{"as_of":"2026-08-07T23:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:22c2c10f2d2f3fdeb5281284043d26f3cd43f85bf2f8e39d8f9a99ae8e96d065","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:38:24.977914Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.05145/citation-record","integrity":"/paper/2506.05145/integrity","json":"/paper/2506.05145/citation-record.json","paper":"/paper/2506.05145"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:31.146814Z","title":"Barred Preferential Arrangements","venue":null,"work_id":"6a05477a-7475-4ca7-b923-86a8e5efeb98","year":2013},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:22.943563Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:5214c6bbb45a0b160b31a9d0363c2f75442fa47bec9434da352578b2c940076d","observation_id":"5e0de5f0-77a2-4ca4-b5f4-942733e79e98","resolution":{"observed_at":"2026-08-07T10:38:31.212075Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:31.000340Z","title":null,"venue":null,"work_id":"db2f042a-8c87-4dbd-b3cd-8895a32effd2","year":2007},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.044122Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:a05ef6d8b4b1dba6959836e7adef1fd7eb4c90a94b1e60d048813b6451bf7906","observation_id":"b8eb3eb3-bcc3-4a95-8143-6365d8e9e3db","resolution":{"observed_at":"2026-08-07T10:38:31.053962Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.896677Z","title":"”Generating functions for generating trees.” Discrete mathematics 246, no","venue":null,"work_id":"e38ecaad-47cb-49b3-b778-948dfe022f6f","year":2002},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.091855Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:042dd454ca997158b00290b179c834c979de0935d81c904d1038f284c154c471","observation_id":"27e73b30-da2c-489f-905a-40b762f9d41b","resolution":{"observed_at":"2026-08-07T10:38:30.928731Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.783464Z","title":"” ¨Uber sturm-liouvillesche polynomsysteme.” Mathematische Zeitschrift 29, no","venue":null,"work_id":"6efea3d4-e68c-47cb-b2a0-cdea48e2e0a3","year":1929},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.163823Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:d7ed1684777d1652b1709c4af7a89dae5790172d10c24cf737b3a6acfb821748","observation_id":"2b52edd0-6ef3-44ea-909e-b47a369afbd1","resolution":{"observed_at":"2026-08-07T10:38:30.846255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.653870Z","title":"Handbook of enumerative combinatorics","venue":null,"work_id":"4ea7b054-3b85-4aa0-9b95-26a56e65521a","year":2015},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.243001Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:b3dff9e7b5750fa0212c900b84016de401ee5d73c0717cbe816a300c6d90eef7","observation_id":"ca5f680f-3e7d-4841-9433-7f7a55a29bdd","resolution":{"observed_at":"2026-08-07T10:38:30.708840Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.535218Z","title":"”The r-Stirling numbers.” Discrete Mathematics 49, no","venue":null,"work_id":"299bee7a-c0c8-4e2a-b5be-adef2662ca53","year":1984},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.304425Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:61c3c78fe7cbebae7b7cf34c8dd436a188881d082b2d0e7f06ef3b35490b4ef4","observation_id":"ac6d6f4d-0581-4436-b725-d89c1c7bc7a5","resolution":{"observed_at":"2026-08-07T10:38:30.594463Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.396153Z","title":"”r-Whitney numbers of Dowling lattices.” Discrete Mathematics 312, no","venue":null,"work_id":"2d7489c7-d5c0-41f7-96da-36ce3d0fc00f","year":2012},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.391512Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:e7a95c7c7deb487e37ae1f95e3a5b08c5f9b4ef4f2968f1dbc68930d9ece1d5b","observation_id":"80cbdfad-d110-4f35-bf92-1cffb09df953","resolution":{"observed_at":"2026-08-07T10:38:30.447723Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.299603Z","title":null,"venue":null,"work_id":"03728405-b809-4119-9651-d59b4ffcb638","year":2013},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.450320Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:76c24596e3dc9ed5473d92ab17c691939f5af1087cf86b2bd0ef1916a9f855d3","observation_id":"e25c3bc0-dcd9-444d-9bff-dedb638a5829","resolution":{"observed_at":"2026-08-07T10:38:30.348363Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.127779Z","title":"”On the unimodality and combinatorics of Bessel num- bers.” Discrete Mathematics 264, no","venue":null,"work_id":"6dcffa60-941a-4f69-914a-f5e2629ddf5f","year":2003},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.537015Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:7fd26fb478ba1f62cc6648109f7bdfa9ed6772f88ce336161577b6d556959ce8","observation_id":"683c9c16-fe81-4080-87f9-3abfa5923f97","resolution":{"observed_at":"2026-08-07T10:38:30.199586Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:30.003364Z","title":"Corcino, Istv´ an Mez˝ o, and Jos´ e L","venue":null,"work_id":"f7b33786-a7e7-46b5-8bda-89467db8ac8b","year":2018},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.617487Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:35b32e32218b808f171c60c4722d6ace51bf48cde720483860a3c0ccaddde769","observation_id":"b23eab41-5be0-415c-9666-71f68a7ce401","resolution":{"observed_at":"2026-08-07T10:38:30.057433Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:29.782721Z","title":"The Art of Computer Programming: Sorting and Searching, volume 3","venue":null,"work_id":"94041e1b-595c-43e0-84b4-e3a0a561feb7","year":1998},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.684264Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:606206f4614a4b10e6bf894fe2be948943fca182e70cb1197d30201961280c02","observation_id":"b4341a77-5566-4787-9c81-b7b707f19b45","resolution":{"observed_at":"2026-08-07T10:38:29.914011Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:29.441189Z","title":"”BESSEL POLYNOMIALS.” (1978)","venue":null,"work_id":"32c5f4ee-b8ed-4a96-9701-ca7c2e7454db","year":1978},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.784178Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:6ef7e50d8990fd7d70c4ad38105170daf1a604237ce95129970cd0c96a153a8d","observation_id":"236775b7-c2fc-43e6-a634-03192490732b","resolution":{"observed_at":"2026-08-07T10:38:29.648933Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:29.057585Z","title":"”A comprehensive study of r-Dowling polynomials.” Aequationes mathematicae 92, no","venue":null,"work_id":"e9f43985-799c-4e53-a770-222ce0ce4119","year":2018},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.836674Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:0863e7cd0f004650b7cc014e41c4a2ae9d8f35c6d6ea0faefb5fbdde457b856c","observation_id":"69ea4cd7-b379-4b9a-922e-488b6b39bc9d","resolution":{"observed_at":"2026-08-07T10:38:29.254142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:28.812249Z","title":"”New combinatorial interpretations of r-Whitney and r- Whitney–Lah numbers.” Discrete Applied Mathematics 255 (2019): 222-233","venue":null,"work_id":"ef778678-91fd-406e-8e17-5df5c72292d6","year":2019},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:23.885184Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:9347420b216c324804e27423321a59b5f1a45e53f802c18b520ef1d828ab8252","observation_id":"57b97c63-b487-4399-a42c-09dc2dcca612","resolution":{"observed_at":"2026-08-07T10:38:28.919763Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:28.520168Z","title":null,"venue":null,"work_id":"d900de49-de8c-4b46-837e-bbcf79fcf586","year":2018},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.020509Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:ea60cbde1fa648342f794e68769c2cd01107ad7dbb1cb23143c65991405189b8","observation_id":"37102dd8-d153-43e2-afe0-27fc1c9bb346","resolution":{"observed_at":"2026-08-07T10:38:28.695226Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:28.247819Z","title":"”Higher order generalized geometric polynomials.” Turkish Journal of Mathematics 42, no","venue":null,"work_id":"f65119e5-3c17-454d-88d5-abce62296387","year":2018},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.074391Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:12dcb27084191ec29b3a4bc6990c82596b8d4584ae720de81d5fc23dc92909c8","observation_id":"9bd1601d-7ade-4ebb-951d-5fd38cbff3bb","resolution":{"observed_at":"2026-08-07T10:38:28.376969Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:27.936750Z","title":null,"venue":null,"work_id":"a17387c7-0db7-4cba-ba4f-4ee35905ceaa","year":2016},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.189714Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:7e0b0089c9ac8224ba306b6e4c6a6ddfcf0fcb5d0f13c148ed7ce8aeee2a11d6","observation_id":"d59157f7-5190-48ea-a2d3-4600fcce842d","resolution":{"observed_at":"2026-08-07T10:38:28.106445Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:27.589772Z","title":"”A new class of orthogonal polynomials: The Bessel polynomials.” Transactions of the American Mathematical Society 65, no","venue":null,"work_id":"b68658d3-3122-4125-ae15-869fe3cabe1f","year":1949},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.244856Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:138e17dceaac7f069ff9d026835880b2ef1aa7ecff19e3f6c172ea3b9179b4f4","observation_id":"3a954732-2964-4163-8874-9027c798b066","resolution":{"observed_at":"2026-08-07T10:38:27.747290Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:27.290940Z","title":"”The r-Bell numbers.” J","venue":null,"work_id":"5ce5618c-8968-4993-a8e1-304ff09046e7","year":2011},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.313484Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:bbe9c56d91254c304756511bc9f73581498096ad282869381ec8c8fd4fdb2269","observation_id":"52e3d7ea-c6a7-4706-9b2f-f4511f86b048","resolution":{"observed_at":"2026-08-07T10:38:27.452018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:26.909217Z","title":"”Periodicity of the Last Digits of Some Combinatorial Sequences.” Journal of Integer Sequences 17, no","venue":null,"work_id":"5c2f12e5-5c9b-445c-9b81-af5504abee13","year":2014},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.396097Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:cf746fb95b4acc300cec44e54d45ce0facbecc688e0e008243a0354a6d3ba466","observation_id":"e7bc275c-7a68-4bbe-8ab7-c27dfa8a4c17","resolution":{"observed_at":"2026-08-07T10:38:27.127959Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:26.549875Z","title":"Corcino, and Cristina B","venue":null,"work_id":"8ddcc280-d993-457b-91aa-d7b656b06ee4","year":2020},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.455763Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:e0e31647f11afcaa4bea695c56c0a372baf66d1a48194d636c0d99cc47985b54","observation_id":"2f0931d3-e7e3-4ce1-bd53-501be95e82d4","resolution":{"observed_at":"2026-08-07T10:38:26.746012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:26.304408Z","title":"”The hypercube of resistors, asymptotic expansions, and preferential arrange- ments.” Mathematics Magazine 83, no","venue":null,"work_id":"d0d71677-f5c0-432f-8a5d-293b605d8351","year":2010},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.574756Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:46cc4bf8bf334210949fcba167f87f58a40cfaf9d613b60ed4c8aee168ee6548","observation_id":"da53ad46-aa2c-45d5-9e6d-ec5fe754c95b","resolution":{"observed_at":"2026-08-07T10:38:26.436595Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:25.995842Z","title":"Teichmann","venue":null,"work_id":"30f9882e-643b-494f-8c0f-26c835428ef3","year":1959},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.656406Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:99d9fd14b34cfc667d6e7ffc127d45a7150ca0573d26a5267b682ff4266345f2","observation_id":"e27422d3-76f3-4f4d-8b5a-4e9e38bc4b56","resolution":{"observed_at":"2026-08-07T10:38:26.133247Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:25.674287Z","title":null,"venue":null,"work_id":"699efda4-39c7-489c-aac0-09e775f917f5","year":2005},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.784425Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:c3ee4ba6ec7bc5f560c2f8b11993df935729d799c10cf7cde00b7ebfb7192611","observation_id":"ba94827b-fa4d-4f5a-8b23-5858a4de67e8","resolution":{"observed_at":"2026-08-07T10:38:25.848227Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:25.414745Z","title":"”Enumerative combinatorics volume 1 second edition.” Cambridge studies in advanced mathematics (2011)","venue":null,"work_id":"90b22225-1f10-432b-a3b1-a0e029b5eee0","year":2011},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.898266Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:aa6f86e14bb5e9126df1c8143b944da00b243e0c2d94843e0aff2325763cb552","observation_id":"781aa7e6-0ef5-44d8-a917-22f9ce15bd4c","resolution":{"observed_at":"2026-08-07T10:38:25.549231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:38:25.207349Z","title":"”The Bessel numbers and Bessel matrices.” In J","venue":null,"work_id":"d4deba36-c51e-47ad-bfac-7b52ccea4b3f","year":2011},"citing_paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T10:38:24.977914Z"},"links":{"citing_paper":"/paper/2506.05145"},"observation_digest":"sha256:4a7df5e1bb469da6cd28b83cc2c7721d0dbf84835c3f80e5bfb892157c84fd86","observation_id":"8354d640-05eb-4372-baa8-994a510deb0c","resolution":{"observed_at":"2026-08-07T10:38:25.321260Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.05145","last_updated":"2025-06-05T15:26:02Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T10:21:02.120317Z","submitted_at":"2025-06-05T15:26:02Z","title":"The Telephone Exchange Problem Revisited: A Combinatorial Approach"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":21},"total_outbound_references":26},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2506.05145."}