{"as_of":"2026-08-16T09:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f8225361a820f18c2a95821b03a0fe5a9225bb38131a2ae9ac00b1f0566ceeb8","coverage":[{"denominator":25,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":25,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:52:09.778518Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"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/1908.06642/citation-record","integrity":"/paper/1908.06642/integrity","json":"/paper/1908.06642/citation-record.json","paper":"/paper/1908.06642"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:52:10.317677Z","title":"Adiga and D","venue":null,"work_id":"75759369-2447-4716-8456-a31514fb33e0","year":2017},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.620692Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:b64e9456437f57cdd44512ea99ae8cde95f10c6d1c8b6f96f785f95caaeb1a76","observation_id":"b95f41bf-0dad-4ccc-bfb2-c03431acc1e9","resolution":{"observed_at":"2026-08-14T12:52:10.322120Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:52:09.628068Z","title":"Berndt, Ramanujan’s Notebooks, Part III, Springer, New York, 1991","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.628068Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:42743e5d82541ac1ba4c488c0dfc8709e1634d17d8c351e7f9c7d5418b7d415a","observation_id":"ce3fab87-b798-4456-9a2b-b6dc7fdafeb3","resolution":{"observed_at":"2026-08-14T12:52:09.628068Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:52:10.289207Z","title":"Berndt, Ramanujan’s Notebooks, Part IV, Springer, New Y ork, 1994","venue":null,"work_id":"79a7a086-cd67-4a99-ac3b-477134538ca8","year":1994},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.636276Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:ac057984fc023de740bd964c626659481920be576aeaaae8028ca809e72b18b9","observation_id":"f13772ee-d1bd-43c2-8254-6674e53654d4","resolution":{"observed_at":"2026-08-14T12:52:10.294350Z","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":"2026-08-14T12:52:10.270608Z","title":"Berndt, A.J","venue":null,"work_id":"432afbea-f3d9-4841-a861-163daf6a2638","year":2003},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.642075Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:6d85e4f44cd79873d29c2a9ddf06b5d5364ca6e23f3949410d424423809c18e4","observation_id":"dceda792-879f-4c43-aa2f-3138aa0b609c","resolution":{"observed_at":"2026-08-14T12:52:10.277615Z","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":"2026-08-14T12:52:10.254375Z","title":"Carlson and J.J","venue":null,"work_id":"1552c7a7-b422-46b3-8333-e71820320697","year":2014},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.648865Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:3c3be606cad4ebbd3b5fdb1941169de1ffeb4bf975543c53074b44620545c1fe","observation_id":"952637d1-ef39-4180-9d05-41ab9838afb2","resolution":{"observed_at":"2026-08-14T12:52:10.259370Z","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":"2026-08-14T12:52:10.237684Z","title":"Cui and N.S.S","venue":null,"work_id":"9dd45a20-f77b-469e-9b5d-bc77e077d355","year":2013},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.655310Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:2063e07982613c0be09435a1fd975f7aafbafeb857a5ad197f7dd86a0cbb2c75","observation_id":"3463e58c-f725-4517-99dd-478372fe2928","resolution":{"observed_at":"2026-08-14T12:52:10.242848Z","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":"2026-08-14T12:52:10.219861Z","title":"Dandurand and D","venue":null,"work_id":"d794c3ff-d35e-4391-a47e-a4e8a6f8d229","year":2009},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.662200Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:3fb5698cd35c0ef73602c060e287b1510bdcac845633c9505788e7c26a698e93","observation_id":"5c1a0e72-e94d-4c92-9a8d-81696c4ef827","resolution":{"observed_at":"2026-08-14T12:52:10.226021Z","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":"2026-08-14T12:52:10.200821Z","title":"Dou, Congruences for (3 , 11)-regular bipartitions modulo 11, Ramanujan J., 40, (2016) 535–540","venue":null,"work_id":"8e331f18-ed7e-4c86-bb98-21ffb6e31503","year":2016},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.668034Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:c39892af218640a7307406220859f1122485ee45b2fab8a7afb64b963bb91767","observation_id":"f91c5777-68c3-413c-9621-87d378ec0f24","resolution":{"observed_at":"2026-08-14T12:52:10.207122Z","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":"2026-08-14T12:52:10.179913Z","title":"Furcy and D","venue":null,"work_id":"39c024e8-e7df-4770-8c87-6cfe6bcd4c62","year":2012},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.674807Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:591f7d4218d844978e21c43d508f1ada593194d8117e184a74921c78166db973","observation_id":"82ac1b69-0215-47d4-a773-befb3e081cad","resolution":{"observed_at":"2026-08-14T12:52:10.189249Z","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":"2026-08-14T12:52:10.156326Z","title":"Gordon and K","venue":null,"work_id":"edfc7719-3c6a-474b-b414-06de59818a4b","year":1997},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.684328Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:5e4fcd20f75e8c9e13e6ed60964facdf447fd908dca871a587d8a8efbe4e2b68","observation_id":"550196ef-2756-4e6e-bcf1-817d5657f300","resolution":{"observed_at":"2026-08-14T12:52:10.161585Z","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":"2026-08-14T12:52:10.127674Z","title":"Hirschhorn and J.A","venue":null,"work_id":"575a7f27-f65f-4ae8-8bb7-e725b7596fa9","year":2010},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.691085Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:3ff9956c8e114e9a6aba7500cbff0d52a03debf1fb301b4e4bbc5e74e5f27ae0","observation_id":"c7618bbd-69cc-4b82-a54f-6aa6ef8d68d6","resolution":{"observed_at":"2026-08-14T12:52:10.142178Z","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":"2026-08-14T12:52:10.106701Z","title":"Hirschhorn and J.A","venue":null,"work_id":"ea8501ab-929d-480c-8514-d9e3d8e07b67","year":2010},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.697824Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:49e4284053961d7c3b95144c1f891923022cb5872f5f7c3b33adef70c4794ee1","observation_id":"4044c5dc-fca4-41b1-b3f8-4ae346e1f28e","resolution":{"observed_at":"2026-08-14T12:52:10.111877Z","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":"2026-08-14T12:52:10.087128Z","title":"Hirschhorn, The Power of q","venue":null,"work_id":"ca41cf88-a947-4ee3-a5b3-080100be4f61","year":2017},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.706253Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:851c4af5c5ada89b02ee1f43c03f6057b6f618f0fe8d4d2e549695955b828631","observation_id":"5a2b4914-9e7b-450b-9c2e-f9547f781660","resolution":{"observed_at":"2026-08-14T12:52:10.092638Z","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":"2026-08-14T12:52:10.062541Z","title":"Kathiravan and S.N","venue":null,"work_id":"4c757789-26ec-40d5-a568-92177d727d0a","year":2017},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.711791Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:21489907d58b0ed3c39fce76b37e4316f2210f4538d1ffdeb212b721bb7d7b93","observation_id":"d5afccc2-742b-4e2a-8b71-903cb09d8710","resolution":{"observed_at":"2026-08-14T12:52:10.071885Z","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":"1907.13450","last_updated":"2019-08-08T11:36:50Z","snapshot_observed_at":"2026-08-14T15:59:39.593490Z","submitted_at":"2019-07-31T12:30:25Z","title":"Ramanujan type of congruences modulo m for (l, m)-regular bipartitions","version":2},"cited_work":{"arxiv_id":"1907.13450","doi":null,"metadata_source":"pith","pith_arxiv_id":"1907.13450","snapshot_observed_at":"2026-08-14T12:52:09.843163Z","title":"Ramanujan type of congruences modulo m for (l, m)-regular bipartitions","venue":"math.NT","work_id":"0d291400-54dd-4d3f-bfee-6d76608f9c30","year":2019},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.717265Z"},"links":{"cited_paper":"/paper/1907.13450","citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:278397f63501f952c7348ceb0b8548c7a14aed964afb664af6c50b62cb4442f5","observation_id":"b9274d38-4edb-4ab3-a326-867b79a38176","resolution":{"observed_at":"2026-08-14T12:52:09.852174Z","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":"2026-08-14T12:52:10.044420Z","title":"Lin, Arithmetic of the 7-regular bipartition function modulo 3, Ramanujan J., 37, (2015) 469–478","venue":null,"work_id":"a55f250d-844a-43a4-8d2b-0f3655f21f62","year":2015},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.722996Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:6c1cb4b1f3e9019b6db5d3e303d8102a4c0d316ea57d029ca9d989b7b2568668","observation_id":"67946c51-d7da-4b53-af1e-3e839defa96c","resolution":{"observed_at":"2026-08-14T12:52:10.050666Z","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":"2026-08-14T12:52:10.020483Z","title":"Lin, An inﬁnite family of congruences modulo 3 for 13-regula r bipartitions, Ramanujan J., 39, (2016) 169–178","venue":null,"work_id":"7a3c62ff-4879-4f4d-9b0d-a4d76bd5363e","year":2016},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.728311Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:61c8a8a43a3be324d0ecc4c4c08ff2078e96d6ff870ccd87a2a4995279cf2ff7","observation_id":"2a66a868-f78b-44cf-94ee-33586c8cd8ad","resolution":{"observed_at":"2026-08-14T12:52:10.026500Z","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":"2026-08-14T12:52:10.001725Z","title":"Ramanujan, Some properties of p(n), the number of partitions of n, Proc","venue":null,"work_id":"8915c263-54ec-439a-a627-40442a49506d","year":1919},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.733444Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:c897366e75a80cd18c51c008eaad725f9062b08ac21103998bd36109108160d4","observation_id":"e4bc325a-a7bf-41fb-b0a7-ab0fa4512c8f","resolution":{"observed_at":"2026-08-14T12:52:10.007016Z","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":"2026-08-14T12:52:09.982280Z","title":"Ramanujan, Collected Papers, Cambridge Univ","venue":null,"work_id":"11417860-48d4-4429-817d-1c885b67f782","year":1927},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.739715Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:f8ac9c0e711e3b994ad3610b25d28166af9198a09a2759a2ed32350e2c940668","observation_id":"d90b8889-fd64-41ce-ad40-fc37441d7456","resolution":{"observed_at":"2026-08-14T12:52:09.987748Z","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:52:09.744784Z","title":"Ramanujan, The Lost Notebook and Other Unpublished Pape rs, Narosa, New Delhi, 1988","venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.744784Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:726f7b26d15e0e0ec6ee0ae277f6a5c18903164986af0385e6cb74921438fd0b","observation_id":"6bc4be03-4396-44d5-8c08-8a29b1fbb6a6","resolution":{"observed_at":"2026-08-14T12:52:09.744784Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:52:09.945754Z","title":"Wang, Arithmetic properties of ( k, ℓ)-regular bipartitions, Bull","venue":null,"work_id":"b66429a6-1ec3-4855-ab22-fd7ecd13a34f","year":2017},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.753204Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:12581674ebf980174c00817557211154d3e64f401e18b668a6ac0e14f13d601a","observation_id":"7c05db91-f1a3-4c5c-a776-a9a84fecf117","resolution":{"observed_at":"2026-08-14T12:52:09.953246Z","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":"2026-08-14T12:52:09.924868Z","title":"Webb, Arithmetic of the 13-regular partition function modu lo 3, Ramanujan J., 25, (2011) 49–56","venue":null,"work_id":"aa20288b-778e-464b-9ac4-d876766dfcce","year":2011},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.759641Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:607e37cb6c7d0c8473821608a01569ed31e85e1d3d4bca397b6c0ca870e80292","observation_id":"ac3e5f4e-9abb-4a70-9dd1-7a57853ad9de","resolution":{"observed_at":"2026-08-14T12:52:09.931934Z","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":"2026-08-14T12:52:09.907500Z","title":"Xia, Congruences for some ℓ-regular partitions modulo ℓ, J","venue":null,"work_id":"384c1ca7-f66c-4bd5-9ef6-b5493dc78fb3","year":2015},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.766942Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:dd42bf026db38f3a6e06d4ec65b02e4e46dd4d001a37f5cf24ccaaa2acf2ba72","observation_id":"e8a3373d-7364-40a1-9426-68531c8f907a","resolution":{"observed_at":"2026-08-14T12:52:09.912884Z","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":"2026-08-14T12:52:09.887096Z","title":"Xia and O.X.M","venue":null,"work_id":"9529ee27-0520-4687-bc6b-88223e41280a","year":2017},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.772503Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:26c951be2294c8fe55590197bf73112b0cb27f16d51cc863e9c94dee6843f21e","observation_id":"5be880c4-12fa-40f7-b20a-63b71c6d1e9c","resolution":{"observed_at":"2026-08-14T12:52:09.893688Z","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":"2026-08-14T12:52:09.864894Z","title":"Yao, New congruences modulo powers of 2 and 3 for 9-reg uar partitions, J","venue":null,"work_id":"2f290c02-74e6-46c6-8c3d-da4a6fed9e24","year":2014},"citing_paper":{"arxiv_id":"1908.06642","last_updated":"2019-10-15T09:17:23Z","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T12:52:09.778518Z"},"links":{"citing_paper":"/paper/1908.06642"},"observation_digest":"sha256:fd6dcf984252340faa95481a3a46e967a7c4dfaacd9ebe1c2627d7634fcc32fb","observation_id":"292c2cfd-1118-4a9f-8e9f-116ddc4e9a37","resolution":{"observed_at":"2026-08-14T12:52:09.870787Z","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":"1908.06642","last_updated":"2019-10-15T09:17:23Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-14T12:36:03.380778Z","submitted_at":"2019-08-19T08:41:36Z","title":"Some congruences for $(s,t)$-regular bipartitions modulo $t$"},"reference_resolution":{"displayed":25,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":22},"total_outbound_references":25},"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 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:1908.06642."}