Paper Citation Record · LEDGER

$x-y$ swap for $(2,2p+1)$ minimal string

As of 7 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 2 inbound Pith citation observations for arXiv:2506.09222.

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

pith.paper-citation-record.v1
2506.09222 v4

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:59:17.706140Z

measured 49 of 49 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T05:57:48.347767Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

47 of 47 outbound references displayed

verified exact11
verified fuzzy8
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6c9464d8-7963-4bcd-96d2-0e2e60ef25aa · outbound

This paper cites On Correlation Numbers in 2D Minimal Gravity and Matrix Models.

$x-y$ swap for $(2,2p+1)$ minimal string On Correlation Numbers in 2D Minimal Gravity and Matrix Models

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:13.161714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7de9627d-b5b9-4db2-a4c8-495da9c22fc3 · outbound

This paper cites The Virasoro Minimal String.

$x-y$ swap for $(2,2p+1)$ minimal string The Virasoro Minimal String

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:13.358883Z

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Unavailable: canonical work link unavailable.

Observation c7b7c35b-cdec-4a3c-bf0d-2805489319b8 · outbound

This paper cites The complex Liouville string: the worldsheet.

$x-y$ swap for $(2,2p+1)$ minimal string The complex Liouville string: the worldsheet

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:13.562767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e131b065-9eba-4d3b-808e-6d95526d1f35 · outbound

This paper cites The complex Liouville string: the matrix integral.

$x-y$ swap for $(2,2p+1)$ minimal string The complex Liouville string: the matrix integral

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:13.709354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3c07b2c-0034-4df6-a3f4-1cfe536763a0 · outbound

This paper cites Intersection numbers of spectral curves.

$x-y$ swap for $(2,2p+1)$ minimal string Intersection numbers of spectral curves

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:13.823566Z

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Unavailable: canonical work link unavailable.

Observation 1553d2f7-4469-46a1-95a4-6f79eba4967a · outbound

This paper cites On pq-duality and explicit solutions in $c \le 1$ $2d$ gravity models.

$x-y$ swap for $(2,2p+1)$ minimal string On pq-duality and explicit solutions in $c \le 1$ $2d$ gravity models

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:20.606600Z

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 830e7b1f-5239-4051-9c86-9e17302c58d3 · outbound

This paper cites Fukuma, H.

$x-y$ swap for $(2,2p+1)$ minimal string Fukuma, H

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:23.637925Z

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 6096afd7-f998-4983-9a89-d6e405e7e404 · outbound

This paper cites A universal formula for the $x-y$ swap in topological recursion.

$x-y$ swap for $(2,2p+1)$ minimal string A universal formula for the $x-y$ swap in topological recursion

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:14.228712Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ce53039-4c73-450f-94e8-8dd810ab76fc · outbound

This paper cites an unresolved cited work.

$x-y$ swap for $(2,2p+1)$ minimal string Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:59:23.497283Z

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 42dd0806-b6ed-4357-bcb0-782bbb2ec22a · outbound

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

$x-y$ swap for $(2,2p+1)$ minimal string Structure Constants and Conformal Bootstrap in Liouville Field Theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:14.476717Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17b04b35-eecc-4ed9-9d44-bb7c53e73d7a · outbound

This paper cites On the Three-point Function in Minimal Liouville Gravity.

$x-y$ swap for $(2,2p+1)$ minimal string On the Three-point Function in Minimal Liouville Gravity

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:14.546896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d57c564-87e9-4232-80f3-89ec33389785 · outbound

This paper cites Polchinski, String Theory, vol.

$x-y$ swap for $(2,2p+1)$ minimal string Polchinski, String Theory, vol

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:14.657894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08b6fdc0-118f-4417-8ec8-14dde30841bd · outbound

This paper cites an unresolved cited work.

$x-y$ swap for $(2,2p+1)$ minimal string Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:59:23.332817Z

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 f54090d6-2b79-427a-a237-19ae012b85ea · outbound

This paper cites Witten, Ground ring of two-dimensional string theory , Nuclear Physics B 373 (Mar, 1992) 187–213.

$x-y$ swap for $(2,2p+1)$ minimal string Witten, Ground ring of two-dimensional string theory , Nuclear Physics B 373 (Mar, 1992) 187–213

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:23.141061Z

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 d9683ce3-6b5e-4a33-a0c6-ea8065493068 · outbound

This paper cites Imbimbo, S.

$x-y$ swap for $(2,2p+1)$ minimal string Imbimbo, S

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:22.956849Z

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 7c0c250e-10ee-4509-b4c3-6b486a57ccfa · outbound

This paper cites an unresolved cited work.

$x-y$ swap for $(2,2p+1)$ minimal string Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:59:22.729705Z

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 5d20f3c5-90aa-4e1d-bfbe-cf74ffd605da · outbound

This paper cites Higher Equations of Motion in Liouville Field Theory.

$x-y$ swap for $(2,2p+1)$ minimal string Higher Equations of Motion in Liouville Field Theory

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:15.152917Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a96e5453-e962-4e4b-868c-8f8790238764 · outbound

This paper cites On the construction of the correlation numbers in Minimal Liouville Gravity.

$x-y$ swap for $(2,2p+1)$ minimal string On the construction of the correlation numbers in Minimal Liouville Gravity

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:20.309804Z

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 e3f67437-a7b4-4ffe-9d3f-f92594626ce2 · outbound

This paper cites Torus one-point correlation numbers in minimal Liouville gravity.

$x-y$ swap for $(2,2p+1)$ minimal string Torus one-point correlation numbers in minimal Liouville gravity

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:20.156816Z

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 255c20b7-608a-4166-b4eb-6483628b87a2 · outbound

This paper cites Multi-instantons in minimal string theory and in matrix integrals.

$x-y$ swap for $(2,2p+1)$ minimal string Multi-instantons in minimal string theory and in matrix integrals

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:15.432253Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd87f71f-ff45-4601-8367-7298270bd03e · outbound

This paper cites From Minimal Strings towards Jackiw-Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes.

$x-y$ swap for $(2,2p+1)$ minimal string From Minimal Strings towards Jackiw-Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:15.473766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16580208-8fa0-4188-b018-719ac8ed4c1b · outbound

This paper cites Invariants of algebraic curves and topological expansion.

$x-y$ swap for $(2,2p+1)$ minimal string Invariants of algebraic curves and topological expansion

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:15.555571Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1dbd90b-3037-47c3-afb5-e2e30a13b009 · outbound

This paper cites Branes, Rings and Matrix Models in Minimal (Super)string Theory.

$x-y$ swap for $(2,2p+1)$ minimal string Branes, Rings and Matrix Models in Minimal (Super)string Theory

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:15.656345Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1be20f9-e685-4f1b-ac1a-71471f5777e1 · outbound

This paper cites On Krichever tau-function and Verlinde formula.

$x-y$ swap for $(2,2p+1)$ minimal string On Krichever tau-function and Verlinde formula

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:19.800396Z

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 4366262d-695b-4443-b588-57a9d892f9d2 · outbound

This paper cites The $\tau$-function of the universal Whitham hierarchy, matrix models and topological field theories.

$x-y$ swap for $(2,2p+1)$ minimal string The $\tau$-function of the universal Whitham hierarchy, matrix models and topological field theories

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:19.485772Z

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 0984aadb-3ef9-4cbe-b09d-5dee9b08be31 · outbound

This paper cites KP integrability through the $x-y$ swap relation.

$x-y$ swap for $(2,2p+1)$ minimal string KP integrability through the $x-y$ swap relation

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:19.277531Z

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 a63f785b-8117-4681-9ba1-93d516e7da5f · outbound

This paper cites Five-point Correlation Numbers in One-Matrix Model.

$x-y$ swap for $(2,2p+1)$ minimal string Five-point Correlation Numbers in One-Matrix Model

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:19.084274Z

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 6b94a376-dd73-494d-a9da-b2b25e32444f · outbound

This paper cites Two dimensional gravity in genus one in Matrix Models, Topological and Liouville approaches.

$x-y$ swap for $(2,2p+1)$ minimal string Two dimensional gravity in genus one in Matrix Models, Topological and Liouville approaches

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:18.849622Z

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

Observation 511871e6-e713-474c-b628-d475ebbfc725 · outbound

This paper cites $(2,2p+1)$ minimal string and intersection theory I.

$x-y$ swap for $(2,2p+1)$ minimal string $(2,2p+1)$ minimal string and intersection theory I

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:16.164432Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3401932e-ceb3-43b9-ba03-c51a77423083 · outbound

This paper cites Liouville quantum gravity -- holography, JT and matrices.

$x-y$ swap for $(2,2p+1)$ minimal string Liouville quantum gravity -- holography, JT and matrices

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:16.252323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 313548d8-a38a-4cc6-ad2e-9e6a2cf3bc4d · outbound

This paper cites Matrix model approach to minimal Liouville gravity revisited.

$x-y$ swap for $(2,2p+1)$ minimal string Matrix model approach to minimal Liouville gravity revisited

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:18.509028Z

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 d6c1df0e-3d9c-4fab-b2f7-92568002a743 · outbound

This paper cites an unresolved cited work.

$x-y$ swap for $(2,2p+1)$ minimal string Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:16.398295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb985061-462b-4f73-aa15-a151d7ce8611 · outbound

This paper cites Zvonkine, An introduction to moduli spaces of curves and their intersection theory , 2012.

$x-y$ swap for $(2,2p+1)$ minimal string Zvonkine, An introduction to moduli spaces of curves and their intersection theory , 2012

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:22.505568Z

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 ff51f619-1caa-4153-9a56-9ca181b3f7ea · outbound

This paper cites Identification of the Givental formula with the spectral curve topological recursion procedure.

$x-y$ swap for $(2,2p+1)$ minimal string Identification of the Givental formula with the spectral curve topological recursion procedure

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:16.597957Z

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Unavailable: canonical work link unavailable.

Observation e4e71b12-d384-4595-a403-5eb75ad21844 · outbound

This paper cites Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent.

$x-y$ swap for $(2,2p+1)$ minimal string Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:22.266855Z

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 c0373fa4-1b64-4b99-9aeb-3c584229ab8b · outbound

This paper cites JT gravity as a matrix integral.

$x-y$ swap for $(2,2p+1)$ minimal string JT gravity as a matrix integral

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:16.752257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cfa97df-8995-4a47-b341-9f1bc301b8ef · outbound

This paper cites 2D dilaton gravity and the Weil-Petersson volumes with conical defects.

$x-y$ swap for $(2,2p+1)$ minimal string 2D dilaton gravity and the Weil-Petersson volumes with conical defects

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:16.844293Z

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Unavailable: canonical work link unavailable.

Observation f0c7b025-c130-49f3-b3ec-63e06a166f0f · outbound

This paper cites Anagnostou, S.

$x-y$ swap for $(2,2p+1)$ minimal string Anagnostou, S

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:22.039356Z

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 ff657364-1ca1-4dd7-be11-82c3a3b4aa12 · outbound

This paper cites Note on large-$p$ limit of $(2,2p+1)$ minimal Liouville gravity and moduli space volumes.

$x-y$ swap for $(2,2p+1)$ minimal string Note on large-$p$ limit of $(2,2p+1)$ minimal Liouville gravity and moduli space volumes

Reference 39

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:18.231504Z

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

Observation 89b7737d-fe76-4ce0-8e78-16dddb35bbfd · outbound

This paper cites Dilaton-gravity, deformations of the minimal string, and matrix models.

$x-y$ swap for $(2,2p+1)$ minimal string Dilaton-gravity, deformations of the minimal string, and matrix models

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:17.074179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 116dd9a4-9e67-4464-82f1-4739dae64406 · outbound

This paper cites Teichm\"uller theory for conic surfaces.

$x-y$ swap for $(2,2p+1)$ minimal string Teichm\"uller theory for conic surfaces

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:17.128579Z

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Unavailable: canonical work link unavailable.

Observation 1fe46ee3-9838-47fc-8a5c-273f54739d30 · outbound

This paper cites Harlow, J.

$x-y$ swap for $(2,2p+1)$ minimal string Harlow, J

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:21.742337Z

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 77113036-208a-4128-8cd8-120374202889 · outbound

This paper cites Five-point correlation numbers in minimal Liouville gravity and matrix models.

$x-y$ swap for $(2,2p+1)$ minimal string Five-point correlation numbers in minimal Liouville gravity and matrix models

Reference 43

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:59:18.042447Z

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 196c1092-3dd5-4bb3-ad1d-db26fa7d0483 · outbound

This paper cites The c=1 String Theory S-Matrix Revisited.

$x-y$ swap for $(2,2p+1)$ minimal string The c=1 String Theory S-Matrix Revisited

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-07T04:59:17.430232Z

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Unavailable: canonical work link unavailable.

Observation 9d3b0155-92a3-40af-b057-0186fb4abee1 · outbound

This paper cites Artemev and V.

$x-y$ swap for $(2,2p+1)$ minimal string Artemev and V

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:59:21.508917Z

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 82aaa971-446c-4165-8a27-7e8b5ba0f88b · outbound

This paper cites an unresolved cited work.

$x-y$ swap for $(2,2p+1)$ minimal string Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:59:21.285142Z

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 44f35873-6974-422f-9176-ad3336c44f37 · outbound

This paper cites an unresolved cited work.

$x-y$ swap for $(2,2p+1)$ minimal string Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:59:21.029683Z

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

Observation fae3ce4c-4783-4f69-94c2-c6d407ff1c44 · inbound

WKB-asymptotics for multipoint Virasoro conformal blocks and applications cites this paper.

WKB-asymptotics for multipoint Virasoro conformal blocks and applications $x-y$ swap for $(2,2p+1)$ minimal string

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T05:57:48.347767Z

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Unavailable: canonical work link unavailable.

Observation 1806acd0-4e35-4c42-bd4f-e499f6cd6669 · inbound

The Runkel-Watts string cites this paper.

The Runkel-Watts string $x-y$ swap for $(2,2p+1)$ minimal string

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T12:47:52.403412Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.