{"as_of":"2026-08-13T15:08:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:68f593c7bc9c41421e86713399b8d11891dce962f5b799bd15ba2753e4317d24","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T12:31:38.865253Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"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/2412.14344/citation-record","integrity":"/paper/2412.14344/integrity","json":"/paper/2412.14344/citation-record.json","paper":"/paper/2412.14344"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:39.085880Z","title":"Andrews, The theory of partitions , Cambridge University Press, Cambridge, 1984","venue":null,"work_id":"cb3be13a-7d27-4efd-917e-aa0b7d46ca1b","year":1984},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.808961Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:b0b77b5621716dc476bde0800e4f215446d50fa0c85c30cace021f23f356632e","observation_id":"5dc1eccf-df82-41e0-8c1f-aa189766fcee","resolution":{"observed_at":"2026-08-11T12:31:39.098086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:39.068819Z","title":"Andrews, R","venue":null,"work_id":"9982b63d-2872-4462-9c0a-24d0b2d1b7c5","year":1999},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.815120Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:04a2563d96c7174e073cea134b98073e1bdeef038717d2b0ea550ff11edafb88","observation_id":"04450d85-f2be-44f3-a058-cc12bd565b9c","resolution":{"observed_at":"2026-08-11T12:31:39.073890Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:39.052177Z","title":"Bringmann, A","venue":null,"work_id":"213f7672-ef3b-43f8-bb85-73fa3231c27f","year":2017},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.820272Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:61b3f8d8d65dcbcb871817500700e4414900b54ed929fe664a6f0d913fe32676","observation_id":"66c021eb-9c56-4799-bfe6-90f02cd6541e","resolution":{"observed_at":"2026-08-11T12:31:39.057112Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:39.036381Z","title":"Bringmann and K","venue":null,"work_id":"80651978-3673-4391-a426-ab8a36b50cbc","year":2012},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.825048Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:ef32e9c767e29a979798836fcd4fb3dd257d65b10b8e63764d80645308020f10","observation_id":"0c51abe4-2f6e-40b2-a308-aa6523aaf71e","resolution":{"observed_at":"2026-08-11T12:31:39.041444Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:39.019979Z","title":"Choliy, L.W","venue":null,"work_id":"d67e04bc-2b64-4a32-b36b-99a2df9d5a5f","year":2018},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.830097Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:d474440559bc20b70c506e5b0ac9e6ced20b6ff6efc5f6467ed163fe27d62193","observation_id":"31ae690e-b7f1-474c-96de-de4607b0d633","resolution":{"observed_at":"2026-08-11T12:31:39.025050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:39.002647Z","title":"Gandhi, Congruences for pr(n) and Ramanujan’s τ function, Amer","venue":null,"work_id":"9695ebf2-8db3-4f25-a561-35c62209b759","year":1963},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.835202Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:6fb71b063c434661c19e9869a5d434ae40186a0db1d105b686878e30648a4aa1","observation_id":"60c2fe35-4042-43ba-b671-6707e3c3941d","resolution":{"observed_at":"2026-08-11T12:31:39.007938Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.16968","last_updated":"2025-04-21T11:47:10Z","snapshot_observed_at":"2026-08-12T12:38:54.198879Z","submitted_at":"2024-11-25T22:37:34Z","title":"Pentagonal number recurrence relations for $p(n)$","version":2},"cited_work":{"arxiv_id":"2411.16968","doi":null,"metadata_source":"pith","pith_arxiv_id":"2411.16968","snapshot_observed_at":"2026-08-11T12:31:38.900166Z","title":"Pentagonal number recurrence relations for $p(n)$","venue":"math.NT","work_id":"d199058c-6f72-45be-8b22-a719e7dd3d4f","year":2024},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.840741Z"},"links":{"cited_paper":"/paper/2411.16968","citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:de09db7a9b284991c6b7a5a4af3ef5443f525fedc4efbea90d907b17fb2e2456","observation_id":"a7ee0efa-f5ae-46e3-8357-92f0959950a6","resolution":{"observed_at":"2026-08-11T12:31:38.907349Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:38.985102Z","title":"Lazarev and H","venue":null,"work_id":"31ec4e0b-ee45-40ea-8e1a-7527b2ff9a70","year":2012},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.845898Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:edd618e219a84a50e564807176b34ee5de1c175555d8fb494ff38b70c1c284bb","observation_id":"4706beb6-8f6d-413c-b345-97d82c0fdf7a","resolution":{"observed_at":"2026-08-11T12:31:38.990406Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:38.968404Z","title":"Ono, The web of modularity: Arithmetic of the coefficients of modul ar forms and q-series, CBMS, Regional Conference series in Mathematics, 102, Amer","venue":null,"work_id":"e4951563-b91e-46ae-86cd-6048f93d488f","year":2004},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.850870Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:2fec36ae15fddee517fc8917acac6ae0fde2fc8822c66b04ed5a742951acf8b7","observation_id":"bd169768-7300-4015-9030-138fb4a913af","resolution":{"observed_at":"2026-08-11T12:31:38.973514Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:38.952846Z","title":"http://dlmf.nis t.gov/, Release 1.0.19 of 2018-06-22","venue":null,"work_id":"a4313b37-777b-4c44-83b1-bf2dad60247b","year":2018},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.855875Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:1d1eb9e5c59eace6d477e8c767d6b766d8531e14f0314d39aceb416da4c12fbe","observation_id":"e62d32a9-20bd-4613-bbb5-0659c7fe0655","resolution":{"observed_at":"2026-08-11T12:31:38.957393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:38.935718Z","title":"Sellers, Recurrences for 2-colored and 3-colored F-partitions, Discrete Mathematics, 156 (1996), 303–310","venue":null,"work_id":"2a7a8de1-0795-42b3-b714-dcfa3442c17f","year":1996},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.860629Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:ce4c4d75afc26cfd00075bc6462aebabd3d39abc6b0cdd5b5a8e108ffdfa1cf3","observation_id":"29cc2a3a-cca5-41da-ad13-05e71c5fda3c","resolution":{"observed_at":"2026-08-11T12:31:38.941393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T12:31:38.918772Z","title":"Zagier, Modular forms and differential operators , Proc","venue":null,"work_id":"e2cf5c7c-b7e3-4661-b3fd-7d5c5b94652c","year":1994},"citing_paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T12:31:38.865253Z"},"links":{"citing_paper":"/paper/2412.14344"},"observation_digest":"sha256:9ed54b85d7f3e4cfb9c13d070eb9ca94577675d1f19a25d6b947da240169fda6","observation_id":"a6ca696e-112c-4e8a-94c0-b7d6efa698ab","resolution":{"observed_at":"2026-08-11T12:31:38.924016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"paper":{"arxiv_id":"2412.14344","last_updated":"2024-12-22T18:50:40Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-11T12:17:14.674274Z","submitted_at":"2024-12-18T21:29:16Z","title":"Euler-type recurrences for $t$-color and $t$-regular partition functions"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":1,"verified_fuzzy":11},"total_outbound_references":12},"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 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2412.14344."}