Paper Citation Record · LEDGER

Modular transformations of tau functions and conformal blocks on the torus

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.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2508.14030 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T18:54:04.400124Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T20:40:40.261037Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-14T17:32:30.720458Z

Reference resolution

34 of 34 outbound references displayed

verified exact14
verified fuzzy5
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 132892bb-829a-4581-be18-f94ddb1180e1 · outbound

This paper cites an unresolved cited work.

Modular transformations of tau functions and conformal blocks on the torus Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:54:10.014763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 852dabf9-df70-4af1-a3a8-59c6be86e5d6 · outbound

This paper cites Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions.

Modular transformations of tau functions and conformal blocks on the torus Fredholm determinant and Nekrasov sum representations of isomonodromic tau functions

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:07.993310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b93b9a5a-1fe2-4f31-a72f-66e18355ee8f · outbound

This paper cites Painlev\'e VI connection problem and monodromy of c=1 conformal blocks.

Modular transformations of tau functions and conformal blocks on the torus Painlev\'e VI connection problem and monodromy of c=1 conformal blocks

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:07.731226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a84bb57f-bc3b-4581-8900-8cc03ea0d5ad · outbound

This paper cites Connection problem for the sine-Gordon/Painlev\'e III tau function and irregular conformal blocks.

Modular transformations of tau functions and conformal blocks on the torus Connection problem for the sine-Gordon/Painlev\'e III tau function and irregular conformal blocks

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:07.525925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 67d53bf3-a803-4a7e-b858-fd5f7446d370 · outbound

This paper cites Monodromy dependence and connection formulae for isomonodromic tau functions.

Modular transformations of tau functions and conformal blocks on the torus Monodromy dependence and connection formulae for isomonodromic tau functions

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:07.275153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b3381c57-d394-47ce-b1d8-67b950d57371 · outbound

This paper cites Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions.

Modular transformations of tau functions and conformal blocks on the torus Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:06.980645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d27b583f-6a19-49af-8957-33d9d247ce78 · outbound

This paper cites $\mathcal{N}=2^*$ gauge theory, free fermions on the torus and Painlev\'e VI.

Modular transformations of tau functions and conformal blocks on the torus $\mathcal{N}=2^*$ gauge theory, free fermions on the torus and Painlev\'e VI

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:01.050976Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d00f7cb6-aa69-40c0-ae64-18f494cdc613 · outbound

This paper cites Bonelli, F.

Modular transformations of tau functions and conformal blocks on the torus Bonelli, F

Reference 8

Resolution: verified exact; raw_fallback, observed 2026-08-05T18:54:06.692550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 215f7152-4ced-41de-a995-0d042e897c19 · outbound

This paper cites Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus.

Modular transformations of tau functions and conformal blocks on the torus Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:06.411198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 295b9ec1-5cc1-4365-91f6-31f201c9470a · outbound

This paper cites Tau-functions and monodromy symplectomorphisms.

Modular transformations of tau functions and conformal blocks on the torus Tau-functions and monodromy symplectomorphisms

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:01.418196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60c757c7-8e0e-44b3-8072-6f8df940070d · outbound

This paper cites On some Hamiltonian properties of the isomonodromic tau functions.

Modular transformations of tau functions and conformal blocks on the torus On some Hamiltonian properties of the isomonodromic tau functions

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:06.115062Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 698a9b5f-6060-4f44-91f0-08e6029f1db3 · outbound

This paper cites Liouville Correlation Functions from Four-dimensional Gauge Theories.

Modular transformations of tau functions and conformal blocks on the torus Liouville Correlation Functions from Four-dimensional Gauge Theories

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:01.632762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b889672e-dedd-47c4-bac8-aa0dcb1fa3d9 · outbound

This paper cites Painlev\'e/CFT correspondence on a torus.

Modular transformations of tau functions and conformal blocks on the torus Painlev\'e/CFT correspondence on a torus

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:05.797996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 82eb357f-b13b-410e-a650-9a97e19a6740 · outbound

This paper cites Seiberg-Witten Theory and Random Partitions.

Modular transformations of tau functions and conformal blocks on the torus Seiberg-Witten Theory and Random Partitions

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:01.873604Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45149267-61a1-4068-9019-9f27d8e6684d · outbound

This paper cites NIST Digital Library of Mathematical Functions.

Modular transformations of tau functions and conformal blocks on the torus NIST Digital Library of Mathematical Functions

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:54:09.674538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e624adf7-ef0e-413e-9675-0eabecab1ee4 · outbound

This paper cites Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$.

Modular transformations of tau functions and conformal blocks on the torus Sixth Painlev\'e Equation, Universal Elliptic Curve, and Mirror of $\bold{P}^2$

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:05.602967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 71b2b121-cf5d-4218-97aa-dc45e341bc2f · outbound

This paper cites Darboux coordinates, Yang-Yang functional, and gauge theory.

Modular transformations of tau functions and conformal blocks on the torus Darboux coordinates, Yang-Yang functional, and gauge theory

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:02.357394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecd8c3fd-b5eb-4df2-92c4-cd1063da0d47 · outbound

This paper cites From Liouville Theory to the Quantum Geometry of Riemann Surfaces.

Modular transformations of tau functions and conformal blocks on the torus From Liouville Theory to the Quantum Geometry of Riemann Surfaces

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:02.435532Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06ea354e-f719-4658-b10d-4d7368be9c69 · outbound

This paper cites On modular transformations of non-degenerate toric conformal blocks.

Modular transformations of tau functions and conformal blocks on the torus On modular transformations of non-degenerate toric conformal blocks

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:05.307376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2de30daf-31d8-47c1-87f8-aaa4214bc8b3 · outbound

This paper cites Notes on crossing transformations of Virasoro conformal blocks.

Modular transformations of tau functions and conformal blocks on the torus Notes on crossing transformations of Virasoro conformal blocks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:02.741892Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c6fadcc-ec85-4cec-8033-2eeceb5046ac · outbound

This paper cites Instanton counting on blowup. I. 4-dimensional pure gauge theory.

Modular transformations of tau functions and conformal blocks on the torus Instanton counting on blowup. I. 4-dimensional pure gauge theory

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:02.858119Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9a2d1ca-d54f-401a-b50e-d9f3803de494 · outbound

This paper cites Quantum spectral problems and isomonodromic deformations.

Modular transformations of tau functions and conformal blocks on the torus Quantum spectral problems and isomonodromic deformations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:02.975194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8317f9f3-a396-4c07-82c1-196d2690870e · outbound

This paper cites Probabilistic conformal blocks for Liouville CFT on the torus.

Modular transformations of tau functions and conformal blocks on the torus Probabilistic conformal blocks for Liouville CFT on the torus

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:03.113024Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf158671-f1e2-4885-bf51-5598c713e14e · outbound

This paper cites Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus.

Modular transformations of tau functions and conformal blocks on the torus Proof of Zamolodchikov conjecture for semi-classical conformal blocks on the torus

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:03.217711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1fc234a3-29b3-4e66-84f3-287f0e7fdbfb · outbound

This paper cites Painlev´ e functions, accessory parameters and conformal blocks.

Modular transformations of tau functions and conformal blocks on the torus Painlev´ e functions, accessory parameters and conformal blocks

Reference 25

Resolution: verified exact; raw_fallback, observed 2026-08-05T18:54:05.116439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cbcf9500-7c9a-47be-814d-88e1d3328328 · outbound

This paper cites Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general $q$-Painlev\'e III$_3$ tau functions.

Modular transformations of tau functions and conformal blocks on the torus Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general $q$-Painlev\'e III$_3$ tau functions

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:04.877100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 14bf5820-69a8-41c3-bc97-53f679daf655 · outbound

This paper cites Reshetikhin, The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem, Letters in Mathematical Physics 26 (1992) 167.

Modular transformations of tau functions and conformal blocks on the torus Reshetikhin, The Knizhnik-Zamolodchikov system as a deformation of the isomonodromy problem, Letters in Mathematical Physics 26 (1992) 167

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:54:09.324380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2068994b-d720-49eb-b46f-9ab3ed0fb33d · outbound

This paper cites Quantum Isomonodromic Deformations and the Knizhnik--Zamolodchikov Equations.

Modular transformations of tau functions and conformal blocks on the torus Quantum Isomonodromic Deformations and the Knizhnik--Zamolodchikov Equations

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-05T18:54:04.622609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e94f10dd-a990-4fd6-8652-d10195fe8af6 · outbound

This paper cites an unresolved cited work.

Modular transformations of tau functions and conformal blocks on the torus Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-05T18:54:09.084370Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 46492690-c739-480d-a805-936b3f171fed · outbound

This paper cites Bernard, On the Wess-Zumino-Witten Models on the Torus , Nucl.

Modular transformations of tau functions and conformal blocks on the torus Bernard, On the Wess-Zumino-Witten Models on the Torus , Nucl

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:54:08.798471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 284678dc-408d-4d20-b625-0c2b024da71e · outbound

This paper cites Bernard, On the Wess-Zumino-Witten Models on Riemann Surfaces , Nucl.

Modular transformations of tau functions and conformal blocks on the torus Bernard, On the Wess-Zumino-Witten Models on Riemann Surfaces , Nucl

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:54:08.542250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 91c12c6e-999f-4ba5-8ca5-262f355e1828 · outbound

This paper cites Witten, Quantization of Chern-Simons Gauge Theory With Complex Gauge Group , Commun.

Modular transformations of tau functions and conformal blocks on the torus Witten, Quantization of Chern-Simons Gauge Theory With Complex Gauge Group , Commun

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T18:54:08.213319Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 916f0809-077a-4dec-afdd-f4bee1f264d7 · outbound

This paper cites Chern-Simons Theory and S-duality.

Modular transformations of tau functions and conformal blocks on the torus Chern-Simons Theory and S-duality

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:04.315076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c7d0145-77b4-493e-8832-92c90ab5719b · outbound

This paper cites RG Domain Walls and Hybrid Triangulations.

Modular transformations of tau functions and conformal blocks on the torus RG Domain Walls and Hybrid Triangulations

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-05T18:54:04.400124Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation c615261d-9e3d-4058-b640-589bb9e3a75c · inbound

On the Virasoro Crossing Kernels at Rational Central Charge cites this paper.

On the Virasoro Crossing Kernels at Rational Central Charge Modular transformations of tau functions and conformal blocks on the torus

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T18:57:04.783250Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2be91da9-b388-49d5-8584-a0c5bfaac5df · inbound

Irregular SLE(4) martingales and isomonodromic deformations cites this paper.

Irregular SLE(4) martingales and isomonodromic deformations Modular transformations of tau functions and conformal blocks on the torus

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-05-14T17:32:30.723682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d20930bf-7835-417d-afb4-a7176e9ad5fc · inbound

A Tau function for $q$-Painlev\'e VI as a Fredholm determinant cites this paper.

A Tau function for $q$-Painlev\'e VI as a Fredholm determinant Modular transformations of tau functions and conformal blocks on the torus

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T20:40:40.261037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.