Paper Citation Record · LEDGER

Recursive relations for the S-matrix of Liouville theory

As of 7 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2507.11760.

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

pith.paper-citation-record.v1
2507.11760 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:09:52.705415Z

measured 15 of 15 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

15 of 15 outbound references displayed

verified exact6
verified fuzzy5
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cc5893c7-9358-4b94-a968-9724eb01fe32 · outbound

This paper cites Liouville theory revisited,.

Recursive relations for the S-matrix of Liouville theory Liouville theory revisited,

Reference 1

Resolution: verified exact; raw_fallback, observed 2026-08-06T17:09:53.941990Z

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 3d9c77f3-149c-41bf-8564-284bad86d1dd · outbound

This paper cites Liouville Field Theory -- A decade after the revolution.

Recursive relations for the S-matrix of Liouville theory Liouville Field Theory -- A decade after the revolution

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T17:09:50.885190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e400e790-b7bd-4ddf-affe-6b8958f7bc95 · outbound

This paper cites Review on the probabilistic construction and Conformal bootstrap in Liouville Theory.

Recursive relations for the S-matrix of Liouville theory Review on the probabilistic construction and Conformal bootstrap in Liouville Theory

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T17:09:51.030672Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e0d9580-46fa-4bac-bfd6-6c9d070ef298 · outbound

This paper cites The Virasoro structure and the scattering matrix for Liouville conformal field theory.

Recursive relations for the S-matrix of Liouville theory The Virasoro structure and the scattering matrix for Liouville conformal field theory

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:09:53.648366Z

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 0440892b-98d2-4772-8b76-17a4ac1d0831 · outbound

This paper cites Liouville Theory: An Introduction to Rigorous Approaches.

Recursive relations for the S-matrix of Liouville theory Liouville Theory: An Introduction to Rigorous Approaches

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:09:53.413392Z

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 c5d469d9-0c49-4d89-8717-bce233e04c43 · outbound

This paper cites On the S-matrix of Liouville theory.

Recursive relations for the S-matrix of Liouville theory On the S-matrix of Liouville theory

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:09:53.242886Z

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 ea23841f-ff54-4861-85f8-044931a79a80 · outbound

This paper cites Generating Functional for the S-Matrix in Liouville Theory,.

Recursive relations for the S-matrix of Liouville theory Generating Functional for the S-Matrix in Liouville Theory,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:09:54.966050Z

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 a5a8d637-a744-47f7-9fc3-ca88587ff798 · outbound

This paper cites Functional Integral Representation for the S-matrix in Integrable 2d Conformal Field Theories,.

Recursive relations for the S-matrix of Liouville theory Functional Integral Representation for the S-matrix in Integrable 2d Conformal Field Theories,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:09:54.822045Z

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 49748d05-4f95-4a36-94d6-0f1bec314ed1 · outbound

This paper cites An Exact Operator Solution of the Quan- tum Liouville Field Theory,.

Recursive relations for the S-matrix of Liouville theory An Exact Operator Solution of the Quan- tum Liouville Field Theory,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:09:54.680705Z

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 ea7df3f2-2945-49ca-a9b8-b188d1d97fd1 · outbound

This paper cites Construction Of Exponential Liouville Field Operators For Closed String Models,.

Recursive relations for the S-matrix of Liouville theory Construction Of Exponential Liouville Field Operators For Closed String Models,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:09:54.393195Z

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 cb40bd0f-9099-4801-8054-930f2c0bdbac · outbound

This paper cites Operator Approach to Boundary Liouville Theory.

Recursive relations for the S-matrix of Liouville theory Operator Approach to Boundary Liouville Theory

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:09:53.103322Z

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 253ced82-a4bd-4c6c-905a-590737567734 · outbound

This paper cites Two and three-point functions in Liouville theory.

Recursive relations for the S-matrix of Liouville theory Two and three-point functions in Liouville theory

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T17:09:52.414472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c0c2d85-24f0-40fd-9dc1-e6c3e61b49c7 · outbound

This paper cites Structure Constants and Conformal Bootstrap in Liouville Field Theory.

Recursive relations for the S-matrix of Liouville theory Structure Constants and Conformal Bootstrap in Liouville Field Theory

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T17:09:52.548823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49943a41-fc6b-4003-b688-63d8c399b2db · outbound

This paper cites Continous Spins in 2D Gravity: Chiral Vertex Operators and Local Fields.

Recursive relations for the S-matrix of Liouville theory Continous Spins in 2D Gravity: Chiral Vertex Operators and Local Fields

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-06T17:09:52.873371Z

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 f395312d-0eba-4d9a-9e2e-34dd420d329a · outbound

This paper cites Four Point Correlation Functions and the Oper- ator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c < 1,.

Recursive relations for the S-matrix of Liouville theory Four Point Correlation Functions and the Oper- ator Algebra in the Two-Dimensional Conformal Invariant Theories with the Central Charge c < 1,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:09:54.198401Z

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.

Pith citing papers

No inbound Pith citation observations are available.