Paper Citation Record · LEDGER

The Minimum Cardinality of a Dependent Finite Gabor System Is Four

As of 12 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2608.08190.

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

pith.paper-citation-record.v1
2608.08190 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T00:29:35.580669Z

measured 16 of 16 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 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

16 of 16 outbound references displayed

verified exact10
verified fuzzy1
unresolved4
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 369192c2-1414-41a1-bd3d-5c26cbd659b2 · outbound

This paper cites Benedetto and Abdelkrim Bourouihiya, Linear independence of finite Gabor systems determined by behavior at infinity,J.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Benedetto and Abdelkrim Bourouihiya, Linear independence of finite Gabor systems determined by behavior at infinity,J

Reference 1

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.713937Z

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.

Observation 5c973d77-3bee-43da-b582-45d91d299533 · outbound

This paper cites an unresolved cited work.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Unresolved cited work

Reference 2

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.702415Z

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.

Observation 64ceb103-3618-4182-86c4-618590322a6e · outbound

This paper cites an unresolved cited work.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Unresolved cited work

Reference 3

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.689523Z

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.

Observation ff9e481d-5cd9-4fe5-8624-bedeec8e421d · outbound

This paper cites an unresolved cited work.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Unresolved cited work

Reference 4

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.678774Z

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.

Observation 1079f9ca-5550-4192-815e-67d774d36da9 · outbound

This paper cites Linear dependence of time-frequency shifts of a Schwartz function.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Linear dependence of time-frequency shifts of a Schwartz function

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-12T00:29:35.546201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a6214d3-cad2-4a29-99a1-b2bdbe7329fe · outbound

This paper cites Folland,Harmonic Analysis in Phase Space, Annals of Mathematics Studies, vol.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Folland,Harmonic Analysis in Phase Space, Annals of Mathematics Studies, vol

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T00:29:35.825828Z

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.

Observation 92dfffa9-71bc-4183-8eea-a47bdb6aa69d · outbound

This paper cites DOI: 10.1007/978-1-4612-0003-1.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four DOI: 10.1007/978-1-4612-0003-1

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-12T00:29:35.553201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ed597e0-581c-4522-95f8-931f2817280b · outbound

This paper cites Math.177(2015), no.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Math.177(2015), no

Reference 8

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.659239Z

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.

Observation dd31da22-4dc5-4495-9eec-5315e34c8d84 · outbound

This paper cites The HRT Conjecture for Symmetric Configurations and Real-Valued Functions.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four The HRT Conjecture for Symmetric Configurations and Real-Valued Functions

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-12T00:29:35.805703Z

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.

Observation 1f99957d-09c4-4e4a-b3b2-95881964834a · outbound

This paper cites an unresolved cited work.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Unresolved cited work

Reference 10

Resolution: malformed identifier; doi_truncated, observed 2026-08-12T00:29:35.645954Z

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.

Observation 2258e8e1-383a-4671-b6f9-984b60c82f69 · outbound

This paper cites an unresolved cited work.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Unresolved cited work

Reference 11

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.636176Z

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.

Observation f844b2d4-db65-4ef5-99dd-136e6cd05677 · outbound

This paper cites an unresolved cited work.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T00:29:35.569473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f58f359-c1ec-4861-9363-89b2f50e3c82 · outbound

This paper cites Linnell, Von Neumann algebras and linear independence of translates,Proc.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Linnell, Von Neumann algebras and linear independence of translates,Proc

Reference 13

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.626390Z

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.

Observation 7ae02a6d-7920-46fd-9208-d4b3a6604ff0 · outbound

This paper cites Fourier Anal.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Fourier Anal

Reference 14

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.616689Z

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.

Observation 3fbfcc18-cf28-4c50-b449-039676c648ae · outbound

This paper cites Okoudjou, Extension and restriction principles for the HRT conjecture,J.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Okoudjou, Extension and restriction principles for the HRT conjecture,J

Reference 15

Resolution: verified exact; doi, observed 2026-08-12T00:29:35.605748Z

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.

Observation 489123ea-0c3e-485f-a65c-db4b2665059f · outbound

This paper cites Lean-certified four-point HRT results for three lattice points and one off-lattice point.

The Minimum Cardinality of a Dependent Finite Gabor System Is Four Lean-certified four-point HRT results for three lattice points and one off-lattice point

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-12T00:29:35.580669Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.