Paper Citation Record · LEDGER

Mixed Solutions to the Liouville Equation

As of 8 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2506.02196.

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

pith.paper-citation-record.v1
2506.02196 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:35:28.733043Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

27 of 27 outbound references displayed

verified exact10
verified fuzzy6
unresolved9
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b3924ffc-ce6f-4271-8b36-48917ce31d5f · outbound

This paper cites Sur l’´ equation aux diff´ erences partielles 2log d2λ dudv ± λ 2a2 = 0,.

Mixed Solutions to the Liouville Equation Sur l’´ equation aux diff´ erences partielles 2log d2λ dudv ± λ 2a2 = 0,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:35:31.966429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 92367bef-454a-48e9-9c6a-97eeb615cf50 · outbound

This paper cites Exact Quantum Three Point Function of Liouville Highest Weight States,.

Mixed Solutions to the Liouville Equation Exact Quantum Three Point Function of Liouville Highest Weight States,

Reference 2

Resolution: verified exact; doi, observed 2026-08-07T11:35:29.487706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 954d8d19-3227-483f-bd11-cb9ef5d560a3 · outbound

This paper cites Notes on quantum Liouville theory and quantum gravity,.

Mixed Solutions to the Liouville Equation Notes on quantum Liouville theory and quantum gravity,

Reference 3

Resolution: verified exact; doi, observed 2026-08-07T11:35:29.275791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1cd60e9b-056b-48d8-bce7-89949775f178 · outbound

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

Mixed Solutions to the Liouville Equation Structure Constants and Conformal Bootstrap in Liouville Field Theory

Reference 4

Resolution: malformed identifier; no resolver link, observed 2026-08-07T11:35:26.428192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d4eb56b-badb-4476-9fd2-de2df30efe4a · outbound

This paper cites Classical Liouville action on the sphere with three hyperbolic singularities.

Mixed Solutions to the Liouville Equation Classical Liouville action on the sphere with three hyperbolic singularities

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:35:30.794857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 300b4105-a410-486b-a743-698cdb940003 · outbound

This paper cites Polyakov conjecture for hyperbolic singularities.

Mixed Solutions to the Liouville Equation Polyakov conjecture for hyperbolic singularities

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:26.652133Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c668885-fca6-4761-b723-3ef5beded4ae · outbound

This paper cites Hyperbolic three-string vertex.

Mixed Solutions to the Liouville Equation Hyperbolic three-string vertex

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:26.726307Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fed185f6-53ea-4d01-87a9-8e9b846370f0 · outbound

This paper cites Explicit solutions for Point Particles and Black Holes in spaces of constant curvature in 2+1-D Gravity.

Mixed Solutions to the Liouville Equation Explicit solutions for Point Particles and Black Holes in spaces of constant curvature in 2+1-D Gravity

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:35:30.638395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0777e280-e33e-4ec1-b43a-93b4dd482bd2 · outbound

This paper cites Time-Symmetric Initial Data for Multi-Body Solutions in Three Dimensions.

Mixed Solutions to the Liouville Equation Time-Symmetric Initial Data for Multi-Body Solutions in Three Dimensions

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:35:30.460043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ddca70b5-b650-45ee-acf1-c79f86c6366e · outbound

This paper cites Hyperbolic String Vertices.

Mixed Solutions to the Liouville Equation Hyperbolic String Vertices

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:26.990688Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c27e37f8-cd53-4b50-b2dc-37a585a10a2b · outbound

This paper cites Sullo svolgimento del quoziente di due serie ipergeometriche in frazione continua infinita,.

Mixed Solutions to the Liouville Equation Sullo svolgimento del quoziente di due serie ipergeometriche in frazione continua infinita,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:35:31.829040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7044eea2-408e-4751-aa0e-69f54c6f91a0 · outbound

This paper cites Asymptotic Expansions of Hypergeometric Functions,.

Mixed Solutions to the Liouville Equation Asymptotic Expansions of Hypergeometric Functions,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:35:31.655840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3fe4caf9-7e86-43aa-9c36-cf73ae4c51db · outbound

This paper cites An extension of the method of steepest descents,.

Mixed Solutions to the Liouville Equation An extension of the method of steepest descents,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:35:31.447144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 185d1a0b-fd54-4a7e-a213-c6af3ae52ced · outbound

This paper cites Asymptotics of the hypergeometric function,.

Mixed Solutions to the Liouville Equation Asymptotics of the hypergeometric function,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:35:31.297914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 67130079-c547-43c9-a6ea-a7718c73e83b · outbound

This paper cites Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited,.

Mixed Solutions to the Liouville Equation Exponentially accurate uniform asymptotic approximations for integrals and Bleistein’s method revisited,

Reference 15

Resolution: verified exact; raw_fallback, observed 2026-08-07T11:35:30.311311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b2acf8f5-0958-4c2f-9ea6-a7143d8835e3 · outbound

This paper cites Asymptotics of the Gauss hypergeometric function with large parameters, II,.

Mixed Solutions to the Liouville Equation Asymptotics of the Gauss hypergeometric function with large parameters, II,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:35:31.122202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b075b456-c090-4045-b661-ed7115ccc7d9 · outbound

This paper cites an unresolved cited work.

Mixed Solutions to the Liouville Equation Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:35:30.949179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2da871a4-f96e-471b-8596-6d27429efeef · outbound

This paper cites Three-Dimensional Einstein Gravity: Dynamics of Flat Space,.

Mixed Solutions to the Liouville Equation Three-Dimensional Einstein Gravity: Dynamics of Flat Space,

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:27.802352Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ea45987-9ecd-4037-8add-c5b21f7b8d46 · outbound

This paper cites Three-Dimensional Cosmological Gravity: Dynamics of Con- stant Curvature,.

Mixed Solutions to the Liouville Equation Three-Dimensional Cosmological Gravity: Dynamics of Con- stant Curvature,

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:27.913440Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3fae31fb-548a-45bf-b72d-85610b25e052 · outbound

This paper cites Exact quasistatic particle scattering in (2+1) gravity,.

Mixed Solutions to the Liouville Equation Exact quasistatic particle scattering in (2+1) gravity,

Reference 20

Resolution: verified exact; doi, observed 2026-08-07T11:35:29.081031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fe9aa7b1-9586-483e-ad51-bea1a57ff967 · outbound

This paper cites (2+1)-Gravity with Moving Particles in an Instantaneous Gauge.

Mixed Solutions to the Liouville Equation (2+1)-Gravity with Moving Particles in an Instantaneous Gauge

Reference 21

Resolution: malformed identifier; local_arxiv, observed 2026-08-07T11:35:30.099413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 074bb46e-70ae-4b94-b259-3dad24a2bb23 · outbound

This paper cites Non-Perturbative Particle Dynamics.

Mixed Solutions to the Liouville Equation Non-Perturbative Particle Dynamics

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-07T11:35:29.925711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation eda047b0-4be5-49af-887c-6ce7941b0d1c · outbound

This paper cites Perturbative analysis of the two-body problem in (2+1) - AdS gravity,.

Mixed Solutions to the Liouville Equation Perturbative analysis of the two-body problem in (2+1) - AdS gravity,

Reference 23

Resolution: verified exact; raw_fallback, observed 2026-08-07T11:35:29.718806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 209016e6-0e75-432d-a95b-baa977473ceb · outbound

This paper cites Nonperturbative Two Particle Scattering Amplitudes in (2+1)-Dimensional Quantum Gravity,.

Mixed Solutions to the Liouville Equation Nonperturbative Two Particle Scattering Amplitudes in (2+1)-Dimensional Quantum Gravity,

Reference 24

Resolution: verified exact; doi, observed 2026-08-07T11:35:28.891677Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8633b5ee-d8bb-4f14-8d68-ada929d3f3f9 · outbound

This paper cites Multi-Black-Hole Geometries in (2+1)-Dimensional Gravity.

Mixed Solutions to the Liouville Equation Multi-Black-Hole Geometries in (2+1)-Dimensional Gravity

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:28.511081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2de4780-b044-469d-9cb4-f9f43349e004 · outbound

This paper cites Geometry of the 2+1 Black Hole.

Mixed Solutions to the Liouville Equation Geometry of the 2+1 Black Hole

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:28.638344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f61b2817-7082-4330-a203-f5e6cd24ba50 · outbound

This paper cites Black Hole Creation in 2+1 Dimensions.

Mixed Solutions to the Liouville Equation Black Hole Creation in 2+1 Dimensions

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T11:35:28.733043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.