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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 2026-08-10T06:31:04.303077+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
  • metadata mismatch0

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:07.739842Z digest=sha256:8aa91c6a2751c89927fad5d8a585d9d67e0e383ac44502c3358f5636bbada78d

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:07.882061Z digest=sha256:ea380c726a4eba85ccdb8963768874047de39ef4ba9c5cf828b688729a8b98a4

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.010189Z digest=sha256:25050df4eeb8275d9e7f926924d66bba0814b76eac079267c16eda1a26eb3b94

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.173979Z digest=sha256:94d49eb551eb87bc4919e24329218a22e60fbb6e23eec76f814e1d618f1195e5

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.559493Z digest=sha256:34ef1abf45acc80c84ab097443d5e60092408b808a2f7ab3def10a3754441c38

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=sha256:54bb71182ef2d1e6a615369b50126a8da5f5118affb8bcc0af9718b918780a1d

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:08.863891Z digest=sha256:ed902422d9e7421ec69f7276a70b8fb4837a4a0cecc3616e15d8c4219d8fcd41

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.043457Z digest=sha256:4080d5fe2e05596c38690bea3c8729c161cdca158f02f563dc791d00a5232572

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.197271Z digest=sha256:83ea453341dd576692b5d4559b19fc0c530fa0472d1421420cbc1ad8017ab9c7

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.328076Z digest=sha256:fe075cb03c6ab7681c71a7e1d11976c2387b8e9a90278c797bd1d9ea6ff707d6

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.751700Z digest=sha256:32e98e21cc79ad6ecdc3f2ca40c40e38e28099f793dce21f4596370663b0a177

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:09.951895Z digest=sha256:2edf572aa74c745896d5e11d7083fe39be8220947f274fa3914351ad890b09e4

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.118854Z digest=sha256:197a61ac39034c72e84ecd1b3d4037843ef9fdb58f52350a2a42f66cd4467851

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.259574Z digest=sha256:5027903caea9ca85628b8b0c97797a2e395b05496280ae5ed1227b04d379cb1b

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.391769Z digest=sha256:5e7214bfb4226ab20a24ce19ebd3bd4aee2fc3e40fa94c72888d6b5f782fe519

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 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-08-06T10:49:10.472408Z digest=sha256:9e3dea9841c26b95f1865ad935c2fb45ead4966631125527c7a9786cba475ce5

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