{"as_of":"2026-08-16T17:57:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8e6570d486633aa986a7ab3147e019267ffc79cca52c56598dc5fd070856f741","coverage":[{"denominator":18,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":18,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T13:31:23.635323Z","state":"measured"},{"denominator":18,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":18,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.05123/citation-record","integrity":"/paper/1908.05123/integrity","json":"/paper/1908.05123/citation-record.json","paper":"/paper/1908.05123"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T13:31:24.018008Z","title":"Almkvist and J","venue":null,"work_id":"6bf1b873-f5ef-4c27-b7fb-168c2c8c4215","year":2012},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.538673Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:04dba268a0218e51f66c5b3dc10c84d73699ae8b5013bfb37e0ef22af7190f8a","observation_id":"ee4e74a4-0226-48e5-ade0-dce0f7997101","resolution":{"observed_at":"2026-08-14T13:31:24.024721Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.997816Z","title":"Baruah, B.C","venue":null,"work_id":"ee664623-b2bd-4d5b-8360-0bd5b693d505","year":2009},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.544860Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:17c830ecfe37636c2ebe2115c38edfcc3037fffc2bb070bb6a49b0599b7721f3","observation_id":"b7a50841-5c14-4b9b-91cf-d4173f67b606","resolution":{"observed_at":"2026-08-14T13:31:24.004183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.977575Z","title":"Chisholm, A","venue":null,"work_id":"4d914af8-3cf1-411a-83e9-4b50967dbf64","year":2013},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.550820Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:ba3442811ab0c87bde7ca6074aee7984c974e19c69ff850b27a3b7af31c4247a","observation_id":"010777c3-1176-413d-a4f6-df27a0e44efa","resolution":{"observed_at":"2026-08-14T13:31:23.983025Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1906.07384","last_updated":"2020-02-27T12:37:40Z","snapshot_observed_at":"2026-08-16T10:34:53.078233Z","submitted_at":"2019-06-18T05:31:24Z","title":"Special hypergeometric motives and their $L$-functions: Asai recognition","version":3},"cited_work":{"arxiv_id":"1906.07384","doi":null,"metadata_source":"pith","pith_arxiv_id":"1906.07384","snapshot_observed_at":"2026-08-14T13:31:23.682505Z","title":"Special hypergeometric motives and their $L$-functions: Asai recognition","venue":"math.NT","work_id":"436a2e7c-e51b-426b-9107-d15d63d232e6","year":2019},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.557951Z"},"links":{"cited_paper":"/paper/1906.07384","citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:6642cb9994f9207394f729fa0b313b381ea814c25a04b8592b6cffa75300837e","observation_id":"8a6b7a8a-7cac-4567-bf00-702f72782a0a","resolution":{"observed_at":"2026-08-14T13:31:23.691359Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.960097Z","title":"Guillera , A matrix form of Ramanujan-type series for 1 /π , Gems in Experimental Mathematics: Contemp","venue":null,"work_id":"7b51ec25-02d7-4220-8314-20e49b7f1bba","year":2010},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.564136Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:c53de9e4d3005c12003c93edd06fa3279667c7e1b3e3a39c1ed6484bd6e1f9e4","observation_id":"67340b4c-3f64-46a8-a684-4d4144368cc8","resolution":{"observed_at":"2026-08-14T13:31:23.965930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.940841Z","title":"Guillera , More hypergeometric identities related to Ramanujan-type serie s, The Ramanujan J","venue":null,"work_id":"e7c10222-2608-4967-86f0-b17d3ab474fa","year":2013},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.569593Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:0136cb6a311aab8d91c3c7d139857953fcbf33ca7bae57b04279791944e855f4","observation_id":"9e97abe8-dec5-4131-b917-d54f06bb429f","resolution":{"observed_at":"2026-08-14T13:31:23.946753Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.920054Z","title":"Guillera , WZ pairs and q-analogues of Ramanujan series for 1 /π (with an appendix by Wadim Zudilin), Journal of Difference Equations and Applications 24, 1871– 1879","venue":null,"work_id":"f9b03b10-8fd6-4134-aa5e-93d7777c599b","year":null},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.575350Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:0382631a46b7b153e88687c5a0fc91184f87a5be181cc81cf7e7164eb2964ad8","observation_id":"8a296d9a-e12c-4bfb-b626-fd8a0c754fce","resolution":{"observed_at":"2026-08-14T13:31:23.927689Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.897835Z","title":"Divergent","venue":null,"work_id":"3cd742dd-be62-4265-9896-4d9a1b072467","year":2012},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.580816Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:641b9ffa97729612c177a4987a1e3445b1ef528a10abcba6fddfa43c43e938ea","observation_id":"06484bc5-ad7e-42d3-affd-32fdc8d8b602","resolution":{"observed_at":"2026-08-14T13:31:23.903448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.878414Z","title":null,"venue":null,"work_id":"3bd759d5-583a-4100-9e0c-649eb967ab2c","year":2019},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.587003Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:f0e29bb33883e98c58e21c2a814e03a21087740b9ae9892dc20e09983d5925fa","observation_id":"66d0f2cc-9eea-4817-b332-4f4a14f8b2fa","resolution":{"observed_at":"2026-08-14T13:31:23.884624Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.859614Z","title":"Long , Hypergeoemetric evaluation identities and supercongruences, P acific Journal of Mathe- matics 249 (2011), 405–418","venue":null,"work_id":"b3544082-e413-4f8d-9066-3f041a933502","year":2011},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.591950Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:7cf4e6e000333d1ce9eb18838214f57626fed7d819cc9fc5b97585a82ad46c39","observation_id":"62d06fc7-b7cc-41b6-8524-f30222bc898e","resolution":{"observed_at":"2026-08-14T13:31:23.865646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.842224Z","title":"Morley , Note on the congruence 2 4n ≡ (−1)n(2n)!/ (n!)2, where 2 n + 1 is prime, Ann","venue":null,"work_id":"9ff0fb8d-4217-4bad-b667-7f582c74ba34","year":null},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.598690Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:f3970d4167542c73946d62806e50004b1fe25f4285542cd1debfd2a81c0da893","observation_id":"2673b4cf-4cd5-4f6c-9598-b8cf3444080c","resolution":{"observed_at":"2026-08-14T13:31:23.848224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.825142Z","title":"Petkov˘sek, H","venue":null,"work_id":"9bf058e3-875e-4069-98b1-526021116deb","year":1996},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.603907Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:889e58643679653f4514e808cb9714f358d831707da705598b86e963ce06935b","observation_id":"76574214-5b53-4bb9-ad7f-8360e3a8ac27","resolution":{"observed_at":"2026-08-14T13:31:23.830919Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.807446Z","title":"Wolstenholme , On certain properties of prime numbers, Quart","venue":null,"work_id":"27af6a72-5d87-433c-a9be-c823e6778234","year":null},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.609336Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:988f71897b6ebc457e0cef47bfe0ed328e3dd6b8fb8e661374c0e1d175f39803","observation_id":"a8cf0c3e-5fad-4ebc-adef-f9e1c6ae947d","resolution":{"observed_at":"2026-08-14T13:31:23.813306Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.787093Z","title":null,"venue":null,"work_id":"ef071b93-b094-455f-85d4-e4bbef8c4849","year":null},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.614703Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:be3a53d8db5d048ca57ed2536d2982c7d0484748ed313cf4cb51288b17280390","observation_id":"0bda36dd-35aa-4461-be73-31b33eecc041","resolution":{"observed_at":"2026-08-14T13:31:23.792529Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.766003Z","title":null,"venue":null,"work_id":"65686f87-c4a3-48e6-a0b8-527c2ec0ca9d","year":null},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.619934Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:572e6f6c9c458a8b661f7cddb4461760cff24745702dfaf4e85427dd34cdb185","observation_id":"a3d30175-9452-4838-bbc2-12f5a3cbd148","resolution":{"observed_at":"2026-08-14T13:31:23.772598Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.746145Z","title":"Zudilin , Ramanujan-type formulae for 1 /π : A second wind? in Modular Forms and String Duality (Banff, June 3–8, 2006), N","venue":null,"work_id":"1258d390-96ab-492c-997f-36098d781a1b","year":2008},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.625173Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:227a2a36026d65345b06ebb5ae7c9fe76f0817df9e594451571bfcafccd0e561","observation_id":"51d4632d-e03b-4341-be3a-98f1916cdbc3","resolution":{"observed_at":"2026-08-14T13:31:23.752086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.724691Z","title":"Zudilin , Ramanujan-type supercongruences, J","venue":null,"work_id":"a65534ee-3c63-492f-ab61-257328e3367d","year":2009},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.630033Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:e5ee487b92ce6b3c135c66f3bb586527010c08e76954d73b1ba1a019263cbe5e","observation_id":"0b8003e8-4cdf-44c4-8acb-14eb1a678c1d","resolution":{"observed_at":"2026-08-14T13:31:23.731159Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T13:31:23.705246Z","title":"Zudilin , Arithmetic hypergeometric series, Russian Math","venue":null,"work_id":"dc607e95-8544-4f68-a699-8f92a7fc1d35","year":2011},"citing_paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T13:31:23.635323Z"},"links":{"citing_paper":"/paper/1908.05123"},"observation_digest":"sha256:298ed82a2a9e069dfba4caedb12c902b2991d7ba6e4389c9054b385d3f2afa59","observation_id":"3ebeb59b-99ee-40fe-93bf-a48a07caa504","resolution":{"observed_at":"2026-08-14T13:31:23.711612Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.05123","last_updated":"2019-08-14T13:44:01Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T10:56:01.940273Z","submitted_at":"2019-08-14T13:44:01Z","title":"Bilateral Ramanujan-like series for $1/\\pi^k$ and their congruences"},"reference_resolution":{"displayed":18,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":1,"verified_fuzzy":14},"total_outbound_references":18},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:1908.05123."}