Paper Citation Record · LEDGER

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities

As of 14 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2608.02459.

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

pith.paper-citation-record.v1
2608.02459 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T07:06:48.992757Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

22 of 22 outbound references displayed

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External citation measurements

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Outbound references

Observation c2954de7-289b-4d07-8302-7d083f36d0a8 · outbound

This paper cites Berestycki, Diffusion in planar Liouville quantum gravity,Annales de l’Institut Henri Poincare, Probabilites et Statistiques, 51(3):947–964, 2015.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Berestycki, Diffusion in planar Liouville quantum gravity,Annales de l’Institut Henri Poincare, Probabilites et Statistiques, 51(3):947–964, 2015

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.441435Z

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Observation 1dee3083-134b-4d4f-a8de-0463c5b52fa3 · outbound

This paper cites Berestycki, On the spectral geometry of Liouville quantum gravity, arXiv:2512.02538, 2025.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Berestycki, On the spectral geometry of Liouville quantum gravity, arXiv:2512.02538, 2025

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.473557Z

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Observation cb2e9327-e983-4eb8-8dbd-16f9fcd203ca · outbound

This paper cites Spectral expansion of LQG heat trace and KPZ scaling.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Spectral expansion of LQG heat trace and KPZ scaling

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.588251Z

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Observation 2fb66694-d7c6-4135-bf87-fa50d4c66eb5 · outbound

This paper cites Weyl's law in Liouville quantum gravity.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Weyl's law in Liouville quantum gravity

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.669982Z

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Observation 4510ed26-aec9-4d7d-a471-42083b7b914d · outbound

This paper cites Andres and N.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Andres and N

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.732897Z

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Observation 53faac10-a4c4-4a17-8399-a6b42ee712c9 · outbound

This paper cites an unresolved cited work.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.814496Z

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Observation 93011487-cd25-4bdc-a157-a0117669ea22 · outbound

This paper cites Bouleau and F.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Bouleau and F

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.897589Z

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Observation 31b73699-6ad4-44f9-9b24-0e86951c08e0 · outbound

This paper cites Bouleau and F.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Bouleau and F

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:47.985094Z

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Observation 6bbecf0d-c745-47a0-89cf-b17cedb0ed7f · outbound

This paper cites Chen and M.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Chen and M

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.068677Z

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Observation d5d4572f-cabb-4847-b3d3-3524cb41f303 · outbound

This paper cites Generic simplicity for self-adjoint operators under bounded potential perturbations.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Generic simplicity for self-adjoint operators under bounded potential perturbations

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.124463Z

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Observation 15b48c51-39de-4537-aa10-cb745b192202 · outbound

This paper cites Dello Schiavo, R.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Dello Schiavo, R

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.212801Z

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Observation c0d7bbe5-5e55-4647-8403-2a48aa06c99e · outbound

This paper cites Fukushima, Y.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Fukushima, Y

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.299043Z

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Observation bc44c4cb-416b-412e-a18e-686be0eab3cc · outbound

This paper cites Garban, R.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Garban, R

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.382184Z

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Observation 26adfe57-0b12-4897-bdb9-bca35d25d659 · outbound

This paper cites Garban, R.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Garban, R

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.460126Z

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Observation 8fa24fb5-5935-4950-a378-bb3b4184686b · outbound

This paper cites Kahane, Sur le chaos multiplicatif,Annales des Sciences Mathematiques du Quebec, 9(2):105–150, 1985.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Kahane, Sur le chaos multiplicatif,Annales des Sciences Mathematiques du Quebec, 9(2):105–150, 1985

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.569378Z

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Observation 3e234c79-8168-4d0b-877f-4aa542df8334 · outbound

This paper cites Kato,Perturbation Theory for Linear Operators, 2nd ed., Classics in Mathematics, Springer, 1995.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Kato,Perturbation Theory for Linear Operators, 2nd ed., Classics in Mathematics, Springer, 1995

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.626944Z

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Observation 6cafa6ce-c903-4f93-ac37-e379a6933502 · outbound

This paper cites Maillard, R.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Maillard, R

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.693230Z

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Observation 66ce2038-b00d-4892-936c-c5be5c23b7c5 · outbound

This paper cites an unresolved cited work.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.735687Z

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Observation fd8fc826-3aa9-4cc6-a012-3b135fe8bf45 · outbound

This paper cites Privat and M.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Privat and M

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.789622Z

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Observation db2dbd13-e16b-4e13-82ba-23dfe06b16c2 · outbound

This paper cites Rhodes and V.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Rhodes and V

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.847241Z

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Observation f32cae0d-df9b-41fc-9004-95c52f30007f · outbound

This paper cites Shamov, On Gaussian multiplicative chaos,Journal of Functional Analysis, 270(9):3224–3261, 2016.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Shamov, On Gaussian multiplicative chaos,Journal of Functional Analysis, 270(9):3224–3261, 2016

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.932339Z

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Observation 90be6140-c779-4913-bb2a-89c36bcbc851 · outbound

This paper cites Sheffield, Gaussian free fields for mathematicians,Probability Theory and Related Fields, 139(3–4):521–541, 2007.

A Response Calculus for Liouville Brownian Motion I: Simple Spectrum, Joint Eigenvalue Densities, and Ward Identities Sheffield, Gaussian free fields for mathematicians,Probability Theory and Related Fields, 139(3–4):521–541, 2007

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T07:06:48.992757Z

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Pith citing papers

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