{"as_of":"2026-08-13T11:17:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5e088d61c98e86b8c99960aabb495cb16db418c640552641f20dc71f023737bf","coverage":[{"denominator":53,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":53,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T02:34:51.730831Z","state":"measured"},{"denominator":53,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":53,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2607.16331/citation-record","integrity":"/paper/2607.16331/integrity","json":"/paper/2607.16331/citation-record.json","paper":"/paper/2607.16331"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T02:34:45.470509Z","title":"Gaussian hypergeometric series and combinatorial congruences","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:45.470509Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:06fd1b7df4bc3f66c1b45e0552b7f1743fabc3985f6f27a721f994a613b2fd23","observation_id":"f7b65a4a-c198-47f2-a365-67243aa48712","resolution":{"observed_at":"2026-08-02T02:34:45.470509Z","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":"2026-08-02T02:34:45.561682Z","title":"A Gaussian hypergeometric series evaluation and Ap´ ery number congruences","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:45.561682Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:34f505fdb7524fa0aa4abcf592a5f6b53b04743801b7ac7ce96e5919ff0e2b48","observation_id":"ca4a492c-d09c-4b07-a1af-06bcd362df7f","resolution":{"observed_at":"2026-08-02T02:34:45.561682Z","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":"2026-08-02T02:34:45.703864Z","title":"The explicit hypergeometric-modularity method I.Adv","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:45.703864Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:7132171550e19566aab5cf3b5d3f721c3806645a4579191376b6f3f812c24cd6","observation_id":"b247af09-8621-470d-8784-3e7f1c565f11","resolution":{"observed_at":"2026-08-02T02:34:45.703864Z","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":"2026-08-02T02:34:45.850216Z","title":"The explicit hypergeometric-modularity method II.Res","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:45.850216Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:ae17f415c423690a126bdbb7b35cda69dc8dc61002fca9859172adb08f01b053","observation_id":"b5aae920-347d-482c-92ae-c1bcc0c40092","resolution":{"observed_at":"2026-08-02T02:34:45.850216Z","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":"2026-08-02T02:34:46.006772Z","title":"PhD thesis, ETH Z¨ urich, 2000","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.006772Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:c529d50a821a5ff113224067d80e556759f29c457d3a526a49e88478389b78e5","observation_id":"b27a47e1-c884-466f-a454-ef150c04fe3f","resolution":{"observed_at":"2026-08-02T02:34:46.006772Z","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":"2026-08-02T02:34:46.156303Z","title":"Exceptional sets of hypergeometric series.J","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.156303Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:be1880fa194bbdc32d0033b55424e5b51885312738655daa1be3f1957838acdf","observation_id":"9503ed6b-c0b6-49ac-b650-b9427a513e06","resolution":{"observed_at":"2026-08-02T02:34:46.156303Z","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":"2026-08-02T02:34:46.339335Z","title":"Special L-values of certain CM weight three Hecke eigenforms","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.339335Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:f2c73edb57597475e6110dde5e1efe808edf21312e95881cfc0a1261d5a09de1","observation_id":"b26e285d-0b7d-4afd-a014-560b15f3d264","resolution":{"observed_at":"2026-08-02T02:34:46.339335Z","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":"2026-08-02T02:34:46.485823Z","title":"Quaternionic modular forms and exceptional sets of hypergeometric functions.Int","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.485823Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:b9e744805ffd814e842beccdb6661498c2c3ec21b94a3dd79f2b997adbf73cc0","observation_id":"2b45be7e-6d8e-4c1d-a10b-9b3d02394e38","resolution":{"observed_at":"2026-08-02T02:34:46.485823Z","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":"2026-08-02T02:34:46.635561Z","title":"Picard-Fuchs equations for Shimura curves overQ.Bull","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.635561Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:063c031b7686accbe359bee6e6dab3c377e4eb98bc3813d5f10359be8b76750f","observation_id":"e4b9423e-94c0-4489-ae42-31b4c52be66b","resolution":{"observed_at":"2026-08-02T02:34:46.635561Z","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":"2026-08-02T02:34:46.831943Z","title":"Generalized Ramanujan-Sato series arising from modular forms","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.831943Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:fec92846131980f928451716145ea8bdd1f8e9953b24f2e9fd04041da9d5394b","observation_id":"b3ffe20e-25ed-4621-843e-d15d221f0eca","resolution":{"observed_at":"2026-08-02T02:34:46.831943Z","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":"2026-08-02T02:34:46.991562Z","title":"Beukers and G","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:46.991562Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:626a86dab4807b217320f8e1e052d587a20cb0b3a1cb7b8afe0c9638244ace1c","observation_id":"96a3b50a-4642-459f-807d-d68ce03ddccc","resolution":{"observed_at":"2026-08-02T02:34:46.991562Z","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":"2026-08-02T02:34:47.102753Z","title":"Arithmetic triangle groups, hauptmoduln, complex multiplication, and hypergeometric functions, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.102753Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:96dd5e74b75ccbe41f48453f21b53cba50a135b942c74f6a6e3fbb768f322af1","observation_id":"2a4ba15f-152d-4fa5-8d60-62b53af5108a","resolution":{"observed_at":"2026-08-02T02:34:47.102753Z","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":"2026-08-02T02:34:47.234321Z","title":"American Mathematical Society, Providence, RI, 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.234321Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:53f6a925975530e31f10869172417701d572579a0138ae3f81cb4fd016ad98c5","observation_id":"e4d326ac-3edd-40c5-a21d-1b4b234d12c8","resolution":{"observed_at":"2026-08-02T02:34:47.234321Z","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":"2026-08-02T02:34:47.389776Z","title":"Modular embeddings for some non-arithmetic fuchsian groups.Acta Arithmetica, 56(2):93–110, 1990","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.389776Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:051ba7234b5fd937922413d8a6185c41d4c49720e92b0838de2394802baf41b2","observation_id":"67c14ea2-c945-417a-a98f-de9641bf681b","resolution":{"observed_at":"2026-08-02T02:34:47.389776Z","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":"2026-08-02T02:34:47.521046Z","title":"Cohen and Gisbert W¨ ustholz","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.521046Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:ef6acf58cbf45470122805cd2e516f7a4a6263b1727083558c8018f32e12b27f","observation_id":"47ded506-22e8-463f-b0eb-656604a24891","resolution":{"observed_at":"2026-08-02T02:34:47.521046Z","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":"2026-08-02T02:34:47.600211Z","title":"Fuselier, Ling Long, Holly Swisher, and Fang-Ting Tu","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.600211Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:576d1f29d2a57be6833139e2795f5bd19c7bb31cc70e3288562db4e739b99cd2","observation_id":"45a994e6-ca58-4423-bd1a-de3c0e2c7046","resolution":{"observed_at":"2026-08-02T02:34:47.600211Z","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":"2026-08-02T02:34:47.752513Z","title":"Fuselier, Ling Long, Holly Swisher, and Fang-Ting Tu","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.752513Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:a096e7d235d28e3f13ccf37b749997cb8f5aa44cb2f942f1f2b303a5baf39a48","observation_id":"286e2392-392b-4e2d-ba73-a24d8e0d2774","resolution":{"observed_at":"2026-08-02T02:34:47.752513Z","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":"2026-08-02T02:34:47.814386Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.814386Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:37070b4e9beea9c55d780975ae92bd1eaf4310bda31530c7bcaa7f332747e46f","observation_id":"239acabe-86d2-4547-a76e-64cc0dfa5518","resolution":{"observed_at":"2026-08-02T02:34:47.814386Z","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":"2026-08-02T02:34:47.916800Z","title":"Tretkoff, and Paula Tretkoff","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.916800Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:d42486dc7e92de5370b36a94592ec5120b3d477f45c50ec317a9aa25c89e57e3","observation_id":"1bc30d5b-b495-4e66-930c-c348d4bfebc7","resolution":{"observed_at":"2026-08-02T02:34:47.916800Z","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":"2026-08-02T02:34:47.985742Z","title":"https://dlmf.nist.gov/, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:47.985742Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:20fb7af582e33062e81d9852de725101dc40a5bc0be30b2a0549822fd2f78546","observation_id":"57a30518-11d0-4f0d-ae51-35c4a92e653a","resolution":{"observed_at":"2026-08-02T02:34:47.985742Z","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":"2026-08-02T02:34:48.048736Z","title":"Subvarieties of Shimura varieties.Ann","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.048736Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:066aeae8e27ad6aaceddd2b841c7f1fbd2b5b42eb21d63e5849025a521fe1cb4","observation_id":"5f505e97-10db-411f-b6a0-09c3f389ae57","resolution":{"observed_at":"2026-08-02T02:34:48.048736Z","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":"2026-08-02T02:34:48.187522Z","title":"Hypergeometric functions over finite fields.Mem","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.187522Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:b57e9c014925d309c81d48245e49b72eb07cef913dc60cdd5899e49f5b3f9793","observation_id":"3fbb9860-7cd7-4076-864d-25a33155aa8e","resolution":{"observed_at":"2026-08-02T02:34:48.187522Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.02918","last_updated":"2025-03-03T20:58:38Z","snapshot_observed_at":"2026-08-12T23:08:03.443969Z","submitted_at":"2024-08-06T03:06:45Z","title":"Traces of Hecke Operators via Hypergeometric Character Sums","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.02918","snapshot_observed_at":"2026-08-02T02:34:48.285694Z","title":"Hoffman, Wen-Ching Winnie Li, Ling Long, and Fang-Ting Tu","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.285694Z"},"links":{"cited_paper":"/paper/2408.02918","citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:c169d251a9388f8fe9873e042d800d57a6e19ea5627beb9fdb55b0f0f909bee6","observation_id":"42a8d039-0a8c-4310-91eb-8a33287ed2da","resolution":{"observed_at":"2026-08-02T02:34:48.285694Z","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":"2026-08-02T02:34:48.474331Z","title":"An extension of the Ap´ ery number supercongruence.Acta Arith., 123(4):335–348, 2006","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.474331Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:55bc5043adfe4283e16bc6b23969dc9aed63c54c2137a8295c4ada29a76003d6","observation_id":"17be01e8-7728-436c-95b0-74bcb6ff8baa","resolution":{"observed_at":"2026-08-02T02:34:48.474331Z","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":"2026-08-02T02:34:48.569614Z","title":"Springer-Verlag, New York, 1983","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.569614Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:411051aeec054956aaefcfe0785e0b4aceb1767f412cb3fd9241b28ed99d6377","observation_id":"8d0bf576-9dab-4982-94fa-7d05ef4a7776","resolution":{"observed_at":"2026-08-02T02:34:48.569614Z","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":"2026-08-02T02:34:48.752979Z","title":"Springer-Verlag, New York, second edition, 1987","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.752979Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:39efbe4a419f64f10c5237672257c7da1bd734e6615918c57c87908b646e48c9","observation_id":"e3b21b5c-5ce0-4644-9dad-baca24b9011c","resolution":{"observed_at":"2026-08-02T02:34:48.752979Z","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":"2026-08-02T02:34:48.856949Z","title":"Computing special L-values of certain modular forms with complex multiplication.SIGMA Symmetry Integrability Geom","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:48.856949Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:be026a04586c0cbba2fd2952c56daa10f9dce69c8b70e3ddc1f7a07c53fb66e4","observation_id":"a4020452-e21c-4b66-b759-dc35f82d9c54","resolution":{"observed_at":"2026-08-02T02:34:48.856949Z","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":"2026-08-02T02:34:49.033721Z","title":"Supplement M´ emoire","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.033721Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:f80843d8de22b7f41c08c6d8fad4eae12386ad40ddef7dc7305961f7e61fc414","observation_id":"57f0125e-578c-479f-9c7d-fffbee140f17","resolution":{"observed_at":"2026-08-02T02:34:49.033721Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2604.02723","last_updated":"2026-04-03T04:29:25Z","snapshot_observed_at":"2026-08-09T02:26:23.134249Z","submitted_at":"2026-04-03T04:29:25Z","title":"Explicit hypergeometric modularity of certain weight two and four Hecke eigenforms","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.02723","snapshot_observed_at":"2026-08-02T02:34:49.151593Z","title":"Explicit hypergeometric modularity of certain weight two and four Hecke eigenforms","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.151593Z"},"links":{"cited_paper":"/paper/2604.02723","citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:d02d2f76d35333e50b768f86c152e113655f197bbb8e44e088cffde8e96757ea","observation_id":"fce901b1-f861-4e26-a38b-315a543765c0","resolution":{"observed_at":"2026-08-02T02:34:49.151593Z","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":"2026-08-02T02:34:49.350740Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.350740Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:f137f558c602efa7bbaf12feeec162160ff879749425b1bff3ee1003215622d5","observation_id":"c7927f54-85dc-46f0-a429-71bf62facc60","resolution":{"observed_at":"2026-08-02T02:34:49.350740Z","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":"2026-08-02T02:34:49.453336Z","title":"Distribution of values of Gaussian hypergeometric functions","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.453336Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:f88e5da715806859fc5b97c66935e69ba248510c5234cd851f45481b6111dd6c","observation_id":"1477a884-1816-42a9-9ec8-bed75eda8da7","resolution":{"observed_at":"2026-08-02T02:34:49.453336Z","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":"2026-08-02T02:34:49.626980Z","title":"L-values of certain weight 3 modular forms and transformations of hypergeometric series","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.626980Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:2878994f7900a966aebcd20948637010803ce2669b357f94b2441dfdfb395608","observation_id":"ea84e754-5194-43d3-a7b7-ca339dc06d37","resolution":{"observed_at":"2026-08-02T02:34:49.626980Z","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":"2026-08-02T02:34:49.743338Z","title":"Modular forms and certain 2F1(1) hypergeometric series.Proc","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.743338Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:9ed84a40d4dfed7b72b74c854ab22f24e4234c0e493fa3987c065e245424f75c","observation_id":"b67e3230-8888-4b78-ac27-65ecef680a20","resolution":{"observed_at":"2026-08-02T02:34:49.743338Z","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":"2026-08-02T02:34:49.920151Z","title":"Arithmetische Untersuchungen elliptischer Integrale.Math","venue":null,"work_id":null,"year":1937},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:49.920151Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:a681070a777fec632b8d09ac3711c062f765c33b44681e6e0eeaf7998b4319ce","observation_id":"577eb004-c573-414d-afe9-50a8ec85eea9","resolution":{"observed_at":"2026-08-02T02:34:49.920151Z","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":"2026-08-02T02:34:50.047996Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.047996Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:7b2ae6f717f28f24271d772e206e21141740a68798e42acf5455eff9e8c35f55","observation_id":"15820eb3-f392-45fc-801f-98ae9c2d7a7e","resolution":{"observed_at":"2026-08-02T02:34:50.047996Z","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":"2026-08-02T02:34:50.222633Z","title":"Algebraic values of Schwarz triangle functions","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.222633Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:d61597e4b275b54f1328224f42c0a6fae5e43ac9fabccfa03bd7dae2a3d125b9","observation_id":"79758afe-e63d-4c9a-8578-ea7e490a4b9a","resolution":{"observed_at":"2026-08-02T02:34:50.222633Z","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":"2026-08-02T02:34:50.339526Z","title":"Mathematical Society of Japan, Tokyo, 1961","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.339526Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:be1d5500089ffadff232d616f9e9804f03dceef9c86aba81c8ab412d7ce288ff","observation_id":"5f773386-1753-4972-b4c9-375bfa529165","resolution":{"observed_at":"2026-08-02T02:34:50.339526Z","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":"2026-08-02T02:34:50.514876Z","title":"Silverman.Advanced Topics in the Arithmetic of Elliptic Curves, volume 151 ofGraduate Texts in Mathematics","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.514876Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:22c1e66b818de10bc6b52786b9c52a7eeee59b3a8c124d0e8732cb85b94cc4a4","observation_id":"5979a77c-91d3-49ba-be4d-e412fcc00ae4","resolution":{"observed_at":"2026-08-02T02:34:50.514876Z","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":"2026-08-02T02:34:50.622681Z","title":"Cambridge University Press, Cambridge, 1966","venue":null,"work_id":null,"year":1966},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.622681Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:87a5e4e8ebbf2be7f76ee71731126749c25bc3c0914c4c3a68ecd881519e452a","observation_id":"e1846cc0-15eb-45f7-9d0d-179d212856cf","resolution":{"observed_at":"2026-08-02T02:34:50.622681Z","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":"2026-08-02T02:34:50.746430Z","title":"Arithmetic triangle groups.J","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.746430Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:d22118a1f8780092d273e923d397503ee0c9e2481c2804139ff9ede855640a2d","observation_id":"7c7cc03e-a91e-4350-9636-86f6722ea6a1","resolution":{"observed_at":"2026-08-02T02:34:50.746430Z","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":"2026-08-02T02:34:50.815865Z","title":"Commensurability classes of arithmetic triangle groups.J","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.815865Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:62b3305f4ab13f54633e6254069006d02b73ceca76c5ef50153e458cd5a5a4fb","observation_id":"249abf3a-9214-4a21-b19d-299fcc19ea82","resolution":{"observed_at":"2026-08-02T02:34:50.815865Z","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":"2026-08-02T02:34:50.889686Z","title":"The L-functions and modular forms database","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.889686Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:176b71f674b3fddb9e2fee855ec3d824af80f98b5e982ddb08cf5671b4e3653e","observation_id":"9df46210-4ea8-4e04-ad44-ec20fea12366","resolution":{"observed_at":"2026-08-02T02:34:50.889686Z","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":"2026-08-02T02:34:50.980072Z","title":"Sagemath, the sage mathematics software system (Version 10.6)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:50.980072Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:2ebed4662b35f89913dffeb700ecbe2dcb642b961d8a5127ab87ab8c071d57e3","observation_id":"a4120696-1f71-4a56-81ab-13a05b9e5107","resolution":{"observed_at":"2026-08-02T02:34:50.980072Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-02T02:34:51.056171Z","title":"Transcendence of special values of modular and hypergeometric functions","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.056171Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:7a4caf2732588ab30d4d6c9f5ddfae432ec2ea43eff04337b31a29a8183d4285","observation_id":"4ba02933-57e3-4d39-98cc-b2150c1cd4a0","resolution":{"observed_at":"2026-08-02T02:34:51.056171Z","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":"2026-08-02T02:34:51.114602Z","title":"Transcendence of values of transcendental functions at algebraic points (inaugural Monroe H","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.114602Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:1088146112abc94591101ead6ffa3118ec922c010039da155f71fd7dc4d4797f","observation_id":"4552c0a3-c7cd-4a7e-a586-cca85415c30d","resolution":{"observed_at":"2026-08-02T02:34:51.114602Z","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":"2026-08-02T02:34:51.168141Z","title":"Advanced Textbooks in Mathematics","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.168141Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:00ac80704bc7b3655e0c30550ebdbcf209be1e8eca6c956778d2589eb7880111","observation_id":"3a564451-fc2a-4d2b-aa72-6835eb78094b","resolution":{"observed_at":"2026-08-02T02:34:51.168141Z","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":"2026-08-02T02:34:51.258446Z","title":"Springer, Cham, [2021] ©2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.258446Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:ef93d21ade86550aa462cbd39183a98a628e1f3f7cd52bc3b783bfa426f86593","observation_id":"9fdb88a2-90b2-4d4c-81cf-014277b3c97f","resolution":{"observed_at":"2026-08-02T02:34:51.258446Z","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":"2026-08-02T02:34:51.338326Z","title":"Werte hypergeometrischer Funktionen.Invent","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.338326Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:3fb083a5f7e5e36432262f3ba81626f72c589238e80637c9df3fe32bd2d85e7b","observation_id":"a0852d4b-64a9-4da7-ac22-769fe1d9ae82","resolution":{"observed_at":"2026-08-02T02:34:51.338326Z","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":"2026-08-02T02:34:51.423977Z","title":"Der ¨ uberlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen.Math","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.423977Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:29016495fab40fb82149738f4558654f1e5c9d58aa61b920f3477dbcd2741464","observation_id":"681c72f7-4e7e-4eab-a39e-4c0455f335fa","resolution":{"observed_at":"2026-08-02T02:34:51.423977Z","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":"2026-08-02T02:34:51.493842Z","title":"Mathematica, version 14.1","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.493842Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:378e519754304f22617943fd9c587d5d1b4ddb00e6842e5b7b0117fcded47372","observation_id":"a4ffdcab-4e3c-4dca-b415-862b608c4d37","resolution":{"observed_at":"2026-08-02T02:34:51.493842Z","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":"2026-08-02T02:34:51.588563Z","title":"Schwarzian differential equations and Hecke eigenforms on Shimura curves.Compos","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.588563Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:759e0d18a3a72184706a49797071013ccf9958628cb63ec21aee7b60926eb3df","observation_id":"fd822c54-94c4-4d26-be0e-c719f513e305","resolution":{"observed_at":"2026-08-02T02:34:51.588563Z","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":"2026-08-02T02:34:51.659842Z","title":"Special values of hypergeometric functions and periods of CM elliptic curves.Trans","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.659842Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:9c49de4937bd1738ce7ce8af7eef56933eda94545c35be841f33e354141546e2","observation_id":"49efad43-cd7f-413b-8378-7654e72786cf","resolution":{"observed_at":"2026-08-02T02:34:51.659842Z","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":"2026-08-02T02:34:51.730831Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-02T02:34:51.730831Z"},"links":{"citing_paper":"/paper/2607.16331"},"observation_digest":"sha256:c0ee73284de064e5468237e0bc93334001a5feb11f5249f3b1a108930bc56977","observation_id":"8c411de9-68cf-4314-a1c9-b50dbdb05fce","resolution":{"observed_at":"2026-08-02T02:34:51.730831Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.16331","last_updated":"2026-07-15T20:21:59Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-13T05:53:05.482273Z","submitted_at":"2026-07-15T20:21:59Z","title":"Exceptional Sets for Certain ${}_2F_1$ Hypergeometric Functions"},"reference_resolution":{"displayed":53,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":52,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":53},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:2607.16331."}