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Paper Citation Record · LEDGER

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus

As of 10 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2507.23494.

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

pith.paper-citation-record.v1
2507.23494 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T10:49:10.472408Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

19 of 19 outbound references displayed

  • verified exact0
  • verified fuzzy14
  • unresolved5
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0acd2dfd-a375-483a-b17f-623e1c188b69 · outbound

This paper cites Self-similar and self-affine sets and measures.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Self-similar and self-affine sets and measures

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:14.516514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:07.739842Z digest=sha256:4d7f601e67e8efd5d69793c0773446b6b79e506f4cbfd1afc46b451ed62e57de

Observation 746eac04-7906-4185-8679-3bbe87f0e04c · outbound

This paper cites Modulation spaces, Wiener amalgam spaces, and Brownian motions.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Modulation spaces, Wiener amalgam spaces, and Brownian motions

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:14.197119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:07.882061Z digest=sha256:e142826b175b3e6dadc1934997ca3f437c6588a48a6d5373889e7e88d8da82a9

Observation 270deb15-a058-461e-9c76-9151ace86bc2 · outbound

This paper cites Multifractal analysis of Gaussian multiplicative chaos and applications.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Multifractal analysis of Gaussian multiplicative chaos and applications

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:13.856207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.010189Z digest=sha256:98e13fea6e7d26200fa295f79d22f086eac404d74306fa78a870e1c3196f9917

Observation e3428cd1-58f9-4f68-80da-85aaf4205290 · outbound

This paper cites Functional analysis, Sobolev spaces and partial differential equations.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Functional analysis, Sobolev spaces and partial differential equations

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:13.530352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.173979Z digest=sha256:4ac64e2ed8fa3b4bf826eabc4593a5fb71a0c20f652cef1676ca7f1a584c496d

Observation b5dc499a-d9c1-4661-8729-bd5c6e45894b · outbound

This paper cites Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Harmonic analysis of Mandelbrot cascades -- in the context of vector-valued martingales

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-06T10:49:08.330167Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T10:49:08.330167Z digest=sha256:b1d00aeb2fb1ac0feda58a9f33b7a85ae0d956e4d2ae16e4424b068cf7eeab15

Observation e62c7322-04fc-427c-85bb-901444d0ff10 · outbound

This paper cites Fourier restriction, decoupling, and applications.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Fourier restriction, decoupling, and applications

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:13.192179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.559493Z digest=sha256:08475d0ce2a826e32b0321e8e0f9154ea0e134549b4e3474f5fce2c56a6ed39a

Observation 59766b0c-8cb9-4e97-bd57-564350bfb25b · outbound

This paper cites Harmonic analysis of Gaussian multiplicative chaos on the circle.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Harmonic analysis of Gaussian multiplicative chaos on the circle

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-06T10:49:08.723603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T10:49:08.723603Z digest=sha256:bd1d5dba85dad508d4882168e8b0e96a45ec42c118057a7b575d68b4a6360ed3

Observation 5c5fd765-dc9f-4837-952b-972844a77544 · outbound

This paper cites an unresolved cited work.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:12.943906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.863891Z digest=sha256:3884a334e5a3107c52e199ba2ee0a9e9294702d2bbebbd5227ca0311930a0f40

Observation 4229e194-d596-4caf-9aa2-5e51675f372a · outbound

This paper cites Sur le chaos multiplicatif.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Sur le chaos multiplicatif

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:12.773769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.043457Z digest=sha256:c33272d12820cc21bb9986add4366c9dfd130d5d8d6811ffd1450794bb2609e7

Observation 1585d579-f22e-41f7-89cf-05cd5af120be · outbound

This paper cites Positive martingales and random measures.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Positive martingales and random measures

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:12.514880Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.197271Z digest=sha256:fb5d9eee643e3229c298846fd6a540e93813249716bb326c461c45bff15854d9

Observation a4780798-37df-49fa-b190-4ac934a1765e · outbound

This paper cites Foundations of modern probability.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Foundations of modern probability

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:12.294079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.328076Z digest=sha256:f65f82c67e5108cad8b494a79c874018bd95faf953e94e3a192cd70df66472cb

Observation 3e4fe713-4831-40cd-bd4a-c89282ddc79f · outbound

This paper cites Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Harmonic analysis of multiplicative chaos Part I: the proof of Garban-Vargas conjecture for 1D GMC

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-06T10:49:09.501454Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T10:49:09.501454Z digest=sha256:7341646448e812f68d02e4048fb449886821d16c9056158c7e6f4023cd4e3ee8

Observation d6befb78-ddfc-4d37-afc5-079edde27abd · outbound

This paper cites Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Harmonic analysis of multiplicative chaos Part II: a unified approach to Fourier dimensions

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-06T10:49:09.630961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-06T10:49:09.630961Z digest=sha256:497f89e03c6903a288fb0e29919986c3c35ad28ac8a283059b5626d960f5ed72

Observation 19b6f39a-31ad-4ef3-a364-b5c49ce3a70f · outbound

This paper cites On Landau damping.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus On Landau damping

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:12.026271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.751700Z digest=sha256:b8d8bce58f53dabf38b805546c3c424f96a01cbcaacd0281c8820d648622aafc

Observation 4667315f-3cbb-4ad7-aa6f-19557a0fce8a · outbound

This paper cites Oppenheim and Ronald W.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Oppenheim and Ronald W

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:11.788128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.951895Z digest=sha256:6c4969e49bd0dfa94b6e87f8c70b36e4866dc7cefb458a9dfeb21509b6715b33

Observation a22cd5f2-673d-4074-8288-4c5b33605702 · outbound

This paper cites Martingales in Banach spaces.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Martingales in Banach spaces

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:11.565061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.118854Z digest=sha256:7ab3f1d8174b5796faaa36fd40cd7b5bdb0efc13d7cfabcb0812c4160f86e324

Observation 2ffa45a6-cd3d-4fc2-a60b-a3f9dc0b0cbb · outbound

This paper cites Gaussian multiplicative chaos and applications: a review.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Gaussian multiplicative chaos and applications: a review

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:11.343447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.259574Z digest=sha256:546f1621804bcebc6108e7b9ae7a187b9e36d80aa20fd01e11a169d5a41097e5

Observation 09338e47-0cff-4453-8dd8-945305fd616b · outbound

This paper cites Fourier analysis on groups.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Fourier analysis on groups

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:11.020211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.391769Z digest=sha256:7b1f96035cae5a8902baed74c3d0861589b9cd8fa9eaeb0236afd36f8675a12a

Observation 8fed09fd-74c0-4e79-a84b-49cf994ec74a · outbound

This paper cites Changes of variables in modulation and Wiener amalgam spaces.

Exact values of Fourier dimensions of Gaussian multiplicative chaos on high dimensional torus Changes of variables in modulation and Wiener amalgam spaces

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:10.807762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.472408Z digest=sha256:d6c14dd63c2f4c6e662a83b4dc04a9e8f62fff53bfa1b287001e5ef7eb6b3e49

Pith citing papers

No inbound Pith citation observations are available.