{"as_of":"2026-08-23T17:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d03fd226d51458cf846bac86fb3ad8b2ce9775d23210de294296bcba5149fd58","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T10:41:36.771484Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-23T06:30:58.430688+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:35:35.753913Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-15T17:35:35.830029Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"cited_work":{"arxiv_id":"2504.17737","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.17737","snapshot_observed_at":"2026-08-15T17:35:35.830029Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","venue":"math.NT","work_id":"64687ba2-17e0-4423-83da-3dbf3859acb0","year":2025},"citing_paper":{"arxiv_id":"2508.12468","last_updated":"2025-08-17T18:48:25Z","snapshot_observed_at":"2026-08-19T22:02:48.367239Z","submitted_at":"2025-08-17T18:48:25Z","title":"Some New Modular Rank Four Nahm Sums as Lift-dual of Rank Three Examples","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T17:35:35.753913Z"},"links":{"cited_paper":"/paper/2504.17737","citing_paper":"/paper/2508.12468"},"observation_digest":"sha256:9d61067b35b3a26c700f214649e44690f8a53382d318938e1c2e5ab25091b439","observation_id":"51d2a9cb-ce70-49ec-b627-e8a9a9f3e39f","resolution":{"observed_at":"2026-08-15T17:35:35.836680Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.17737/citation-record","integrity":"/paper/2504.17737/integrity","json":"/paper/2504.17737/citation-record.json","paper":"/paper/2504.17737"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:37.081329Z","title":"Andrews, On the general Rogers–Ramanujan theorem, Pr ovidence, RI: Amer","venue":null,"work_id":"755ff0df-9d5e-465b-a4fb-b8577b3e4eda","year":1974},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.673843Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:9b7db9c78dc21a97243050a18620211a0e8ce4a173f0c32dbe433c1054d45390","observation_id":"d0a26cca-c601-45e0-a5a8-5bb3a36c8336","resolution":{"observed_at":"2026-08-16T10:41:37.086396Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T10:41:36.679726Z","title":"Andrews, The Theory of Partitions, Addison-Wesley, 1976; Reissued Cambridge, 1998","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.679726Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:686374b7e4f212cf20c300f7bbffcb9502e1f1dae5844132b404575e9f239483","observation_id":"d6392ab2-fdb1-46df-a98a-cd93f0d83ea1","resolution":{"observed_at":"2026-08-16T10:41:36.679726Z","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":"2026-08-16T10:41:37.053433Z","title":"Andrews and B.C","venue":null,"work_id":"1c4767c8-8ca3-435d-a26c-975ea9dd87dc","year":2009},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.684613Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:689e5320a2ca16bebb137c169bd2ce2ad4fa07dc76b8ad7e41d46b82c670315f","observation_id":"5011ed11-cafc-4ebd-b913-a81735f63c05","resolution":{"observed_at":"2026-08-16T10:41:37.058882Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T10:41:36.689461Z","title":"Calinescu, A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.689461Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:00d9564a87d7a331de49d56833cbd33d512eef254c78b3ee68f6b0b7897f9303","observation_id":"ad7206cd-9c93-4e18-a6fd-88c4918dce91","resolution":{"observed_at":"2026-08-16T10:41:36.689461Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.694700Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.694700Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:6e8cdb207f13b362fa81afcd600c58ae011da40618184739ef1bad22eb4e95e5","observation_id":"37d1ea5f-1081-4e21-97b8-b84e933ed68f","resolution":{"observed_at":"2026-08-16T10:41:36.694700Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.15767","last_updated":"2024-12-20T10:37:41Z","snapshot_observed_at":"2026-08-15T19:01:48.783993Z","submitted_at":"2024-12-20T10:37:41Z","title":"Some New Modular Rank Three Nahm Sums from a Lift-Dual Operation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.15767","snapshot_observed_at":"2026-08-16T10:41:36.699494Z","title":"Cao and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.699494Z"},"links":{"cited_paper":"/paper/2412.15767","citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:dc18698d218fd49660628262b73a6f996861280e100aaae42279df980c0839b3","observation_id":"fdfd22ff-b917-4d8a-843e-bb7b8bea4e38","resolution":{"observed_at":"2026-08-16T10:41:36.699494Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.704793Z","title":"Cherednik and B","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.704793Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:2b15c4d21d294818b103844d4c465a2e56bf2f1b446e67b1365b4e34737f953b","observation_id":"4cddad4c-4484-4cfd-b612-43409b47598a","resolution":{"observed_at":"2026-08-16T10:41:36.704793Z","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":"2026-08-16T10:41:36.999351Z","title":"Frye and F.G","venue":null,"work_id":"941533e6-b5d3-406d-a458-65c22284c4cd","year":2019},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.709871Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:5bbea8898bf4064b3b4c914ddd74a4e668907488f0bacd768494660a0b82d698","observation_id":"7433b9bf-1f12-4928-83f3-fa6820289c1a","resolution":{"observed_at":"2026-08-16T10:41:37.004567Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T10:41:36.976376Z","title":"Gordon, A combinatorial generalization of the Rogers–Raman ujan identities, Amer","venue":null,"work_id":"ab7ffb1b-0039-4fea-8c01-1a7d4242d83d","year":1961},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.714491Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:f386a762f3b02d3f9767c74ac2e3f5be0c9edeecbaba8c55e51c30b0c14c1d85","observation_id":"d91f0a6b-b64e-4e2a-9108-f0b15e6e9e02","resolution":{"observed_at":"2026-08-16T10:41:36.986194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T10:41:36.719300Z","title":"Milas and L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.719300Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:b132af4de05b960ca8eeb58959ae1af69880aa061d3fb90a9de934031979a34c","observation_id":"aab16fb3-b41e-4354-923d-67008d5023f4","resolution":{"observed_at":"2026-08-16T10:41:36.719300Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.724578Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.724578Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:3710a1d14ca60713b7c06e2e5f6b73b2a7231482d8529e4391ab0fd342b82026","observation_id":"3c24d1e3-14a8-4bcc-8388-289bfec81788","resolution":{"observed_at":"2026-08-16T10:41:36.724578Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.729442Z","title":"Interface between Physics and Mathematics (Proceedings, Conference in Ha ngzhou, People’s Republic of China, September 1993)","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.729442Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:1768f9e73d440b075a39491a06cc2223cd66b6e6aa36389a022ea6743a0b62fd","observation_id":"9767f99c-516b-430e-a385-91ec8640f533","resolution":{"observed_at":"2026-08-16T10:41:36.729442Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.734524Z","title":"Frontiers in Number Theory, Physics and Geometry","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.734524Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:48dcd272cd6911710aa35880e24d11a6a8dd2c995bc90f20588bd0830ea0f3a6","observation_id":"4dd64a3b-7d46-4a73-b320-ce367cb94250","resolution":{"observed_at":"2026-08-16T10:41:36.734524Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.738965Z","title":"Rogers, Second memoir on the expansion of certain infinite p roducts, Proc","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.738965Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:72951f2174634d8c30337f1ce8e6150092f2ba2dc8319d1a65357b47fddd136c","observation_id":"c1893bb9-d521-4871-9533-2b3c6cc3f1b7","resolution":{"observed_at":"2026-08-16T10:41:36.738965Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.743619Z","title":"Rogers, On two theorems of combinatory analysis and some allied identities, Proc","venue":null,"work_id":null,"year":1917},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.743619Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:341d73ae933b9f843fd92df3176be7353010d3357cd244e92377788c895f70ac","observation_id":"5dbb003d-4bf0-4955-b59a-df38cea0a330","resolution":{"observed_at":"2026-08-16T10:41:36.743619Z","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":"2026-08-16T10:41:36.893359Z","title":"Slater, Further identities of the Rogers–Ramanujan type","venue":null,"work_id":"a8be5a71-f40d-415d-b63d-04262d57f355","year":1952},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.748206Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:2b43fdae1e09d87933d70bf6f1b73a7196ab728b07696422c511c0491529681a","observation_id":"cdaffc4b-8580-4a00-81af-c9372777ff95","resolution":{"observed_at":"2026-08-16T10:41:36.898221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T10:41:36.877353Z","title":"Vlasenko and S","venue":null,"work_id":"a2ab0ac0-b786-46d3-9602-ec87331568c8","year":2011},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.752753Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:38f9769dcd2be4fd1f258edc030e83142f46149af46e1cb1be0a78fc5c47f71b","observation_id":"e5c25bd6-25f8-47f4-b97c-df876b67031d","resolution":{"observed_at":"2026-08-16T10:41:36.881848Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+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":"2026-08-16T10:41:36.757162Z","title":"Wang, Identities on Zagier’s rank two examples for Nahm’s pro blem, Res","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.757162Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:4b36379934aa6c2de461c092ae1e84a6f07185c7c8a635cb45f5472e6bc21384","observation_id":"15363a2f-9dce-42a9-9c4d-ea781461f4a3","resolution":{"observed_at":"2026-08-16T10:41:36.757162Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T10:41:36.761660Z","title":"Wang, Explicit forms and proofs of Zagier’s rank three examp les for Nahm’s problem, Adv","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.761660Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:b0daa380606bef952b4376d5a58873858abacc36506506c38f0a83fa7fff66be","observation_id":"4accb087-451a-475c-8f76-78ab30aa1396","resolution":{"observed_at":"2026-08-16T10:41:36.761660Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.09701","last_updated":"2025-01-14T15:31:35Z","snapshot_observed_at":"2026-08-15T09:04:44.781376Z","submitted_at":"2024-11-14T18:59:36Z","title":"Counterexamples to Zagier's Duality Conjecture on Nahm Sums","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.09701","snapshot_observed_at":"2026-08-16T10:41:36.766075Z","title":"Wang, Counterexamples to Zagier’s duality conjecture on Na hm sums, arXiv:2411.09701","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.766075Z"},"links":{"cited_paper":"/paper/2411.09701","citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:7f5f4c001289079c4832709f362d995bda50b2a7e43717b803463c9e7d532271","observation_id":"c15d2be4-9492-463c-b8c5-a33338e3f59f","resolution":{"observed_at":"2026-08-16T10:41:36.766075Z","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":"2026-08-16T10:41:36.837771Z","title":"Zagier, The dilogarithm function, in Frontiers in Number Theor y, Physics and Geometry, II, Springer, 2007, 3–65","venue":null,"work_id":"8440c937-4a94-498b-a5c6-4c4b43909ed2","year":2007},"citing_paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T10:41:36.771484Z"},"links":{"citing_paper":"/paper/2504.17737"},"observation_digest":"sha256:a5654e420ac1ec680ad38831a23f1f6696781364e49b1e3af43614395b193658","observation_id":"0da4a1e4-caa2-4915-a2a3-d93db80268b4","resolution":{"observed_at":"2026-08-16T10:41:36.844078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.17737","last_updated":"2025-04-24T16:49:38Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-19T23:33:30.002112Z","submitted_at":"2025-04-24T16:49:38Z","title":"Modularity of tadpole Nahm sums in ranks 4 and 5"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":14,"verified_exact":0,"verified_fuzzy":7},"total_outbound_references":21},"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":"2026-08-23T06:30:58.430688+00:00","source":"crossref"},{"observed_at":"2026-08-23T06:30:53.778098+00:00","source":"retraction_watch"}],"thesis":"As of 23 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2504.17737."}