{"as_of":"2026-08-23T17:54:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:699ce801b26b17dbf10738a0c9c37ed652a3936286a989d9a70c412f07eb8b3d","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-12T12:10:34.396168Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"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":"2026-08-01T00:03:48.126040Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2606.25866","snapshot_observed_at":"2026-08-01T00:03:48.126040Z","title":"Li, Proofs of four conjectural identities on modular rank four Nahm sums, arXiv:2606.25866","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.23257","last_updated":"2026-08-12T16:00:13Z","snapshot_observed_at":"2026-08-20T03:15:31.751529Z","submitted_at":"2026-07-25T15:51:01Z","title":"Nahm Sums Dual to Zagier's Rank-Three Examples and Related Identities","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T00:03:48.126040Z"},"links":{"cited_paper":"/paper/2606.25866","citing_paper":"/paper/2607.23257"},"observation_digest":"sha256:506b997949f1eecfdf07e0c939d8d7fa4ecbea612175419c77fe04845440d1e7","observation_id":"1991ee7a-ce6c-49f1-8168-2beddf603c33","resolution":{"observed_at":"2026-08-01T00:03:48.126040Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2606.25866/citation-record","integrity":"/paper/2606.25866/integrity","json":"/paper/2606.25866/citation-record.json","paper":"/paper/2606.25866"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-12T12:10:34.396168Z","title":"Andrews,The theory of partitions, Addison-Wesley, Reading, MA, 1976; reissued: Cambridge University Press, Cambridge, 1998","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:90e3897b8f819908ee02b8948108b77c07fa8b6a7e70727847da64d93d4d65b9","observation_id":"5151870b-b85a-4f47-8af4-84f5b3800a63","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Berndt,Number theory in the spirit of Ramanujan, American Mathematical Society, Providence, RI,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:01a31e764b1f35d70a8cec874c4841be10af25678afa5eba83587971961f7f3e","observation_id":"eb658182-84ce-4d94-bff8-759a1bc9fbb6","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Borwein, P.B","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:b832f00cc225330cfa75ce282b8c88ca8464b2cc2470d0cb9531b3800dbb86e7","observation_id":"27adbca5-1392-4b0e-9d68-11be792da92a","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Calinescu, A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:979d529713919788a3e07ebca590855327413c1f23bf7a432e03e8bacf41ffc9","observation_id":"9c63bf01-4ec2-4c23-a497-01675d091b73","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:4c803838080ebadc05f780203fd53aa7c4a5c8379487e5caf4b4f2a744e6a32b","observation_id":"1af494bc-4aa9-4c47-8796-fde3266e15b4","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Cao and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"cited_paper":"/paper/2412.15767","citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:308a32534137c1c330bf0ed5768baa187a1ab862b36e06ea160076330538e238","observation_id":"f3f719cc-34f9-45b2-9728-4f11b7eab829","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.12468","snapshot_observed_at":"2026-07-12T12:10:34.396168Z","title":"Cao and L","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"cited_paper":"/paper/2508.12468","citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:eae7febf86bedbd6b8fb05b1c08848796bcd6b4265e880e4866d9b12774ee42f","observation_id":"e6f554e2-f172-49d0-b845-a19aedf6033b","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Cherednik and B","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:f319f1f8d472db68826b87af87c168034d7c4a214bc88dc4b61baa6bc06e126b","observation_id":"28d0c3b2-36b8-4fc7-9d93-0a5b04057555","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Gasper and M","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:f4086e5e430c6f0cc6538c71a668f794df5d6efbc4213b8bcf035409c39fa0e2","observation_id":"b524ebf8-8077-40ee-b672-f69f4dd496b1","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:c2e234fd739eeaab084dd814b5e848fde265d8997135569db7bf3c687c19907d","observation_id":"e16403fd-b37e-4cf3-b8cb-11ace8e925d4","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Nahm, Conformal field theory, dilogarithm and three dimensional manifold, in: W","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:7455010d810bc6d318ec83e5e4a9c0c351d4bee2db982d4dac994517716bf88e","observation_id":"d567abc8-99dd-4ef2-9cfb-2cd4fee53414","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Nahm, Conformal field theory and torsion elements of the Bloch group, in: Frontiers in Number Theory, Physics and Geometry, II, Springer, 2007, pp","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:6356af12926757d7c98bb6e250a9bb8036865b26638a356ec8eef0c51b1d9075","observation_id":"d1ddb9f7-b42e-47bc-a54a-7ce34e4399d1","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Ramanujan, Problem 584, J","venue":null,"work_id":null,"year":1914},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:11b421b95e3fd17c2303ba8bfac3d728d5066b18367d06fd5d34d69ef2217802","observation_id":"a8c74225-fd01-40d1-8361-6bee2afb1ccf","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Ramanujan, Proof of certain identities in combinatory analysis, Proc","venue":null,"work_id":null,"year":1919},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:7f2aa50dc2f1108c71fe80866d919a42031390f59487ae7ee0f318b28fbdf335","observation_id":"48f62c83-a606-4062-8d32-4722eccc507f","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Rogers, Third memoir on the expansion of certain infinite products, Proc","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:71b093c091aefd0b8e9669e6a3ebcabe5017e814d6ccb0ce460976defa6893b0","observation_id":"503b8a9d-985c-43be-9847-8f4aafb0f86d","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Schur, Ein Beitrag zur additiven Zahlentheorie und zur Theorie der Kettenbrüche, Sitzungsber","venue":null,"work_id":null,"year":1917},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:2dd1d37d24a1b05f5a79b0049534678a12e3af5242c6217ae997c67a2bd1b8a1","observation_id":"a51ca5fa-7583-45b2-aba0-ba0310934bef","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Shi and L","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:0d411dc41cf5a8eca9e0124c7c46eaf439da6eaea03709c6568cf620f9667011","observation_id":"4a107128-5f4e-45bd-a852-edfc9fb7adc7","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Sills,An invitation to the Rogers-Ramanujan identities, CRC Press, Boca Raton (2018)","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:207515dceaf455af76d9cd760d496f045f563c6604775a424e50a08e54814bd5","observation_id":"80d6ed0a-9a05-4a94-86b0-e022891bd8a8","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Vlasenko and S","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:c4c585c967d489e0b5fe0beb5d0ff3a7253ed6a4da1f20bf9e486f5552578ba3","observation_id":"e809a985-7ef6-4d7f-afa7-c2b6bd400afa","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Wang, Identities on Zagier’s rank two examples for Nahm’s conjecture, Res","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:437728102671c688548d8393f88004d834d3dfcf41e0ca14764ce08a36038874","observation_id":"361ff18c-144a-41a9-8f91-7195c679d20e","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Wang, Explicit forms and proofs of Zagier’s rank three examples for Nahm’s problem, Adv","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:277ea9fe4794372c277e2f9862ad1718a8350deeff5520a45ce3b32bd1d20c2e","observation_id":"74f4ef9a-0623-4594-a361-b798e598de55","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","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":"2026-07-12T12:10:34.396168Z","title":"Zagier, The dilogarithm function, in: Frontiers in Number Theory, Physics and Geometry, II, Springer- Verlag, 2007, pp","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-12T12:10:34.396168Z"},"links":{"citing_paper":"/paper/2606.25866"},"observation_digest":"sha256:3ec9d886d268c02afdb546f3d0b50b3694b2eaf820514a47ede7049202bfc184","observation_id":"97619660-b7be-499f-8f34-5e9efb35405f","resolution":{"observed_at":"2026-07-12T12:10:34.396168Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.25866","last_updated":"2026-07-07T04:22:48Z","latest_version":3,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T21:49:59.512472Z","submitted_at":"2026-06-24T14:13:10Z","title":"Proofs of five conjectural identities on modular rank four Nahm sums"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":22,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":22},"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 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2606.25866."}