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Paper Citation Record · LEDGER

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer

As of 12 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2509.05487.

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

pith.paper-citation-record.v1
2509.05487 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:38:10.083382Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:05:04.538471Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T17:05:04.601576Z

Reference resolution

34 of 34 outbound references displayed

  • verified exact2
  • verified fuzzy24
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1790b7a4-f3e6-4da5-bfef-bd7b07c12213 · outbound

This paper cites Adler, P.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Adler, P

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:16.468774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.153913Z digest=sha256:e551ec22b6ab8dbbef97956ae04d42f7f92de27de0e71c65cd7ab038cefe6278

Observation 6544b882-4da1-469d-a7ba-4f4ca2add7c6 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:16.338093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.202986Z digest=sha256:213325f27d895aef26ae47217c791b467129b7a0344549a85243b0822e3fd8ba

Observation 76f91f30-b6c2-473c-a5ce-46769afb0a79 · outbound

This paper cites Coefficients of Wronskian Hermite polynomials.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Coefficients of Wronskian Hermite polynomials

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:16.195887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.269878Z digest=sha256:dc7a5583119cf4cf260db94ab4c968a4df7727913e81cd93279f2f0598d72ad5

Observation 231d7668-0712-481a-9768-f5e199085459 · outbound

This paper cites Wronskian Appell polynomials and symmetric functions.Adv.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Wronskian Appell polynomials and symmetric functions.Adv

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:16.033103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.330131Z digest=sha256:2f069a24cdd0f8fc4f7e2d128462162d714dde54247ad69862e723d207dd7b91

Observation 7d27d4ed-bbdb-48ef-af98-00639f25e6fa · outbound

This paper cites Janossy densities.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Janossy densities

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:15.898739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.424405Z digest=sha256:8ce552e0dca09ea52b45f1eb0aad28de43530479c2cf440e6243412fdb4dd0b0

Observation 741b2aee-2d4b-42c1-9645-6dbeb3394539 · outbound

This paper cites Iterated integrals and exponential homomorphisms.Proc.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Iterated integrals and exponential homomorphisms.Proc

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:15.777790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.503085Z digest=sha256:99545da2bc986fbc87196ed78ee3dbfee954b4c98b2f4bedda1ea85a6b917d98

Observation f2b4e6ae-7044-4b00-b585-baa63ddf8f15 · outbound

This paper cites Matrix models for beta ensembles.J.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Matrix models for beta ensembles.J

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:15.624495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.534773Z digest=sha256:f8df9ba333852f02ffa3f5e583ba54676fe44494fa768f18b3c5483a3bab04cd

Observation 575e518d-a76c-4093-b7c4-a8463308f9a2 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:15.463448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.631535Z digest=sha256:dc012511210d3c8e7b1c2feca0686187de2adf4473328eb5fcf775790fbe5e14

Observation af0ffe6c-d65a-4f21-96f0-fb0bef02d3a0 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:15.310089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.698771Z digest=sha256:bf0b056c382f107e180cc19c582378e2dcccb34e7f9572c5cb16c4f963545ba2

Observation 6db348a8-d378-4ae1-8faf-accb8506b903 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:15.165765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.788901Z digest=sha256:0cf2a5ea9e61e1b275f00ca5cd3e9745d8974e233eb6b43e5476c4a7bdef31ae

Observation 0def699c-aa84-42d5-b97d-4a279617b034 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:14.991286Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:07.910341Z digest=sha256:e24c91a3e33e45cec0ba8cae1a42aeb1335995c690dfafa82efadd36e7c4cbbc

Observation 26b7b834-8944-4b40-93b5-9a9cba04e1a8 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-05T05:38:08.041763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T05:38:08.041763Z digest=sha256:550dea82ed3b2027b9b09587b7e04d2eff0527008aa82d685ac0d52e88853ba5

Observation ae86132c-3246-46f4-a789-c9d007ec1b00 · outbound

This paper cites Felder, A.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Felder, A

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:14.845327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.106574Z digest=sha256:c0c21a26c929c49ffa9cc2664ad3c4156d33e9866926ed8a2a199db29fe47811

Observation 488c7627-c7d6-458b-93b5-e83f26f96674 · outbound

This paper cites Forrester and S.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Forrester and S

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:14.687258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.205835Z digest=sha256:f28f319012b105ebc34890704b345593e035a27b4267197dd8dfa72924dc20ec

Observation 59a885f9-e4ba-4ed5-a2fc-9aa42ab931d6 · outbound

This paper cites The expansion of Wronskian Hermite polynomials in the Hermite basis.SIGMA Symmetry Integrability Geom.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer The expansion of Wronskian Hermite polynomials in the Hermite basis.SIGMA Symmetry Integrability Geom

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:14.504305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.356837Z digest=sha256:eb1e14cc04b2eea8c41a1aa3e5426fbc3ed07cc98cec6d37465666f6d52f112f

Observation d750d0df-13e4-43c3-8f7b-917ce839e370 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:14.279318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.428265Z digest=sha256:6b6ea1c77c531857b593b39725de797c53fdef52ace4e8b2cf0fbb00f6884e6a

Observation 060763ec-824b-4948-a717-111cd332b642 · outbound

This paper cites Minor summation formula of hyperpfaffians and Selberg integrals.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Minor summation formula of hyperpfaffians and Selberg integrals

Reference 17

Resolution
verified exact
local_arxiv, observed 2026-08-05T05:38:10.555446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.530355Z digest=sha256:795004646e1e973e2971748fc04ad93d40cd88fba74655c7e233e2411eedfa4b

Observation b8813870-b40d-4107-bd90-644d873479f7 · outbound

This paper cites Density matrix of an impenetrable Bose gas and the fifth Painlev´ e transcendent.Phys.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Density matrix of an impenetrable Bose gas and the fifth Painlev´ e transcendent.Phys

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:14.039512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.629119Z digest=sha256:c9b00b9ddf108cbe3681f1d2f7696d27e981588e72206efaf3d4f5f538d8943c

Observation 8d371851-1cb2-4c0e-ba09-cf9b965c8671 · outbound

This paper cites Karlin and G.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Karlin and G

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:13.815392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.703817Z digest=sha256:b49384942d3df601c3ec877fb365846c88d9365e8163ed6a815d0dbfe0070a18

Observation af7c4299-3520-4b79-b7d7-f7bce7a1f841 · outbound

This paper cites Pfaffian and Hafnian identities in shuffle algebras.Adv.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Pfaffian and Hafnian identities in shuffle algebras.Adv

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:13.647700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.826071Z digest=sha256:93a65b716f778b4414b3a223269816d82a17c75c794d4dfce3f83a0dd8dfac3f

Observation 22762eef-f2ba-427a-9843-7bb82dc6176d · outbound

This paper cites Hankel hyperdeterminants and Selberg integrals.J.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Hankel hyperdeterminants and Selberg integrals.J

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:13.440497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:08.930122Z digest=sha256:fe1ffd66e29a54da435e8f3db9be3455a1f2588751776a1220341a9072d9e1e7

Observation 1221c21e-6651-450d-9c35-c3502c6a59c5 · outbound

This paper cites Elsevier/Academic Press, Amsterdam, third edition, 2004.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Elsevier/Academic Press, Amsterdam, third edition, 2004

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:13.219550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.035249Z digest=sha256:b8397108ba9800ff8a524537cb846e1876fb86bfb294ea4018b605d16d4ca9f9

Observation 3d589075-b6d7-41eb-9ca6-a6b7145e6fd3 · outbound

This paper cites Ram ´ ırez, Brian Rider, and B´ alint Vir´ ag.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Ram ´ ırez, Brian Rider, and B´ alint Vir´ ag

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:13.045842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.139027Z digest=sha256:76fab0becfbe8c0521a5b29d0ca2b8dc110f7fe353e9de55e1d2d6792c5cab78

Observation cf757c3e-f2ce-4c11-94ad-51ffaac273e8 · outbound

This paper cites Ensemble averages whenβis a square integer.Monatshefte f¨ ur Mathematik, 166:121–144, 2012.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Ensemble averages whenβis a square integer.Monatshefte f¨ ur Mathematik, 166:121–144, 2012

Reference 24

Resolution
verified exact
doi, observed 2026-08-05T05:38:10.327291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.236487Z digest=sha256:d201fc5285fba048a5b80e45cc956642937ef29accdddc7a744cef301ddaebd1

Observation 0ab190f0-2ce2-4f78-8e6d-af5fb36171f6 · outbound

This paper cites The partition function of multicomponent log-gases.Journal of Physics A: Mathematical and Theoretical, 45(16):165002, 2012.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer The partition function of multicomponent log-gases.Journal of Physics A: Mathematical and Theoretical, 45(16):165002, 2012

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:12.837526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.331840Z digest=sha256:038b9dc001b60f246c33b7bc986e88cf6dd01de0b4408c06701a8238966cd7c1

Observation 4f4bfc43-e3b8-4ab8-854c-180b1c1b7581 · outbound

This paper cites Soshnikov.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Soshnikov

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:12.551691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.441389Z digest=sha256:f8c3b002ec0790a6017b24fa537c6fd22386779c34c929b663d1edfb632cb953

Observation 350f2281-49e8-493b-9a1c-2a769512234e · outbound

This paper cites Janossy densities.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Janossy densities

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:12.347298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.506521Z digest=sha256:9d54a3452906985f441e8ced0ab1212cc9d80f51c3cd1b7f7d7938da9e1d99a5

Observation 0ea0791f-119f-46f4-9758-19335dc3d672 · outbound

This paper cites Tracy and Harold Widom.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Tracy and Harold Widom

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:12.090016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.620858Z digest=sha256:60da45ebceafba4b0baeeaa8009364583c4a681f806c9a9d83720db0fa12ec2f

Observation 4580aa76-922d-44d2-865e-a2e44c7ec097 · outbound

This paper cites Tracy and Harold Widom.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Tracy and Harold Widom

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:11.861207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.692691Z digest=sha256:3184b966072bb67075fe3a9d63232fd18f46000937719bb86e210edcab28c923

Observation f6957d0f-fa72-4fdf-b61a-6c17456f3a03 · outbound

This paper cites Tracy and Harold Widom.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Tracy and Harold Widom

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:11.677307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.822132Z digest=sha256:dedc05a728d4ec181503e001f4b70d13eaa7bcaefd6fa00430ea1b58e45d2666

Observation d72ccbeb-e807-42dc-9343-285fa9b19897 · outbound

This paper cites an unresolved cited work.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:38:11.453930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.885286Z digest=sha256:176fa8249ec2f26883e55fe40815131980c396a23df35d5b7575ef4e86e03627

Observation 32bb3cb7-7332-4aff-8d4c-d8fff3999680 · outbound

This paper cites Wells.On the Solvability of Beta-ensembles when Beta Is a Square Integer.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Wells.On the Solvability of Beta-ensembles when Beta Is a Square Integer

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:11.216555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:09.957161Z digest=sha256:a5dedf0299399c586db70e45d4268892349e166159031c06d3c495d932b201d2

Observation 5e0daf00-50be-40fe-83f2-b3197408da0a · outbound

This paper cites On the relation between orthogonal, symplectic and unitary matrix ensembles.J.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer On the relation between orthogonal, symplectic and unitary matrix ensembles.J

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:10.936934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:10.013013Z digest=sha256:c5a271ad58e3b97e783e6d8e214c632d5d36c5cfee4d642b4d5c12ee4bbc1d3c

Observation 1f350b72-4819-4aa5-aa1f-82a9d667384a · outbound

This paper cites Wolff and Jonathan M.

Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer Wolff and Jonathan M

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:38:10.749439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-05T05:38:10.083382Z digest=sha256:610973a1f63e4cfffa6b1a6c69f65a78ca1f9a6ceef69a94f963ad7630e8cf0c

Pith citing papers

Observation 339967d9-4ba7-420b-a059-4d5c1d6cb947 · inbound

Fugacity-Resolved Stabilizer Entropy in Critical Quantum Chains: Discrete Selberg Sums and Exactly Solvable R\'enyi Indices cites this paper.

Fugacity-Resolved Stabilizer Entropy in Critical Quantum Chains: Discrete Selberg Sums and Exactly Solvable R\'enyi Indices Hyperpfaffian Correlations for Beta-Ensembles: Beta an Even Square Integer

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