176f8e57a4f25a61ff33be623896d","observation_id":"25c8538e-96fe-4548-a1ca-1d52450860db","resolution":{"observed_at":"2026-05-16T14:22:59.428757Z","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":"2026-06-05T21:23:00.469572Z","title":"Broman, T","venue":null,"work_id":"f675a4a5-a5ec-4326-93bf-f2d44f6a353b","year":2012},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:e3879aab46c8434f340af792d5f5b6cba53bbcb4494de5f9f3d1ecdc0ccea8ef","observation_id":"a133458d-6226-44a7-8b96-e614f6fcd49f","resolution":{"observed_at":"2026-05-16T14:22:59.426906Z","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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"aced16cc-1db4-47d6-81dc-5a88d137d62e","year":2010},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:8bd6daa8ff56493f8464e73c425034d073db3eb88443d22cdf727cb102c60a93","observation_id":"30983928-f79e-44be-b0ed-c1e6b5224187","resolution":{"observed_at":"2026-05-16T14:22:59.425102Z","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":"2026-06-05T21:23:00.469572Z","title":"Diaconis, S","venue":null,"work_id":"00a0a4b7-2481-4225-bb38-2a2175bdedaf","year":1991},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:2fb8dfc502c87f1970e4a9e60095183ca10d7338cf089b264b12a4a41f7faf0a","observation_id":"0d78e540-7c38-42c3-9e0e-a7c7130d9b4a","resolution":{"observed_at":"2026-05-16T14:22:59.460576Z","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":"2026-06-05T21:23:00.469572Z","title":"Doerr,An elementary analysis of the probability that a binomial random variable exceeds its expectation, Statistics & Probability Letters139(2018) 67–74","venue":null,"work_id":"cbc98c4a-21f5-498d-a21a-f95a9b14aa7c","year":2018},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:d006bc8e3a5f423841967061735249e39973dc3876835edde5fb0f2d909a1e41","observation_id":"e4aa8a0d-a70e-4549-954b-0b30c7ae50fd","resolution":{"observed_at":"2026-05-16T14:22:59.458677Z","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":"2026-06-05T21:23:00.469572Z","title":"Ehm,Binomial approximation to the Poisson binomial distribution, Statistics & Probability Letters11(1) (1991) 7–16","venue":null,"work_id":"fd061cb4-afb2-4eb6-99c1-c1eb5df1639c","year":1991},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:fba07c889a80d2fa6703a136535a7d899c7ab1d4ebfa1a6df6293eb4338a6bfd","observation_id":"9e597569-12ea-48a2-a43e-b6bfd0859422","resolution":{"observed_at":"2026-05-16T14:22:59.454587Z","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":"2026-06-05T21:23:00.469572Z","title":"Greenberg and M","venue":null,"work_id":"fbb70237-16bd-4217-8eac-5bd87e660b13","year":2014},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:ae31eef3418078ea03c1774deb878e3b8bb67939474e39f955296679ab072166","observation_id":"c149a24d-71ca-441f-9222-d4f5cfad0d42","resolution":{"observed_at":"2026-05-16T14:22:59.442113Z","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":"2026-06-05T21:23:00.469572Z","title":"Hui, C.J","venue":null,"work_id":"9b2ad76b-c9f2-4653-aabc-657f7b36e294","year":2014},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:012d1721d181a83afaa8612194fd5a93c6495ce260b115b7472299476303ff0f","observation_id":"938a1b30-1969-4355-be18-9dacf5d98cb5","resolution":{"observed_at":"2026-05-16T14:22:59.462338Z","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":"2026-06-05T21:23:00.469572Z","title":"Jogdeo, S","venue":null,"work_id":"95f1c82e-b02d-4d56-9c3e-a1e6c150fd9e","year":1968},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:564814de160f405cde7d464cbf83b4f202438a69455e48068a28fe289c1e8635","observation_id":"a8a1457f-ad41-49b2-9562-56eff64c1d42","resolution":{"observed_at":"2026-05-16T14:22:59.438200Z","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":"2026-06-05T21:23:00.469572Z","title":"Klenke, L","venue":null,"work_id":"da581853-a1b2-4892-bcc7-4d39856d7b86","year":2010},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:7cbf9885583ecb2a3c8f184904bcd8af3d1eabb455bc1dc0d2613e718b24dc5e","observation_id":"bf5d0538-3c03-4955-8a28-6821a904fa7d","resolution":{"observed_at":"2026-05-16T14:22:59.432488Z","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":"2026-06-05T21:23:00.469572Z","title":"Mattner, J","venue":null,"work_id":"1bbf139f-be35-4d93-a277-1e5c49723572","year":2018},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:b69ed571b004c5a4712a19e2a28513010fd1c79590ee10ee38ad2711a36c53ae","observation_id":"47558a61-ae92-4fba-80d8-a4d12b657403","resolution":{"observed_at":"2026-05-16T14:22:59.436353Z","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":"2026-06-05T21:23:00.469572Z","title":"Pelekis, J","venue":null,"work_id":"8002c2d6-cc75-4e18-ba8b-23f0464d6bbd","year":2016},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:21127bc175f3dd065354d448507c0f702deded3c7942a14853dd06ba92d64282","observation_id":"3e223cdc-c7d8-4496-88e7-27b1ed43cf12","resolution":{"observed_at":"2026-05-16T14:22:59.450039Z","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":"2026-06-05T21:23:00.469572Z","title":"Pinelis,Best lower bound on the probability of a binomial exceeding its expectation, Statistics & Probability Letters179(2021) 109224","venue":null,"work_id":"c1eb3541-ba86-40cd-bdfa-b2096221a548","year":2021},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:58b60b53562c9cd4aa972f2d1d1bd464360626d7c48b836eea808d9577e240cb","observation_id":"7fcf2a48-ec17-4ea2-ac5b-98d2dd233eb2","resolution":{"observed_at":"2026-05-16T14:22:59.434457Z","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":"2026-06-05T21:23:00.469572Z","title":"Pokrovskiy,A linear bound on the Manickam–Mikl´ os–Singhi conjecture, J","venue":null,"work_id":"f44cb151-98ca-4ec2-abbb-1dcc4b2cba2c","year":2015},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:e81a4126ff43fd93ceadc2b8f463789c1d9c17206e9f8dbf9585b3f91e49babd","observation_id":"c2764467-05c5-42b5-97cf-3b16bcb67f19","resolution":{"observed_at":"2026-05-16T14:22:59.440246Z","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":"2026-06-05T21:23:00.469572Z","title":null,"venue":null,"work_id":"b205310a-a613-4fc4-91b1-71baf033508d","year":1958},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:ddc27dab42a517fc667e1b6206d086e9921335818bcfc7e6a0d3c70e0ff4de01","observation_id":"5027d2ee-ce35-4163-9fc0-f82e0cb2d23c","resolution":{"observed_at":"2026-05-16T14:22:59.446129Z","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":"2026-06-05T21:23:00.469572Z","title":"Robbins,A Remark on Stirling’s Formula, The American Mathematical Monthly,62(1) (1955) 26–29","venue":null,"work_id":"17e8b842-f641-47e9-947b-b215960157c0","year":1955},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:b8327a42ca05abc5d1674e6189c36cc827aa33fd68a29a7f002d0a12e4983aab","observation_id":"0358011f-3e3e-437d-ae8a-bebb548e246c","resolution":{"observed_at":"2026-05-16T14:22:59.444389Z","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":"2026-06-05T21:23:00.469572Z","title":"Shaked, G.J","venue":null,"work_id":"534785e7-3462-4b7d-ad55-a4c8809ae7fe","year":2007},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:080552d04473a03c2266e32fffe93d8e9e3072aabd9289b856e0677d3c09f283","observation_id":"328c5d0e-0a6c-4705-90b1-e1d3f668b667","resolution":{"observed_at":"2026-05-16T14:22:59.448119Z","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":"2026-06-05T21:23:00.469572Z","title":"Siegel,Median bounds and their application, Journal of Algorithms38(1) (2001) 184–236","venue":null,"work_id":"61e89d44-172c-40e2-9fcf-7b9ed4900a5e","year":2001},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:ac0e5fa53d9a5f38c50bdc7aa1c1305dc686d331cec6ae174c3a85fec559f440","observation_id":"a1600fd7-da8d-4319-a8f4-5cb38d8a1b8c","resolution":{"observed_at":"2026-05-16T14:22:59.452522Z","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":"2026-06-05T21:23:00.469572Z","title":"Uhlmann,Vergleich der hypergeometrischen mit der binomial-verteilung, Metrika10(1966) 145–158","venue":null,"work_id":"d33bc076-8171-4f3e-aa5d-776666cf98d2","year":1966},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:8cf05c9162d09d7f9ee322b655a490065f3bc40e8e82518f4b189d949df59f52","observation_id":"7744add0-a502-4c5e-a328-d083e130cd84","resolution":{"observed_at":"2026-05-16T14:22:59.456642Z","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":"2026-06-05T21:23:00.469572Z","title":"Vatutin, V .G Mikhailov, (1983).Limit theorems for the number of empty cells in an equiprobable scheme for group allocation of particles, Theory Probab","venue":null,"work_id":"71b2739e-62b6-4d29-932a-47dcfe943316","year":1983},"citing_paper":{"arxiv_id":"2601.09485","last_updated":"2026-04-22T18:37:11Z","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-16T14:21:39.057368Z"},"links":{"citing_paper":"/paper/2601.09485"},"observation_digest":"sha256:a59e75181e9239e806c76c86d99a511fb2d396269370efc93d74ce63bca5e5b0","observation_id":"c17ef09c-843b-4936-a46a-e9b40b052f13","resolution":{"observed_at":"2026-05-16T14:22:59.464527Z","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":"2601.09485","last_updated":"2026-04-22T18:37:11Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-12T19:40:47.115601Z","submitted_at":"2026-01-14T13:48:33Z","title":"On lower bounds for hypergeometric tails"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":0,"verified_fuzzy":19},"total_outbound_references":21},"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 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2601.09485."}