{"as_of":"2026-08-13T08:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c77928e11826f8e2d942f4f5556ca6704e21c04105a4aa82e0c2b6460b9d1494","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T01:56:26.338155Z","state":"measured"},{"denominator":17,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":17,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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":"2026-08-07T12:06:41.844392Z","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":"2026-08-07T12:06:42.922670Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"cited_work":{"arxiv_id":"2607.19844","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.19844","snapshot_observed_at":"2026-08-07T12:06:42.922670Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","venue":"math.PR","work_id":"e6b81eb3-38fc-4770-a63c-1b00cb290f58","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":10,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:41.844392Z"},"links":{"cited_paper":"/paper/2607.19844","citing_paper":"/paper/2608.06232"},"observation_digest":"sha256:07d535caecee0ffb1fe04d65181a858547e2d3ae55d04cfd9dc98259d19bd781","observation_id":"57c068f7-07c2-47ff-98ef-00f741bafde1","resolution":{"observed_at":"2026-08-07T12:06:42.965030Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.19844/citation-record","integrity":"/paper/2607.19844/integrity","json":"/paper/2607.19844/citation-record.json","paper":"/paper/2607.19844"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:24.986645Z","title":"Arratia, L","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:24.986645Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:c516f8c257a137e2ef506bbc6feab132cb7ed7722582d70388730c1ad1982dd0","observation_id":"140a153e-041a-4da8-b967-92261210d622","resolution":{"observed_at":"2026-08-03T01:56:24.986645Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.115339Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.115339Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:acd0208471ed8b9d3e4247e02e366346a64db7ea642569da97465771523ee440","observation_id":"d9a36dd6-b96b-4cb7-a166-3871d45e73da","resolution":{"observed_at":"2026-08-03T01:56:25.115339Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.211813Z","title":"Burić, N","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.211813Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:2a5f3f099a7447086d078fb96430554bedaaf07e5c71f5d539866cb1098ebb4b","observation_id":"8bdb3738-e284-4f4b-8d04-6a1b6826d7db","resolution":{"observed_at":"2026-08-03T01:56:25.211813Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.293479Z","title":"Diaconis, S","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.293479Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:9e1777ace45a539dcf5b81b5708c0518ea057c3df8ab33b90c40b32d41b53b7f","observation_id":"9a9d6c55-3977-4d01-b0a3-5d4814606c94","resolution":{"observed_at":"2026-08-03T01:56:25.293479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.402141Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.402141Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:68f4c987e0d1ed962b18893a4891381253b5b9e618edfb42be22976d07349c45","observation_id":"51ffc7b1-5dba-4810-a639-1cc1d5822730","resolution":{"observed_at":"2026-08-03T01:56:25.402141Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.523492Z","title":"Elezović,Asymptotic expansions of central binomial coefficients and Catalan numbers, J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.523492Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:fb47311e5cccc5066611a74fd73dd05affd674e8eae2ec9f23e357e031c12474","observation_id":"a7210b91-8ec0-44b9-b891-4be57faada8e","resolution":{"observed_at":"2026-08-03T01:56:25.523492Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.18494","last_updated":"2026-07-20T20:33:35Z","snapshot_observed_at":"2026-08-12T19:39:54.159590Z","submitted_at":"2026-07-20T20:33:35Z","title":"Local binomial expansions with an Appell shift, and the mean absolute deviation of the binomial distribution","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.18494","snapshot_observed_at":"2026-08-03T01:56:25.608963Z","title":"Elezović,Local binomial expansions with an Appell shift, and the mean absolute deviation of the binomial distribution, preprint,arXiv:2607.18494[math.CA], 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.608963Z"},"links":{"cited_paper":"/paper/2607.18494","citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:95b6751f1d6bdfc3d33dbf2b2732e6d7b7863ca3def1f4d7f8f60b0cda46912f","observation_id":"e2892360-3c23-4844-b99a-83506a51aacc","resolution":{"observed_at":"2026-08-03T01:56:25.608963Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.695222Z","title":"Esseen,Fourier analysis of distribution functions","venue":null,"work_id":null,"year":1945},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.695222Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:b0c37c7f8cb38abb735db3914f054651c8cc7ffe7cba15ce589ad3805250b9a9","observation_id":"b76af395-6542-45fe-a498-c4004d4d31a8","resolution":{"observed_at":"2026-08-03T01:56:25.695222Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.762497Z","title":"Feller,An Introduction to Probability Theory and Its Applications, Vol","venue":null,"work_id":null,"year":1968},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.762497Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:a9fb2b2e2910907c6af2168ac977164cb787787bb144939f4f9d2af487601689","observation_id":"61aaa80e-a48d-40a3-a718-069099e641a8","resolution":{"observed_at":"2026-08-03T01:56:25.762497Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.818950Z","title":null,"venue":null,"work_id":null,"year":1942},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.818950Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:14a100c30193d85d9fba4cbf0f610f62fe685d81661633a4d9a14488fa3e294e","observation_id":"89e087b5-b0ac-4eeb-b224-3f2683ad1e3c","resolution":{"observed_at":"2026-08-03T01:56:25.818950Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:25.903986Z","title":"Hall,On the limiting behaviour of the mode and median of a sum of independent random variables, Ann","venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.903986Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:a03f5fa9bd7534e08ff21e6af8a9ea3bda4726a85582fef73d634a2358652c28","observation_id":"0ce97296-c51d-41e6-9d15-e538681fb7d2","resolution":{"observed_at":"2026-08-03T01:56:25.903986Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.13781","last_updated":"2020-10-19T08:06:23Z","snapshot_observed_at":"2026-08-12T16:57:20.886820Z","submitted_at":"2020-09-29T05:07:50Z","title":"On the probability that a binomial variable is at most its expectation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.13781","snapshot_observed_at":"2026-08-03T01:56:25.986514Z","title":"Lett.171(2021), 109020; preprintarXiv:2009.13781","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:25.986514Z"},"links":{"cited_paper":"/paper/2009.13781","citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:9b4880e504abe10576b9f3ce2629cd0c3010dd39b0423371e0c5c340cfcfe659","observation_id":"3a5456e0-0348-450c-82e8-050adcdb4a24","resolution":{"observed_at":"2026-08-03T01:56:25.986514Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:26.076841Z","title":null,"venue":null,"work_id":null,"year":1980},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:26.076841Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:5616a8bc15ac61781e1eb0f47663a24d9104f6856b8c26c88fae4c8eb37c4246","observation_id":"a8b85887-eac6-4271-b369-8e4088306f69","resolution":{"observed_at":"2026-08-03T01:56:26.076841Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.15025","last_updated":"2023-10-16T17:36:38Z","snapshot_observed_at":"2026-07-30T17:35:35.021675Z","submitted_at":"2021-05-31T15:06:35Z","title":"Faulhaber polynomials and reciprocal Bernoulli polynomials","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.15025","snapshot_observed_at":"2026-08-03T01:56:26.161661Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:26.161661Z"},"links":{"cited_paper":"/paper/2105.15025","citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:e851043ad43320c05ba62f0c2e1af3f5ce097f5f637f3997c9de9ba9efc1621d","observation_id":"c05ba2f8-965d-4730-b54f-5a5911dc870d","resolution":{"observed_at":"2026-08-03T01:56:26.161661Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:26.259199Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:26.259199Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:7d72e5602f6a002ce3dd6c6d28c45bfcf509c6bd70269e4b5ba011231a1e70cc","observation_id":"0a952ccc-f7e6-41ae-9812-aa8201c1dd2c","resolution":{"observed_at":"2026-08-03T01:56:26.259199Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-03T01:56:26.338155Z","title":null,"venue":null,"work_id":null,"year":1937},"citing_paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-03T01:56:26.338155Z"},"links":{"citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:ace2d266c16e5dc323d558b70478fa090f4c3d35ae481f4ad401cdb1d9c0cc9f","observation_id":"154632b0-58bc-4946-a0e7-f11f85bf4c20","resolution":{"observed_at":"2026-08-03T01:56:26.338155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.19844","last_updated":"2026-07-31T17:00:38Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-12T19:44:38.817296Z","submitted_at":"2026-07-22T07:30:15Z","title":"Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":16},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2607.19844."}