{"as_of":"2026-08-07T10:34:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ef064c8c1ca9c472858a0b2ef917a817a098cd02e616c22b575131dfd065075e","coverage":[{"denominator":34,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":34,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T18:54:04.400124Z","state":"measured"},{"denominator":37,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":37,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T20:40:40.261037Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-14T17:32:30.720458Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.14030","snapshot_observed_at":"2026-08-03T18:57:04.783250Z","title":"Del Monte, H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2512.03172","last_updated":"2026-01-26T09:52:58Z","snapshot_observed_at":"2026-08-03T18:57:00.619976Z","submitted_at":"2025-12-02T19:15:44Z","title":"On the Virasoro Crossing Kernels at Rational Central Charge","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-03T18:57:04.783250Z"},"links":{"cited_paper":"/paper/2508.14030","citing_paper":"/paper/2512.03172"},"observation_digest":"sha256:6426e98131c99258153bfec6e68714780cb7718992437c282b35de401e617e6b","observation_id":"c615261d-9e3d-4058-b640-589bb9e3a75c","resolution":{"observed_at":"2026-08-03T18:57:04.783250Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"cited_work":{"arxiv_id":"2508.14030","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2508.14030","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Modular transformations of tau functions and conformal blocks on the torus","venue":null,"work_id":"74467941-8f84-4fd3-a2d9-39240cfbc06d","year":2025},"citing_paper":{"arxiv_id":"2605.13802","last_updated":"2026-05-13T17:24:46Z","snapshot_observed_at":"2026-07-06T23:25:21.032938Z","submitted_at":"2026-05-13T17:24:46Z","title":"Irregular SLE(4) martingales and isomonodromic deformations","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-05-14T17:30:45.910038Z"},"links":{"cited_paper":"/paper/2508.14030","citing_paper":"/paper/2605.13802"},"observation_digest":"sha256:c779b4a8057a3e241b0003bac0d16b875bf324efa81c13050ce98566e0a4e63c","observation_id":"2be91da9-b388-49d5-8584-a0c5bfaac5df","resolution":{"observed_at":"2026-05-14T17:32:30.723682Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.14030","snapshot_observed_at":"2026-08-05T20:40:40.261037Z","title":"Schlesinger transformations of Painlev´ e II–V","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2608.03345","last_updated":"2026-08-04T08:54:49Z","snapshot_observed_at":"2026-08-07T10:16:15.803973Z","submitted_at":"2026-08-04T08:54:49Z","title":"A Tau function for $q$-Painlev\\'e VI as a Fredholm determinant","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T20:40:40.261037Z"},"links":{"cited_paper":"/paper/2508.14030","citing_paper":"/paper/2608.03345"},"observation_digest":"sha256:511f2faab9b70f59e1dfaf8c691fa489cc9a2ddb1362b47401f4f21a15eae8f7","observation_id":"d20930bf-7835-417d-afb4-a7176e9ad5fc","resolution":{"observed_at":"2026-08-05T20:40:40.261037Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2508.14030/citation-record","integrity":"/paper/2508.14030/integrity","json":"/paper/2508.14030/citation-record.json","paper":"/paper/2508.14030"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:54:09.861438Z","title":null,"venue":null,"work_id":"72b54b83-82a6-46d8-8e39-f96749fcde9a","year":1991},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:00.305837Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:914de65f57086162d398d1a77b5d0ac759d336713bfb9e5177decd2cf3176146","observation_id":"132892bb-829a-4581-be18-f94ddb1180e1","resolution":{"observed_at":"2026-08-05T18:54:10.014763Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1608.00958","last_updated":"2018-10-29T14:03:56Z","snapshot_observed_at":"2026-08-06T15:02:35.071577Z","submitted_at":"2016-08-02T19:43:10Z","title":"Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions","version":3},"cited_work":{"arxiv_id":"1608.00958","doi":null,"metadata_source":"pith","pith_arxiv_id":"1608.00958","snapshot_observed_at":"2026-08-05T18:54:07.848409Z","title":"Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions","venue":"math-ph","work_id":"ab24e876-e35b-4592-a6cd-a494b49be8d6","year":2016},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:00.394487Z"},"links":{"cited_paper":"/paper/1608.00958","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:f37066863db6216e5b836de2ad2909397ca8083879891c8cccd754a193220487","observation_id":"852dabf9-df70-4af1-a3a8-59c6be86e5d6","resolution":{"observed_at":"2026-08-05T18:54:07.993310Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1308.4092","last_updated":"2013-09-09T18:37:33Z","snapshot_observed_at":"2026-08-06T15:01:08.999724Z","submitted_at":"2013-08-19T18:43:26Z","title":"Painlev\\'e VI connection problem and monodromy of c=1 conformal blocks","version":2},"cited_work":{"arxiv_id":"1308.4092","doi":null,"metadata_source":"pith","pith_arxiv_id":"1308.4092","snapshot_observed_at":"2026-08-05T18:54:07.674568Z","title":"Painlev\\'e VI connection problem and monodromy of c=1 conformal blocks","venue":"hep-th","work_id":"12cfe7de-2be5-4723-aa62-b2b3ff50e802","year":2013},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:00.526675Z"},"links":{"cited_paper":"/paper/1308.4092","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:31cb011696b76f9a405af87e0bc0cf050128f538eaa9d07a1653e547370a4f5f","observation_id":"b93b9a5a-1fe2-4f31-a72f-66e18355ee8f","resolution":{"observed_at":"2026-08-05T18:54:07.731226Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1403.1235","last_updated":"2014-03-05T19:47:04Z","snapshot_observed_at":"2026-07-06T03:37:41.825265Z","submitted_at":"2014-03-05T19:47:04Z","title":"Connection problem for the sine-Gordon/Painlev\\'e III tau function and irregular conformal blocks","version":1},"cited_work":{"arxiv_id":"1403.1235","doi":null,"metadata_source":"pith","pith_arxiv_id":"1403.1235","snapshot_observed_at":"2026-08-05T18:54:07.405763Z","title":"Connection problem for the sine-Gordon/Painlev\\'e III tau function and irregular conformal blocks","venue":"math-ph","work_id":"92cd60be-f8ec-4337-b400-0f60e7b247a9","year":2014},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:00.653384Z"},"links":{"cited_paper":"/paper/1403.1235","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:a2cdea861ad3fe5d743a34393a7dfdeeeefffce3d285247f26813ae70f0e72c0","observation_id":"a84bb57f-bc3b-4581-8900-8cc03ea0d5ad","resolution":{"observed_at":"2026-08-05T18:54:07.525925Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1604.03082","last_updated":"2018-10-29T12:39:31Z","snapshot_observed_at":"2026-08-06T15:01:35.152864Z","submitted_at":"2016-04-11T19:46:16Z","title":"Monodromy dependence and connection formulae for isomonodromic tau functions","version":4},"cited_work":{"arxiv_id":"1604.03082","doi":null,"metadata_source":"pith","pith_arxiv_id":"1604.03082","snapshot_observed_at":"2026-08-05T18:54:07.138727Z","title":"Monodromy dependence and connection formulae for isomonodromic tau functions","venue":"math-ph","work_id":"2fa9c1b0-0c7a-4d7b-87b0-7da74f24aea9","year":2016},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:00.760135Z"},"links":{"cited_paper":"/paper/1604.03082","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:e5cc24548c5ef0909091f483831d2f70e652de2c5122b6827b6f713914d34620","observation_id":"67d53bf3-a803-4a7e-b858-fd5f7446d370","resolution":{"observed_at":"2026-08-05T18:54:07.275153Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2011.06292","last_updated":"2021-05-04T21:20:13Z","snapshot_observed_at":"2026-08-07T06:12:11.338743Z","submitted_at":"2020-11-12T10:08:43Z","title":"Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions","version":2},"cited_work":{"arxiv_id":"2011.06292","doi":null,"metadata_source":"pith","pith_arxiv_id":"2011.06292","snapshot_observed_at":"2026-08-05T18:54:06.834292Z","title":"Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions","venue":"math-ph","work_id":"29ffcf3c-7e24-4262-bc98-a01b0f020eb9","year":2020},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:00.910279Z"},"links":{"cited_paper":"/paper/2011.06292","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:abbda71e6997dfa27bd9b9b536415e5ae7939d07a5176cb77dcfb634b2aa3e92","observation_id":"b3381c57-d394-47ce-b1d8-67b950d57371","resolution":{"observed_at":"2026-08-05T18:54:06.980645Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1901.10497","last_updated":"2019-07-16T09:15:52Z","snapshot_observed_at":"2026-08-04T22:11:49.815722Z","submitted_at":"2019-01-29T19:00:29Z","title":"$\\mathcal{N}=2^*$ gauge theory, free fermions on the torus and Painlev\\'e VI","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1901.10497","snapshot_observed_at":"2026-08-05T18:54:01.050976Z","title":"Bonelli, F","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.050976Z"},"links":{"cited_paper":"/paper/1901.10497","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:af32d679fd21401eb2b737050687faec85d291ac467f47a86b7800f90b1ea80a","observation_id":"d27b583f-6a19-49af-8957-33d9d247ce78","resolution":{"observed_at":"2026-08-05T18:54:01.050976Z","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":"1909.07990","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:54:06.572786Z","title":"Bonelli, F","venue":null,"work_id":"27d1fd5d-522c-4dc8-8a12-d5a7c9293435","year":2021},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.168108Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:64f956bd17ef1ac53ca69b8f599ff30eea6fccdac7c43424dcfa74dbb6788531","observation_id":"d00f7cb6-aa69-40c0-ae64-18f494cdc613","resolution":{"observed_at":"2026-08-05T18:54:06.692550Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.01139","last_updated":"2022-11-02T14:18:29Z","snapshot_observed_at":"2026-07-06T14:13:35.791125Z","submitted_at":"2022-11-02T14:18:29Z","title":"Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus","version":1},"cited_work":{"arxiv_id":"2211.01139","doi":null,"metadata_source":"pith","pith_arxiv_id":"2211.01139","snapshot_observed_at":"2026-08-05T18:54:06.270269Z","title":"Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus","venue":"math-ph","work_id":"57f04e7a-0727-49dd-a29b-ddff113486c1","year":2022},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.287449Z"},"links":{"cited_paper":"/paper/2211.01139","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:0f66280a3ca5709c671b45a8442f781c2a88a988fad21c0b95ba05a71980d67a","observation_id":"215f7152-4ced-41de-a995-0d042e897c19","resolution":{"observed_at":"2026-08-05T18:54:06.411198Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1910.03370","last_updated":"2022-01-17T17:43:02Z","snapshot_observed_at":"2026-07-06T08:27:46.186150Z","submitted_at":"2019-10-08T13:00:21Z","title":"Tau-functions and monodromy symplectomorphisms","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1910.03370","snapshot_observed_at":"2026-08-05T18:54:01.418196Z","title":"Bertola and D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.418196Z"},"links":{"cited_paper":"/paper/1910.03370","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:d31063359ad30b1133bdda66589e9f9be5bf357d5a3e77674919723094bcd2da","observation_id":"295b9ec1-5cc1-4365-91f6-31f201c9470a","resolution":{"observed_at":"2026-08-05T18:54:01.418196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1803.04212","last_updated":"2024-08-05T16:42:30Z","snapshot_observed_at":"2026-07-06T06:27:46.580255Z","submitted_at":"2018-03-12T12:03:08Z","title":"On some Hamiltonian properties of the isomonodromic tau functions","version":3},"cited_work":{"arxiv_id":"1803.04212","doi":null,"metadata_source":"pith","pith_arxiv_id":"1803.04212","snapshot_observed_at":"2026-08-05T18:54:05.991461Z","title":"On some Hamiltonian properties of the isomonodromic tau functions","venue":"math-ph","work_id":"07e44b3c-3f4a-445c-b2b4-6f9b35012c8e","year":2018},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.537967Z"},"links":{"cited_paper":"/paper/1803.04212","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:1e29353711878698e122a0655fd46a29de21b68a0c2ea50a87ffaa0416f63788","observation_id":"60c757c7-8e0e-44b3-8072-6f8df940070d","resolution":{"observed_at":"2026-08-05T18:54:06.115062Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0906.3219","last_updated":"2010-02-09T15:57:35Z","snapshot_observed_at":"2026-07-06T01:54:44.463533Z","submitted_at":"2009-06-17T15:51:28Z","title":"Liouville Correlation Functions from Four-dimensional Gauge Theories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0906.3219","snapshot_observed_at":"2026-08-05T18:54:01.632762Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.632762Z"},"links":{"cited_paper":"/paper/0906.3219","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:c6f5e725da4dcc3a793f5c0a53f83e7c44cf4e7054ea84cbfe67fd1916104206","observation_id":"698a9b5f-6060-4f44-91f0-08e6029f1db3","resolution":{"observed_at":"2026-08-05T18:54:01.632762Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.04240","last_updated":"2023-05-07T10:18:02Z","snapshot_observed_at":"2026-07-06T15:24:15.063725Z","submitted_at":"2023-05-07T10:18:02Z","title":"Painlev\\'e/CFT correspondence on a torus","version":1},"cited_work":{"arxiv_id":"2305.04240","doi":null,"metadata_source":"pith","pith_arxiv_id":"2305.04240","snapshot_observed_at":"2026-08-05T18:54:05.706780Z","title":"Painlev\\'e/CFT correspondence on a torus","venue":"math-ph","work_id":"2ddad892-8a25-490b-9962-bf10303eb378","year":2023},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.762728Z"},"links":{"cited_paper":"/paper/2305.04240","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:5b0292cc6760cb5a67f28412561b877b14c6da63d663942c86ac80e6316bb3fd","observation_id":"b889672e-dedd-47c4-bac8-aa0dcb1fa3d9","resolution":{"observed_at":"2026-08-05T18:54:05.797996Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0306238","last_updated":"2003-06-25T22:23:36Z","snapshot_observed_at":"2026-07-07T04:47:28.422616Z","submitted_at":"2003-06-25T01:02:14Z","title":"Seiberg-Witten Theory and Random Partitions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0306238","snapshot_observed_at":"2026-08-05T18:54:01.873604Z","title":"Nekrasov and A","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:01.873604Z"},"links":{"cited_paper":"/paper/hep-th/0306238","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:e048a7fcc956582f87cc18d94ffc485a2f12cf7c8a99765a5a721261aec78bea","observation_id":"82eb357f-b13b-410e-a650-9a97e19a6740","resolution":{"observed_at":"2026-08-05T18:54:01.873604Z","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":"2026-08-05T18:54:09.512473Z","title":"NIST Digital Library of Mathematical Functions","venue":null,"work_id":"02a35b04-871b-4821-a338-780ce38c65e1","year":2025},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.047143Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:7a592c8b8d3594c3ae2171371fa8f9cfde7dc78fae06d9bc16a95cc0b9193425","observation_id":"45149267-61a1-4068-9019-9f27d8e6684d","resolution":{"observed_at":"2026-08-05T18:54:09.674538Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"alg-geom/9605010","last_updated":"1996-05-22T11:02:16Z","snapshot_observed_at":"2026-07-07T00:08:48.976823Z","submitted_at":"1996-05-22T11:02:16Z","title":"Sixth Painlev\\'e Equation, Universal Elliptic Curve, and Mirror of $\\bold{P}^2$","version":1},"cited_work":{"arxiv_id":"alg-geom/9605010","doi":null,"metadata_source":"pith","pith_arxiv_id":"alg-geom/9605010","snapshot_observed_at":"2026-08-05T18:54:05.461655Z","title":"Sixth Painlev\\'e Equation, Universal Elliptic Curve, and Mirror of $\\bold{P}^2$","venue":"alg-geom","work_id":"3272eb54-361e-42d1-920c-a961d8476546","year":1996},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.214147Z"},"links":{"cited_paper":"/paper/alg-geom/9605010","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:83128d3d1e0fd025368d7b7d8d17f08fa63a37c203f5f95e5068219bc1c775cd","observation_id":"e624adf7-ef0e-413e-9675-0eabecab1ee4","resolution":{"observed_at":"2026-08-05T18:54:05.602967Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1103.3919","last_updated":"2013-10-29T12:51:03Z","snapshot_observed_at":"2026-07-06T02:25:06.571479Z","submitted_at":"2011-03-21T05:01:41Z","title":"Darboux coordinates, Yang-Yang functional, and gauge theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1103.3919","snapshot_observed_at":"2026-08-05T18:54:02.357394Z","title":"Nekrasov, A","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.357394Z"},"links":{"cited_paper":"/paper/1103.3919","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:3f2f6bab7a113d7b266f57e4d4cc70c98e376d9acb868a85682661b0be163ec4","observation_id":"71b2b121-cf5d-4218-97aa-dc45e341bc2f","resolution":{"observed_at":"2026-08-05T18:54:02.357394Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0308031","last_updated":"2003-10-27T12:59:45Z","snapshot_observed_at":"2026-07-07T04:47:57.962875Z","submitted_at":"2003-08-05T09:55:42Z","title":"From Liouville Theory to the Quantum Geometry of Riemann Surfaces","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0308031","snapshot_observed_at":"2026-08-05T18:54:02.435532Z","title":"Teschner, From Liouville theory to the quantum geometry of Riemann surfaces , in 14th International Congress on Mathematical Physics , 8, 2003, hep-th/0308031","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.435532Z"},"links":{"cited_paper":"/paper/hep-th/0308031","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:2a2dcc62479ff480ba5175624d9de86867c71a1dce9632b6eb12ca98ca7c9c41","observation_id":"ecd8c3fd-b5eb-4df2-92c4-cd1063da0d47","resolution":{"observed_at":"2026-08-05T18:54:02.435532Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1504.04360","last_updated":"2015-04-27T08:47:29Z","snapshot_observed_at":"2026-08-04T05:16:28.340557Z","submitted_at":"2015-04-16T19:53:37Z","title":"On modular transformations of non-degenerate toric conformal blocks","version":2},"cited_work":{"arxiv_id":"1504.04360","doi":null,"metadata_source":"pith","pith_arxiv_id":"1504.04360","snapshot_observed_at":"2026-08-05T18:54:05.239444Z","title":"On modular transformations of non-degenerate toric conformal blocks","venue":"hep-th","work_id":"f27f749d-33be-4b36-bbc5-0f751720e4d7","year":2015},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.560382Z"},"links":{"cited_paper":"/paper/1504.04360","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:ad06d7a2fb1f0fdda335c080d09f95ac47448e4b4370ad3a282dc6498bba9943","observation_id":"06ea354e-f719-4658-b10d-4d7368be9c69","resolution":{"observed_at":"2026-08-05T18:54:05.307376Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2309.11540","last_updated":"2023-09-20T18:00:01Z","snapshot_observed_at":"2026-07-06T16:21:25.401345Z","submitted_at":"2023-09-20T18:00:01Z","title":"Notes on crossing transformations of Virasoro conformal blocks","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.11540","snapshot_observed_at":"2026-08-05T18:54:02.741892Z","title":"Eberhardt, Notes on crossing transformations of Virasoro conformal blocks , 2309.11540","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.741892Z"},"links":{"cited_paper":"/paper/2309.11540","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:8e8170c53880cd565bbe6b0b30f7dced6397a27220e6ab9ec7262fdbf7177361","observation_id":"2de30daf-31d8-47c1-87f8-aaa4214bc8b3","resolution":{"observed_at":"2026-08-05T18:54:02.741892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0306198","last_updated":"2005-02-17T01:23:05Z","snapshot_observed_at":"2026-07-07T05:35:29.780377Z","submitted_at":"2003-06-12T06:01:32Z","title":"Instanton counting on blowup. I. 4-dimensional pure gauge theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0306198","snapshot_observed_at":"2026-08-05T18:54:02.858119Z","title":"Nakajima and K","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.858119Z"},"links":{"cited_paper":"/paper/math/0306198","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:e7c66019f49585c4af21f8da7c585e4f07d96c79d15c30baf05bdb7b0533f2ff","observation_id":"6c6fadcc-ec85-4cec-8033-2eeceb5046ac","resolution":{"observed_at":"2026-08-05T18:54:02.858119Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.00985","last_updated":"2021-09-15T20:33:20Z","snapshot_observed_at":"2026-07-06T11:05:52.466639Z","submitted_at":"2021-05-03T16:33:41Z","title":"Quantum spectral problems and isomonodromic deformations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.00985","snapshot_observed_at":"2026-08-05T18:54:02.975194Z","title":"Bershtein, P","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:02.975194Z"},"links":{"cited_paper":"/paper/2105.00985","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:90af5a4e70eda69e2eda318cf161597023e1225b76c079842dbf809f11707242","observation_id":"c9a2d1ca-d54f-401a-b50e-d9f3803de494","resolution":{"observed_at":"2026-08-05T18:54:02.975194Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.03802","last_updated":"2024-01-28T23:41:05Z","snapshot_observed_at":"2026-08-06T11:00:47.669322Z","submitted_at":"2020-03-08T15:40:51Z","title":"Probabilistic conformal blocks for Liouville CFT on the torus","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.03802","snapshot_observed_at":"2026-08-05T18:54:03.113024Z","title":"Ghosal, G","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.113024Z"},"links":{"cited_paper":"/paper/2003.03802","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:18705385cf3e258f1cfbbfb3b2cd81bbe4db757a599938b2b05e9638d3ee3862","observation_id":"8317f9f3-a396-4c07-82c1-196d2690870e","resolution":{"observed_at":"2026-08-05T18:54:03.113024Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.05839","last_updated":"2026-07-14T16:55:56Z","snapshot_observed_at":"2026-08-04T07:40:16.027647Z","submitted_at":"2024-07-08T11:38:28Z","title":"Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.05839","snapshot_observed_at":"2026-08-05T18:54:03.217711Z","title":"Desiraju, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.217711Z"},"links":{"cited_paper":"/paper/2407.05839","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:45aa982bcad34b25c6a585120e66e1955a343f7ac031afed4e25cba5f2e8cba4","observation_id":"cf158671-f1e2-4885-bf51-5598c713e14e","resolution":{"observed_at":"2026-08-05T18:54:03.217711Z","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":"media/3088980","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T18:54:05.024234Z","title":"Painlev´ e functions, accessory parameters and conformal blocks","venue":null,"work_id":"dc7ea867-0946-4103-bb43-9bae9991da2e","year":2019},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.314298Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:b69d8b5e931661f1167805ea07e20ce933cf0c9f1a431f04fb6215345771fd70","observation_id":"1fc234a3-29b3-4e66-84f3-287f0e7fdbfb","resolution":{"observed_at":"2026-08-05T18:54:05.116439Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.01419","last_updated":"2025-01-02T18:58:54Z","snapshot_observed_at":"2026-08-07T08:08:05.379748Z","submitted_at":"2025-01-02T18:58:54Z","title":"Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general $q$-Painlev\\'e III$_3$ tau functions","version":1},"cited_work":{"arxiv_id":"2501.01419","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.01419","snapshot_observed_at":"2026-08-05T18:54:04.759685Z","title":"Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general $q$-Painlev\\'e III$_3$ tau functions","venue":"math-ph","work_id":"7494c41d-1138-4b04-820b-4e00f0c37f75","year":2025},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.444427Z"},"links":{"cited_paper":"/paper/2501.01419","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:ef4261e52419915fa0f24380f5063cdd5c00aaf55c765cde06b3264995750e99","observation_id":"cbcf9500-7c9a-47be-814d-88e1d3328328","resolution":{"observed_at":"2026-08-05T18:54:04.877100Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-05T18:54:09.186282Z","title":"Reshetikhin, The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem, Letters in Mathematical Physics 26 (1992) 167","venue":null,"work_id":"1699668a-09dd-4c66-890f-3b858d084ac4","year":1992},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.570162Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:2e1a109e4a54b39d2df0258a8c468966d1d8c780bd00c997e6ca7b8636300658","observation_id":"14bf5820-69a8-41c3-bc97-53f679daf655","resolution":{"observed_at":"2026-08-05T18:54:09.324380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9406078","last_updated":"1994-06-15T19:01:46Z","snapshot_observed_at":"2026-08-02T14:25:20.412677Z","submitted_at":"1994-06-14T00:33:54Z","title":"Quantum Isomonodromic Deformations and the Knizhnik--Zamolodchikov Equations","version":2},"cited_work":{"arxiv_id":"hep-th/9406078","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/9406078","snapshot_observed_at":"2026-08-05T18:54:04.539110Z","title":"Quantum Isomonodromic Deformations and the Knizhnik--Zamolodchikov Equations","venue":"hep-th","work_id":"ac1c991f-b561-45d5-b458-dd39a25da420","year":1994},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.671190Z"},"links":{"cited_paper":"/paper/hep-th/9406078","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:79eeff8335c6d873ee17c4b176e2565069cf2460c8ae94eaab308be0ce04a929","observation_id":"2068994b-d720-49eb-b46f-9ab3ed0fb33d","resolution":{"observed_at":"2026-08-05T18:54:04.622609Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-05T18:54:08.934081Z","title":null,"venue":null,"work_id":"90f6c0b1-1a31-4f78-9f46-536692f875a5","year":1984},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.823051Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:be43dd04c2a1cd4a32f3a435be4ff7d43b73b2cffd93300787708c334f41b9ae","observation_id":"e94f10dd-a990-4fd6-8652-d10195fe8af6","resolution":{"observed_at":"2026-08-05T18:54:09.084370Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-05T18:54:08.690218Z","title":"Bernard, On the Wess-Zumino-Witten Models on the Torus , Nucl","venue":null,"work_id":"bffbe843-490e-40c6-9d39-5033f38f4551","year":1988},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:03.976940Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:4ca69458d374872adca3df4304b7c8f3cc7e53d803cbf101d101196718abe782","observation_id":"46492690-c739-480d-a805-936b3f171fed","resolution":{"observed_at":"2026-08-05T18:54:08.798471Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-05T18:54:08.397608Z","title":"Bernard, On the Wess-Zumino-Witten Models on Riemann Surfaces , Nucl","venue":null,"work_id":"7ab80de6-3ecb-4e8d-a6e1-0547ee8e75e2","year":1988},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:04.083575Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:b8e0cb11e60dac9de6e64b2002f5489e3078b37292743f438b7ca3c72b6d20b5","observation_id":"284678dc-408d-4d20-b625-0c2b024da71e","resolution":{"observed_at":"2026-08-05T18:54:08.542250Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-05T18:54:08.086964Z","title":"Witten, Quantization of Chern-Simons Gauge Theory With Complex Gauge Group , Commun","venue":null,"work_id":"ca545275-a715-4af9-9891-0fdba1ac2979","year":1991},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:04.209716Z"},"links":{"citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:3f913b400b10a1c662ae86c976ced27c99048ddaa1dfde7c343b37a15f2573bb","observation_id":"91c12c6e-999f-4ba5-8ca5-262f355e1828","resolution":{"observed_at":"2026-08-05T18:54:08.213319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1106.4550","last_updated":"2011-06-22T20:00:05Z","snapshot_observed_at":"2026-07-06T02:29:43.476297Z","submitted_at":"2011-06-22T20:00:05Z","title":"Chern-Simons Theory and S-duality","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1106.4550","snapshot_observed_at":"2026-08-05T18:54:04.315076Z","title":"Dimofte and S","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:04.315076Z"},"links":{"cited_paper":"/paper/1106.4550","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:f2aaac44b57f6e184d002e9557afa880d683194aec5fc590b6cdb5c260fe20ed","observation_id":"916f0809-077a-4dec-afdd-f4bee1f264d7","resolution":{"observed_at":"2026-08-05T18:54:04.315076Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1304.6721","last_updated":"2013-04-24T20:00:02Z","snapshot_observed_at":"2026-07-31T17:05:29.348429Z","submitted_at":"2013-04-24T20:00:02Z","title":"RG Domain Walls and Hybrid Triangulations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1304.6721","snapshot_observed_at":"2026-08-05T18:54:04.400124Z","title":"Dimofte, D","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T18:54:04.400124Z"},"links":{"cited_paper":"/paper/1304.6721","citing_paper":"/paper/2508.14030"},"observation_digest":"sha256:11ffbb6653e6c48b5178ebae672f050d286eb87125b9d313b799da38e68058f7","observation_id":"0c7d0145-77b4-493e-8832-92c90ab5719b","resolution":{"observed_at":"2026-08-05T18:54:04.400124Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2508.14030","last_updated":"2025-08-19T17:43:35Z","latest_version":1,"primary_category":"math-ph","snapshot_observed_at":"2026-08-06T15:01:10.425723Z","submitted_at":"2025-08-19T17:43:35Z","title":"Modular transformations of tau functions and conformal blocks on the torus"},"reference_resolution":{"displayed":34,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":14,"verified_fuzzy":5},"total_outbound_references":34},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 3 inbound Pith citation observations for arXiv:2508.14030."}