{"as_of":"2026-08-12T18:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:64f2a5c9a42405b5d26d2836d8cf6a4b951c4b775e77687836d2403f0ece0bfe","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T13:17:55.400245Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":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/2507.20965/citation-record","integrity":"/paper/2507.20965/integrity","json":"/paper/2507.20965/citation-record.json","paper":"/paper/2507.20965"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2506.12868","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.567094Z","title":"Aliniaeifard and S.X","venue":null,"work_id":"5369e365-82e9-4bf7-bd48-8972ff73dee2","year":null},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.303522Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:13045b5b10f8bcd759b51882bb833b2ceaedd07ab521787f6ce35a6076d83f83","observation_id":"ff56c2f0-7b1e-463b-a53f-77a2aa7772ac","resolution":{"observed_at":"2026-08-06T13:17:55.574032Z","resolver_source":"raw_fallback","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.867384Z","title":"André, Développement desec x and tan x, C","venue":null,"work_id":"378ffb84-9ceb-498c-8d15-3b3b36a2ed09","year":null},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.308632Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:b5f947e47b03e6a4c7ccf98657fcd3999b9a26cddacb90c9ba3f5f9ea0c9571c","observation_id":"11aae5eb-4abf-4d60-bdf8-d24b1deac0f4","resolution":{"observed_at":"2026-08-06T13:17:55.871535Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.853460Z","title":"Andrews and I","venue":null,"work_id":"206ae2ef-9250-469b-b771-9926e7ab0660","year":1978},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.313203Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:bc3f0a0472a740f120f875577ce3de1c2ae393168643fa769509e74e797b8d70","observation_id":"38faeb0c-4489-42a8-9792-9c4911e350d0","resolution":{"observed_at":"2026-08-06T13:17:55.858193Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.839017Z","title":"Barsky, Congruences pour les nombres de Genocchi de deuxième espèce, Group","venue":null,"work_id":"9bb5308b-2cea-4a4d-b9aa-c6a4f460cfd0","year":1980},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.317516Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:e472bdaf1aeb5105bb43420242e2b9a2eb1e7baf382d0349027ecfad7c642368","observation_id":"d2c08d61-54f8-4e55-ad82-12fb199aa336","resolution":{"observed_at":"2026-08-06T13:17:55.843312Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.824876Z","title":"Carlitz, The Staudt–Clausen theorem, Math","venue":null,"work_id":"b2ae2897-26ea-45d3-a5cb-4f24766aa39b","year":1960},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.322314Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:c50dc32f3c1aa90adf8756768b11876c8a2ffb728eeb75e4aaceffc0652f7c42","observation_id":"bdcaaf5c-ccc2-4764-97e5-ac054e2697dc","resolution":{"observed_at":"2026-08-06T13:17:55.829504Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.810428Z","title":"Carlitz, A conjecture concerning Genocchi numbers, Norske Vid","venue":null,"work_id":"f616f2b0-61f2-4aaf-ba8d-8a1c877dce35","year":1971},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.326923Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:2be8c231497fe7112543b22244f10ec427c738857fcaaa2c9a92d09dcd5f36bf","observation_id":"595918dc-e3d9-4ae0-8c7b-704203785585","resolution":{"observed_at":"2026-08-06T13:17:55.814961Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.795539Z","title":"Choi and H","venue":null,"work_id":"c2330371-fc75-4f46-843f-4eef20513b93","year":2015},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.331156Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:18ba3b68b9117e29087ef6df57b109fca23f88ab35cd0c4b6edf1451bb642188","observation_id":"3185e28c-c423-4ac6-8475-4f0032edc011","resolution":{"observed_at":"2026-08-06T13:17:55.799886Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.780843Z","title":"Foata, Further divisibility properties of theq-tangent numbers, Proc","venue":null,"work_id":"5be34bf0-bd6d-45ab-bd80-a34cf94056e9","year":1981},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.335059Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:83702369a003674897ecead80a835fc5e8178264d85e4951a03860902f3db215","observation_id":"b35f4778-0478-4c1f-a734-630ecfd4b52e","resolution":{"observed_at":"2026-08-06T13:17:55.785386Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.765021Z","title":"Foata and G.-N","venue":null,"work_id":"c759156c-7b1f-4815-be41-317bd406970b","year":2010},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.340832Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:bb9d47740e19ced457b9d12373e938c8703372145c78095ab49057ef6fb7ac29","observation_id":"4f27a29d-444d-4855-bd09-d3e1a1a746cd","resolution":{"observed_at":"2026-08-06T13:17:55.769956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.750392Z","title":"Foata and G.-N","venue":null,"work_id":"c3c947da-bd5c-445f-8c13-c65232e18224","year":2008},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.345100Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:4aebeda91260e871da89b3aafe7cb928546dbb8dfa61bdf0e47d733c276ebd95","observation_id":"156b604f-16b6-4e1d-8c1c-559da8cba9ee","resolution":{"observed_at":"2026-08-06T13:17:55.754569Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.735715Z","title":null,"venue":null,"work_id":"67a590da-0d2a-4982-b344-2e2dc3f152b4","year":2025},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.349226Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:2b984f3f8a0ad0f4ebd6c1f207673252bd5c091f10db084ce347772e4dd7b4f9","observation_id":"24d79ad4-0127-4a0f-828e-beb8a1f8589f","resolution":{"observed_at":"2026-08-06T13:17:55.739944Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.721712Z","title":"Han and J.-Y","venue":null,"work_id":"a5b0b98b-7913-4afd-a579-4b5824b93e26","year":2018},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.353391Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:5a6cd1742cf6f8de504519ebe945cf749e8dabe8cae76b3119391a6f66bf8e0b","observation_id":"e6ed0439-ef88-4f34-b165-ae28330532e2","resolution":{"observed_at":"2026-08-06T13:17:55.725736Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.707625Z","title":"Lin, S.-M","venue":null,"work_id":"d1311001-63f7-4a2c-8b8e-71a27ee8db8c","year":2022},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.358378Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:ed1aa976398e6dc26453d3f552a7e65fa16e191a201b830b658a7327cca19fc9","observation_id":"6c05074b-9b3a-4042-b07d-14cfa8fba5d6","resolution":{"observed_at":"2026-08-06T13:17:55.711939Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.694079Z","title":null,"venue":null,"work_id":"48d3216f-f8c1-4eda-b5a8-4c3297bbe7dc","year":2025},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.362510Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:2aee8d8a984f626bba14680ff6d09fa9eb249141fe163bc6463a153bb415cd52","observation_id":"3c293467-5073-443d-8978-7ffd9b31a76b","resolution":{"observed_at":"2026-08-06T13:17:55.698093Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.679611Z","title":"Lin and J","venue":null,"work_id":"c19ae386-1027-409b-8a0c-4cd63452c190","year":2015},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.367384Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:80dca217456e23de2b106428d79960e8de25babe75f8582344bedfe9103b58f3","observation_id":"bf3c10b7-e466-4459-b62a-4dff7cddfa25","resolution":{"observed_at":"2026-08-06T13:17:55.684018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.664684Z","title":"Riordan and P","venue":null,"work_id":"fa0bb2be-f476-4bd0-8e0a-8e14045a7519","year":1973},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.371619Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:f7d360fd68c7a6f082bd4a099a02dbcc2c22e4347da19c3c36d78d6981cfbe30","observation_id":"f0035688-65ef-48c9-b361-88562eb54934","resolution":{"observed_at":"2026-08-06T13:17:55.669325Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.648671Z","title":"Sagan, Generalized Euler numbers and ordered set partitions, Discrete Math.,349 (2026), Article 114715","venue":null,"work_id":"c1a83551-56ed-4ac6-90fe-520b42a0babd","year":2026},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.375911Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:b8de4cbf469b2c88ead524c14dc8de5b36e451ab969cffcb275dac9c4c6d4bf0","observation_id":"09d5fd17-8c52-4da6-8334-ce68b70a918c","resolution":{"observed_at":"2026-08-06T13:17:55.653932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2506.23355","last_updated":"2026-06-04T18:17:09Z","snapshot_observed_at":"2026-08-11T06:21:20.273354Z","submitted_at":"2025-06-29T18:20:31Z","title":"Ordered set partition posets","version":3},"cited_work":{"arxiv_id":"2506.23355","doi":null,"metadata_source":"pith","pith_arxiv_id":"2506.23355","snapshot_observed_at":"2026-08-06T13:17:55.442881Z","title":"Ordered set partition posets","venue":"math.CO","work_id":"f431cbeb-a26c-4980-ab20-f47bc510e5a4","year":2025},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.380624Z"},"links":{"cited_paper":"/paper/2506.23355","citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:52b4217afffb9260852ecf6f77c6b2a09b22597b4df34789308c01f7f8c0a998","observation_id":"71efd28b-18b2-4a77-b4f5-06b57cbc2423","resolution":{"observed_at":"2026-08-06T13:17:55.448888Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.631937Z","title":"Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J","venue":null,"work_id":"84f51b9d-231d-4e3c-a9fe-ade463f2436c","year":1976},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.385779Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:9f328cd400afa4faad02397c408bfa29444b93bbe4ca23c97ff117572b3b9ccf","observation_id":"f306baab-62cb-40c5-a0e9-67da01492bda","resolution":{"observed_at":"2026-08-06T13:17:55.636903Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.616938Z","title":"Stanley,Enumerative combinatorics, Vol","venue":null,"work_id":"aa8a4c4a-be99-4d5d-94da-81353de24e78","year":1997},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.390823Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:6bad65a53d47ce30e15c07a9bc390e777a20d548caaed3dfcce95673f06b4fc9","observation_id":"326c6696-137f-419c-936c-87cebff6afb7","resolution":{"observed_at":"2026-08-06T13:17:55.621472Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.600939Z","title":"Stanley,Enumerative Combinatorics, Vol","venue":null,"work_id":"b396c425-9185-4f83-b236-e1157b2b104d","year":1999},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.395369Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:ca605c453ea2e8d5c0a5a1d3e1ee3e931b4512a9d8f7a12f03eea817728b538d","observation_id":"4172efb3-9d7b-48b6-bf8a-a81da651d113","resolution":{"observed_at":"2026-08-06T13:17:55.606209Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:55.584670Z","title":"Stanley, A Survey of Alternating Permutations, in Combinatorics and Graphs, R.A","venue":null,"work_id":"54af096d-b3ac-4abd-9dc1-38c54be4ed6c","year":2010},"citing_paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:55.400245Z"},"links":{"citing_paper":"/paper/2507.20965"},"observation_digest":"sha256:303fb1dd5c2177b4ddb903aad53e3e3ac04f3b0d881d8d018a8f7f9814ca392e","observation_id":"03add9ae-949f-48b5-8846-01173e1dab6d","resolution":{"observed_at":"2026-08-06T13:17:55.590014Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.20965","last_updated":"2025-08-12T08:58:12Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-07T10:41:07.109228Z","submitted_at":"2025-07-28T16:20:14Z","title":"An identity relating Catalan numbers to tangent numbers with arithmetic applications"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":18},"total_outbound_references":22},"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 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2507.20965."}