Paper Citation Record · LEDGER

Zariski density of discrete subgroups via critical exponents and unitary representations

As of 19 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 0 inbound Pith citation observations for arXiv:2608.04966.

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

pith.paper-citation-record.v1
2608.04966 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T13:01:24.082538Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

30 of 30 outbound references displayed

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External citation measurements

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Outbound references

Observation f21c368c-94a2-48f5-92ac-18eaf6704524 · outbound

This paper cites On the growth ofL2-invariants for sequences of lattices in Lie groups,.

Zariski density of discrete subgroups via critical exponents and unitary representations On the growth ofL2-invariants for sequences of lattices in Lie groups,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.504827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3939f890-e354-476f-9098-4bbae88a8b27 · outbound

This paper cites Bekka, P.

Zariski density of discrete subgroups via critical exponents and unitary representations Bekka, P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.497638Z

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Observation 532162a6-f7f0-460d-8ba8-68655a8d8a2b · outbound

This paper cites Propriétés asymptotiques des groups linéaires,.

Zariski density of discrete subgroups via critical exponents and unitary representations Propriétés asymptotiques des groups linéaires,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.490798Z

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Observation d425aa7b-d267-4761-830d-1fd54520854e · outbound

This paper cites Geometry of homogeneous spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations Geometry of homogeneous spaces,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.483779Z

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Observation 29a3a70f-217b-47fc-95ab-80f0e4c26bdd · outbound

This paper cites Tempered of reductive homogeneous spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations Tempered of reductive homogeneous spaces,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.476829Z

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Observation b89572e1-83f0-4f97-8310-24dc0347f780 · outbound

This paper cites Tempered homogeneous spaces II,.

Zariski density of discrete subgroups via critical exponents and unitary representations Tempered homogeneous spaces II,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.469352Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ed0d75fd-525e-46eb-b6f4-1ed8cd64cd60 · outbound

This paper cites Tempered homogeneous spaces III,.

Zariski density of discrete subgroups via critical exponents and unitary representations Tempered homogeneous spaces III,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.462309Z

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Observation 38adc6a6-8f5d-4366-80ee-60cfb8740183 · outbound

This paper cites Tempered homogeneous spaces IV,.

Zariski density of discrete subgroups via critical exponents and unitary representations Tempered homogeneous spaces IV,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.455501Z

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Observation d5764d55-a907-4439-a156-21de9f5392fb · outbound

This paper cites On the rate of exponential decay of coefficients on homogeneous spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations On the rate of exponential decay of coefficients on homogeneous spaces,

Reference 9

Resolution: verified exact; raw_fallback, observed 2026-08-06T13:01:24.321435Z

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Observation 78fe6cb0-7c5f-4bb3-bb29-92bdf2c3a7a3 · outbound

This paper cites Density properties for certain subgroups of semi-simple groups without compact components,.

Zariski density of discrete subgroups via critical exponents and unitary representations Density properties for certain subgroups of semi-simple groups without compact components,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.447787Z

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Observation 4d71781b-424c-4828-be30-b9cb0ece7295 · outbound

This paper cites Hausdorff dimensions of limit sets I.

Zariski density of discrete subgroups via critical exponents and unitary representations Hausdorff dimensions of limit sets I

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.439953Z

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Observation b3b09de6-d321-4ee7-a95c-0ab4e303e57d · outbound

This paper cites AlmostL2 matrix coefficients,.

Zariski density of discrete subgroups via critical exponents and unitary representations AlmostL2 matrix coefficients,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.432860Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a8208763-63a1-4d30-bfc0-7a60dca340cd · outbound

This paper cites Complex hyperbolic Kleinian groups of large critical exponents,.

Zariski density of discrete subgroups via critical exponents and unitary representations Complex hyperbolic Kleinian groups of large critical exponents,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.425716Z

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Observation cc7c9a6b-e629-4e98-91d7-6cb856ec7915 · outbound

This paper cites Effective equidistribution for closed orbits of semisimple groups on homogenous spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations Effective equidistribution for closed orbits of semisimple groups on homogenous spaces,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.418728Z

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Observation 33157f91-c4f3-40bc-835e-326e6a843f61 · outbound

This paper cites Infinite volume and infinite injectivity radius,.

Zariski density of discrete subgroups via critical exponents and unitary representations Infinite volume and infinite injectivity radius,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.411320Z

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Observation c89a8d6e-8849-4afa-bd9d-00cfbc921a6e · outbound

This paper cites Benjamini–Schramm convergence of arithmetic locally symmetric spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations Benjamini–Schramm convergence of arithmetic locally symmetric spaces,

Reference 16

Resolution: verified exact; raw_fallback, observed 2026-08-06T13:01:24.256417Z

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Observation b410d730-0ea2-4b8c-bd21-c6c6befad083 · outbound

This paper cites Topological complexity of arithmetic locally symmetric spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations Topological complexity of arithmetic locally symmetric spaces,

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.404078Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e6c4251d-8f25-4737-8ff3-44f6e33b4c0e · outbound

This paper cites Poisson-Voronoi tessellations and fixed price in higher rank.

Zariski density of discrete subgroups via critical exponents and unitary representations Poisson-Voronoi tessellations and fixed price in higher rank

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T13:01:24.054043Z

Source-reported events for the cited work

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Observation bc9eb111-90bc-4ee7-9884-1addb4171fee · outbound

This paper cites Humphreys,Linear algebraic groups, volume 21 ofGrad.

Zariski density of discrete subgroups via critical exponents and unitary representations Humphreys,Linear algebraic groups, volume 21 ofGrad

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.396931Z

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Observation 90e916e8-b21e-4ddf-a93d-c0583c1f4a52 · outbound

This paper cites Knapp,Lie Groups Beyond an Introduction,Progress in Mathematics,Birkhäuser Boston Inc., (1996).

Zariski density of discrete subgroups via critical exponents and unitary representations Knapp,Lie Groups Beyond an Introduction,Progress in Mathematics,Birkhäuser Boston Inc., (1996)

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.389492Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 90047540-6f8c-4931-85b4-ce15eadcea76 · outbound

This paper cites Knapp,Representation theory of semisimple groups: An overview based on examples, volume 36 ofPrinceton.

Zariski density of discrete subgroups via critical exponents and unitary representations Knapp,Representation theory of semisimple groups: An overview based on examples, volume 36 ofPrinceton

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.381892Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 518ae4d0-3111-4ccd-8092-9cdd2a82e488 · outbound

This paper cites Kazhdan’sproperty(T),L 2-spectrum, andisoperimetricinequalitiesforlocally symmetric spaces,.

Zariski density of discrete subgroups via critical exponents and unitary representations Kazhdan’sproperty(T),L 2-spectrum, andisoperimetricinequalitiesforlocally symmetric spaces,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.374838Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e9cde7ce-2b1f-4e90-822f-59b60c3ee942 · outbound

This paper cites Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces.

Zariski density of discrete subgroups via critical exponents and unitary representations Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-06T13:01:24.187654Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4c3dab4a-8633-467c-8bc0-cda459d58321 · outbound

This paper cites Margulis,Discrete subgroups of semisimple Lie groups, volume 17 ofErgebnisse der Mathematik und ihrer Grenzgebiete,Springer-Verlag,Berlin, (1991).

Zariski density of discrete subgroups via critical exponents and unitary representations Margulis,Discrete subgroups of semisimple Lie groups, volume 17 ofErgebnisse der Mathematik und ihrer Grenzgebiete,Springer-Verlag,Berlin, (1991)

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.367827Z

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Observation c5e4c667-a85c-4762-b233-ef880675dc1d · outbound

This paper cites Exponential decay of correlation coefficients for geodesic flows,.

Zariski density of discrete subgroups via critical exponents and unitary representations Exponential decay of correlation coefficients for geodesic flows,

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.360232Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation eb6afe45-3e84-4da0-b0f4-dccebdd5e8ea · outbound

This paper cites Divergence exponentielle des sous-groupes discrets en rang supérieur,.

Zariski density of discrete subgroups via critical exponents and unitary representations Divergence exponentielle des sous-groupes discrets en rang supérieur,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.352986Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 283ded08-5d81-4524-9698-b3bc4c10dc67 · outbound

This paper cites Propriété de Kazhdan et sous-groupes discrets de covolume infini,.

Zariski density of discrete subgroups via critical exponents and unitary representations Propriété de Kazhdan et sous-groupes discrets de covolume infini,

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.345138Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5877241f-eac9-4809-b692-6db167957fc4 · outbound

This paper cites Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups,.

Zariski density of discrete subgroups via critical exponents and unitary representations Asymptotically large free semigroups in Zariski dense discrete subgroups of Lie groups,

Reference 28

Resolution: verified exact; raw_fallback, observed 2026-08-06T13:01:24.175506Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5563379c-a0cc-4068-863d-eaadf3e23c55 · outbound

This paper cites ExoticC∗-algebras of geometric groups,.

Zariski density of discrete subgroups via critical exponents and unitary representations ExoticC∗-algebras of geometric groups,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.337868Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3c2ed00f-b919-419f-8a47-344d2f533079 · outbound

This paper cites Zimmer,Ergodic theory and semisimple groups, volume 81 ofMonogr.

Zariski density of discrete subgroups via critical exponents and unitary representations Zimmer,Ergodic theory and semisimple groups, volume 81 ofMonogr

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T13:01:24.330348Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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