{"as_of":"2026-08-12T22:39:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1860ecf47937099be67c91d8b54764ae30662714abe13e769bd78ca87cc2a5fa","coverage":[{"denominator":31,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":31,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T15:21:42.125899Z","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":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T12:06:41.773526Z","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":"2026-08-07T12:06:43.026105Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":"2026-08-01T11:38:53.533529Z","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":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T11:38:53.533529Z"},"links":{"cited_paper":"/paper/2607.18494","citing_paper":"/paper/2607.19844"},"observation_digest":"sha256:b6031825018bc3f5c084d090162a4ca2200075ea39d62cc0a5552c4fb55aed45","observation_id":"9eb7da21-6b0b-4245-b22c-a09c748dc433","resolution":{"observed_at":"2026-08-01T11:38:53.533529Z","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":{"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":"2026-08-01T11:58:11.603867Z","title":"Elezović,Local binomial expansions with an Appell shift, and the mean absolute deviation of the binomial distribution, arXiv:2607.18494, 2026","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.26636","last_updated":"2026-07-29T08:58:27Z","snapshot_observed_at":"2026-08-12T19:40:29.651014Z","submitted_at":"2026-07-29T08:58:27Z","title":"Appell Polynomials in Shifted Asymptotic Expansions: the Mills ratio, Hermite polynomials, and Stieltjes bounds","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T11:58:11.603867Z"},"links":{"cited_paper":"/paper/2607.18494","citing_paper":"/paper/2607.26636"},"observation_digest":"sha256:115ef06423d7a9abebfc9887c190fcf132b12522f1f2f211e07798d3fbf9b751","observation_id":"c1d1fe58-97b5-46a3-beba-da4bce4b1343","resolution":{"observed_at":"2026-08-01T11:58:11.603867Z","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":"2607.18494","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.18494","snapshot_observed_at":"2026-08-07T12:06:43.026105Z","title":"Local binomial expansions with an Appell shift, and the mean absolute deviation of the binomial distribution","venue":"math.CA","work_id":"c838cbd7-075a-4cc0-a2ee-d9e85cb720ba","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":9,"source":"pdf_text","source_observed_at":"2026-08-07T12:06:41.773526Z"},"links":{"cited_paper":"/paper/2607.18494","citing_paper":"/paper/2608.06232"},"observation_digest":"sha256:0d5b988b0668f1729efb35c8070ecbed2effa8f4bd8648a0e8a6d9b6f9dc57bb","observation_id":"0815cd42-e334-4e4f-b633-1941c5c70ff4","resolution":{"observed_at":"2026-08-07T12:06:43.077597Z","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/2607.18494/citation-record","integrity":"/paper/2607.18494/integrity","json":"/paper/2607.18494/citation-record.json","paper":"/paper/2607.18494"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T15:21:41.779398Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:41.779398Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:2ad7ce4fbef4dba3ab59466ecb96432df6f8d1f670e345f0f5560f42d16e9992","observation_id":"fdc1823b-ce05-465b-9c54-717c9c6a2e69","resolution":{"observed_at":"2026-08-01T15:21:41.779398Z","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":"2026-08-01T15:21:41.850737Z","title":"Berend, A","venue":null,"work_id":null,"year":2013},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:41.850737Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:4ed786dcc911eec6a403601d85b945896470e10c81082b634d06186745cfc4c3","observation_id":"7d3d4649-5294-4fbc-ba30-588cd40042bc","resolution":{"observed_at":"2026-08-01T15:21:41.850737Z","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":"2026-08-01T15:21:41.956503Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:41.956503Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:78fc4ec9f128067d0cc22a8478564650b9636403d0798bacb90370110d7f4c6b","observation_id":"93cbc2ff-17be-4f22-8e7b-9c45ff1c5844","resolution":{"observed_at":"2026-08-01T15:21:41.956503Z","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":"2026-08-01T15:21:42.053773Z","title":null,"venue":null,"work_id":null,"year":1980},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.053773Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:b72e8299fb50b1b5d680065fc4826f47cf96abe03197cc47901d3a9063f32f80","observation_id":"124f4faa-1045-42b5-b06a-d0c5c1d18788","resolution":{"observed_at":"2026-08-01T15:21:42.053773Z","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":"2026-08-01T15:21:42.057266Z","title":null,"venue":null,"work_id":null,"year":1949},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.057266Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:d81e789128d5c50bd135467d68008d77027cfd02538f9abfeeec3922a89e52a6","observation_id":"d4b9d67a-1806-4eba-ab18-2c7ba64f41d9","resolution":{"observed_at":"2026-08-01T15:21:42.057266Z","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":"2026-08-01T15:21:42.060318Z","title":"Burić, N","venue":null,"work_id":null,"year":2011},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.060318Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:9f9a58b57321be29407556a0de96b9a707ed8b050bcc3cdcbbafc021b72d368b","observation_id":"8bde51a0-30f6-4500-8d0d-9386f606b37d","resolution":{"observed_at":"2026-08-01T15:21:42.060318Z","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":"2026-08-01T15:21:42.063872Z","title":"Burić, N","venue":null,"work_id":null,"year":2012},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.063872Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:a1cdcd8e61ae6fb86735f27c057b8e70103dbc96da9373f177ba0c48531b2768","observation_id":"3ef3b1ad-0c3b-4d46-b911-f75b7ae1203f","resolution":{"observed_at":"2026-08-01T15:21:42.063872Z","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":"2026-08-01T15:21:42.066611Z","title":"Burić, N","venue":null,"work_id":null,"year":2013},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.066611Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:a2b7fb3a80438c2314a126935b8a4bf84d330cdc007e8e891ce02f05dd8e9737","observation_id":"55ce50b9-c660-4d1c-be62-f9033a4d80b1","resolution":{"observed_at":"2026-08-01T15:21:42.066611Z","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":"2026-08-01T15:21:42.069148Z","title":"Burić, N","venue":null,"work_id":null,"year":2014},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.069148Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:80c87d20582c8fbc864c9e818c858a62f6043da434554244fa08799afd5dd52a","observation_id":"54a46aaf-2611-4e52-8bc2-25744654f60c","resolution":{"observed_at":"2026-08-01T15:21:42.069148Z","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":"2026-08-01T15:21:42.071550Z","title":"Burić, N","venue":null,"work_id":null,"year":2016},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.071550Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:61a7d00de83284eefebf58006a5de375929d486ba7b4c79df4cabcc4907ce620","observation_id":"33b91973-f9dc-4cc5-adc5-0b9ec62a46a3","resolution":{"observed_at":"2026-08-01T15:21:42.071550Z","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":"2026-08-01T15:21:42.074005Z","title":"Diaconis, S","venue":null,"work_id":null,"year":1991},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.074005Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:daba9722795f5f09b7ed72c65da11c341f71d7dd83b63dcdbd541c6b3b01c49d","observation_id":"c4e4597b-4d81-46ce-b88b-800308b5bdcf","resolution":{"observed_at":"2026-08-01T15:21:42.074005Z","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":"2026-08-01T15:21:42.076626Z","title":"Elezović,Asymptotic expansions of central binomial coefficients and Catalan numbers, J","venue":null,"work_id":null,"year":2014},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.076626Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:fd4cfcd40baa93ec43a4bae1cc0a1bc12e4be6252cc2da9eb04d04a9d39c3310","observation_id":"61c6f729-7b25-4811-9b85-88b29f05f565","resolution":{"observed_at":"2026-08-01T15:21:42.076626Z","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":"2026-08-01T15:21:42.079636Z","title":"Esseen,Fourier analysis of distribution functions","venue":null,"work_id":null,"year":1945},"citing_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},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.079636Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:6d622cd0cb86b54feb617eae8410f67244cf17d0041fce839c5bc950d07c8762","observation_id":"228f0277-6cc1-4512-a3a9-a5c6a3dbb904","resolution":{"observed_at":"2026-08-01T15:21:42.079636Z","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":"2026-08-01T15:21:42.082412Z","title":null,"venue":null,"work_id":null,"year":1945},"citing_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},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.082412Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:a1e44d0297e8b0d424dd9c997c84fee312d29696628f13befd27ac793b29c5b6","observation_id":"2ee1f35f-eb57-4494-a7c6-9229d45795d5","resolution":{"observed_at":"2026-08-01T15:21:42.082412Z","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":"2026-08-01T15:21:42.084965Z","title":"Frisch,Solution d’un problème du calcul des probabilités, Skand","venue":null,"work_id":null,"year":1924},"citing_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},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.084965Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:3a78966747dd6732eefd902fdf85e43af910ea7a7178c8a6bbebcda5f9dc73d5","observation_id":"9f744093-a8ea-442d-9264-66f9b53c41f0","resolution":{"observed_at":"2026-08-01T15:21:42.084965Z","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":"2026-08-01T15:21:42.087467Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_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},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.087467Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:e1ec7db66232bc952845dca4b038fef2e37b92dc5f4d34f5f5c1a2bc2f6508bf","observation_id":"9ded2acc-98c9-418c-b329-93770bff4885","resolution":{"observed_at":"2026-08-01T15:21:42.087467Z","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":"2026-08-01T15:21:42.089853Z","title":null,"venue":null,"work_id":null,"year":1957},"citing_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},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.089853Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:be7b7e0777540778f10b6a6662f66e1b44ac7829e7db71c98c90cf77b361a4b7","observation_id":"2e7cbdc0-fd57-4571-bc44-589da1a5b098","resolution":{"observed_at":"2026-08-01T15:21:42.089853Z","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":"2026-08-01T15:21:42.092258Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_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},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.092258Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:418c9b7d3791d5a7be256d7b944c351aeee7a433318ce037fbc8eb9f36974c24","observation_id":"a1382efc-90e8-471f-b6c1-30d48f0dd6df","resolution":{"observed_at":"2026-08-01T15:21:42.092258Z","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":"2026-08-01T15:21:42.094724Z","title":"Jordan,Statistique Mathématique, Gauthier-Villars, Paris, 1927","venue":null,"work_id":null,"year":1927},"citing_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},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.094724Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:61b958bfea8bfa530cab0f68abad6a77309730750dff1305f8a0a1c15b6d0ecb","observation_id":"073cd0ae-9d25-4462-b23c-a09062b3ed0c","resolution":{"observed_at":"2026-08-01T15:21:42.094724Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.01734","last_updated":"2017-07-06T11:47:50Z","snapshot_observed_at":"2026-08-12T13:03:00.344599Z","submitted_at":"2017-07-06T11:47:50Z","title":"An inverse factorial series for a general gamma ratio and related properties of the N{\\o}rlund-Bernoulli polynomials","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.01734","snapshot_observed_at":"2026-08-01T15:21:42.097304Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.097304Z"},"links":{"cited_paper":"/paper/1707.01734","citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:52e0a209054a13f1621463723cd50b7db16660308d6e51a34976a39ab971f028","observation_id":"fa79fe69-7d7a-446b-8548-720efe70e543","resolution":{"observed_at":"2026-08-01T15:21:42.097304Z","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":"2026-08-01T15:21:42.100375Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_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},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.100375Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:d31f6d776c0d79e6bd48e010d62758a5075b9356786df97507da465952edc279","observation_id":"3e147f07-3081-448f-b4df-bd24dc7d1c6a","resolution":{"observed_at":"2026-08-01T15:21:42.100375Z","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":"2026-08-01T15:21:42.103076Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_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},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.103076Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:625f34279a9f6b8cf8bedff723138ac2e616a5eef1c51a97b90d6cc89a3739df","observation_id":"d393da69-3bf6-469d-abbd-3d04b3162867","resolution":{"observed_at":"2026-08-01T15:21:42.103076Z","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":"2026-08-01T15:21:42.105617Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_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},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.105617Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:bed3d9ea2449cc88ca68212bd7b343ead6caabe7ac2752a9a39f987078747bda","observation_id":"d61cceb0-6d3a-40e7-affc-614bb91ce1ae","resolution":{"observed_at":"2026-08-01T15:21:42.105617Z","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":"2026-08-01T15:21:42.108383Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_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},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.108383Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:a1b0016ff33fbc6752dd5ffa2c432f408cf94de7eca29cb2aa4eef3eff55c43b","observation_id":"78850dd2-9a54-4e84-8265-a61803b67d30","resolution":{"observed_at":"2026-08-01T15:21:42.108383Z","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":"2026-08-01T15:21:42.110886Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_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},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.110886Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:4e7188d310dc73774beec58e7f2e49ed65c4ccf8f9fb48c0dd9ed07437ee364d","observation_id":"2128edad-a9a2-435c-a529-7730257e4573","resolution":{"observed_at":"2026-08-01T15:21:42.110886Z","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":"2026-08-01T15:21:42.113176Z","title":null,"venue":null,"work_id":null,"year":1953},"citing_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},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.113176Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:fba6aa69d68c4cb7d7cd39302ec44bf39fd5d5cdc8e594b630a5a2f4cd4a3c2e","observation_id":"04960ecc-5809-4f6b-9c8a-cebedd65f1fe","resolution":{"observed_at":"2026-08-01T15:21:42.113176Z","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":"2026-08-01T15:21:42.115768Z","title":null,"venue":null,"work_id":null,"year":1958},"citing_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},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.115768Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:ee5439670a0297de1df108282b5b7c65ac1654c9d62c981dbd52d2d627428bec","observation_id":"feeb804b-1c0d-4ac6-98c4-a5646fd4d957","resolution":{"observed_at":"2026-08-01T15:21:42.115768Z","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":"2026-08-01T15:21:42.118177Z","title":"Robbins,A remark on Stirling’s formula, Amer","venue":null,"work_id":null,"year":1955},"citing_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},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.118177Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:5fa2540ddfaf3b8e340d4f6ef0d95caaa181c7f71861eeca1927f13bb321107a","observation_id":"d2d32bee-5dce-4070-bf07-9dfa81887751","resolution":{"observed_at":"2026-08-01T15:21:42.118177Z","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":"2026-08-01T15:21:42.120875Z","title":"Roman,The Umbral Calculus, Academic Press, Orlando, 1984","venue":null,"work_id":null,"year":1984},"citing_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},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.120875Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:219d9836bdfd42d2d5c09534a1890eadcc56acc6f6150f2ffbbba986617db029","observation_id":"89151c3c-dca2-455d-8358-689869da91fe","resolution":{"observed_at":"2026-08-01T15:21:42.120875Z","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":"2026-08-01T15:21:42.123416Z","title":"Siotani, Y","venue":null,"work_id":null,"year":1984},"citing_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},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.123416Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:119c7c2112d9760e48cc3a9ea3c3f2b7b77fcda9f5843fa732e43567aa3dd08b","observation_id":"9af662c6-c985-4cd3-9c4a-8361b3588fba","resolution":{"observed_at":"2026-08-01T15:21:42.123416Z","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":"2026-08-01T15:21:42.125899Z","title":null,"venue":null,"work_id":null,"year":1927},"citing_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},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T15:21:42.125899Z"},"links":{"citing_paper":"/paper/2607.18494"},"observation_digest":"sha256:5ee92a1aec88b685a144793b5ca495291c96733bf36855845e14c607c6ccedda","observation_id":"ed2305aa-5955-4494-9a53-b40a8066250f","resolution":{"observed_at":"2026-08-01T15:21:42.125899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.18494","last_updated":"2026-07-20T20:33:35Z","latest_version":1,"primary_category":"math.CA","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"},"reference_resolution":{"displayed":31,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":31,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":31},"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 31 of 31 outbound references and 4 inbound Pith citation observations for arXiv:2607.18494."}