{"as_of":"2026-08-16T10:43:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:affae485476a1e42e5bea53150eb5dd7fea7c18d5dea20bb68b9bc7368e26790","coverage":[{"denominator":8,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":8,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:13:17.774986Z","state":"measured"},{"denominator":8,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":8,"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/1908.03937/citation-record","integrity":"/paper/1908.03937/integrity","json":"/paper/1908.03937/citation-record.json","paper":"/paper/1908.03937"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:13:17.887068Z","title":"Ahlgren and K","venue":null,"work_id":"09ac72f3-e326-4a4d-9ba0-63432a0dea60","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.744634Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:8f2b6b1dc06bcf2d8edac395bb7eb05ab4a0d72d8360452b4ee183977a713f50","observation_id":"bf471f95-af86-4cbc-8aaa-333f331fcc53","resolution":{"observed_at":"2026-08-14T14:13:17.890737Z","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":"2026-08-14T14:13:17.875119Z","title":null,"venue":null,"work_id":"e80a6ce4-371c-4402-80d4-3e59a9c3b994","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.749562Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:096004c9320a67be55a64e8492bb337e569eb28e2042dc5b26c34090561ac6e6","observation_id":"e5612147-6cde-4f77-830d-255e06dcd509","resolution":{"observed_at":"2026-08-14T14:13:17.879048Z","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":"2026-08-14T14:13:17.863466Z","title":"Carney, A","venue":null,"work_id":"25845321-af98-4209-bc06-753d6b11d1cc","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.753508Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:4d5a03a3b084cc91d563fb06ca3462e348dc06ee1b5cd0275179d4534e97a31a","observation_id":"bcc8a411-aad5-458c-bd47-3906e2b7c0b2","resolution":{"observed_at":"2026-08-14T14:13:17.867408Z","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":"2026-08-14T14:13:17.851791Z","title":null,"venue":null,"work_id":"cfd448f1-4a41-4175-8b25-c60d54fc2c40","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.758447Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:525e970704d97546bc69f17879b3c059e6dbca93f8856b757613f9d733e19294","observation_id":"f49751fb-664f-415b-99d1-8e1f8354d133","resolution":{"observed_at":"2026-08-14T14:13:17.855507Z","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":"2026-08-14T14:13:17.840507Z","title":"Martin, Multiplicative η-quotients, Trans","venue":null,"work_id":"ff93d129-27bb-4a1e-9b79-b11d920c4ef3","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.762824Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:7f6f599c6d95e490d344e44816f250bf87d44879fdab0691b3027ae50a038806","observation_id":"3d7a6738-991d-4eeb-a417-be32c20c1cbe","resolution":{"observed_at":"2026-08-14T14:13:17.844095Z","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":"2026-08-14T14:13:17.828173Z","title":"Ono, The Web of Modularity: Arithmetic of the Coeﬃcients of Modul ar Forms and q-series, American Mathematical Society, Providence, 2004","venue":null,"work_id":"b37bbfec-e3a3-4b16-944d-ac6678f87ac6","year":2004},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.766720Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:e6e3cb80e84839ba25bb0fe7426a1a7370a09b13b209f60e6188c3a337fc10ab","observation_id":"babeea3e-0814-4d34-ae5e-1e0a595b8d75","resolution":{"observed_at":"2026-08-14T14:13:17.832801Z","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":"2026-08-14T14:13:17.815305Z","title":null,"venue":null,"work_id":"988f00ba-bd85-49f8-a4f7-4ca578a8f9bf","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.771153Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:83888d7d4f5efa83eb4b5906a7c9340b166997b42f86a09637af57be401871ce","observation_id":"5c1ac94c-454a-491b-acda-269ca47ce0d2","resolution":{"observed_at":"2026-08-14T14:13:17.820479Z","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":"2026-08-14T14:13:17.802838Z","title":null,"venue":null,"work_id":"81196a27-c760-4462-879f-28404d168c46","year":null},"citing_paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:13:17.774986Z"},"links":{"citing_paper":"/paper/1908.03937"},"observation_digest":"sha256:bd97b3293a09aa4074670a2e4f3b641af563aebdaf560cf31b78a58a49135ce5","observation_id":"57d6f20e-44d5-433b-a6bd-4557e1bdd492","resolution":{"observed_at":"2026-08-14T14:13:17.807643Z","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"}}],"paper":{"arxiv_id":"1908.03937","last_updated":"2021-03-13T14:32:49Z","latest_version":3,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T04:44:44.088981Z","submitted_at":"2019-08-11T17:07:03Z","title":"Congruences in fractional partition functions"},"reference_resolution":{"displayed":8,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":0,"verified_fuzzy":4},"total_outbound_references":8},"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 8 of 8 outbound references and 0 inbound Pith citation observations for arXiv:1908.03937."}