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Paper Citation Record · LEDGER

Linear dependence of time-frequency shifts of a Schwartz function

As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 2 inbound Pith citation observations for arXiv:2608.05044.

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

pith.paper-citation-record.v1
2608.05044 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T10:49:17.198226Z

measured 29 of 29 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T00:29:35.546201Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T00:43:52.296689Z

Reference resolution

27 of 27 outbound references displayed

  • verified exact0
  • verified fuzzy12
  • unresolved15
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 41579569-e444-417d-bb7c-4fb2f03760ca · outbound

This paper cites Antezana, J.

Linear dependence of time-frequency shifts of a Schwartz function Antezana, J

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:23.998653Z

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=2026-08-06T10:49:13.156867Z digest=sha256:7ff6f9e3b31dc75204aa1599c6116c22a899e7e565e183ddcb962416feeba600

Observation b7ad7bd4-1a87-4837-b5c7-aaa9d89e47d0 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:23.694245Z

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=2026-08-06T10:49:13.288004Z digest=sha256:4cd1b0a2435d00e11fc29e8b6cdcc3bc0b56d57230ab3ebaee5445e79ada3123

Observation deed321f-7ba7-4b09-a6c0-176d2aa5366f · outbound

This paper cites Bownik and D.

Linear dependence of time-frequency shifts of a Schwartz function Bownik and D

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:23.346702Z

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=2026-08-06T10:49:13.449257Z digest=sha256:f45a2d37712b753942ac5ad416dc9e93fc02f9a1417f9262a0b8f96f2cef819a

Observation 7d2e23c0-118c-4d97-8dc3-20068e8b4a4a · outbound

This paper cites Bownik and D.

Linear dependence of time-frequency shifts of a Schwartz function Bownik and D

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:23.114002Z

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=2026-08-06T10:49:13.605119Z digest=sha256:312f7546dae8dab3bb06ed3de1ef1ae8cb914951a073bb5a0d06521642871d5a

Observation b904c721-3baa-4049-9cd3-a163c5fb69bd · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:22.803485Z

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=2026-08-06T10:49:13.771716Z digest=sha256:218b9238c7cc537faaf493e4173b192a73470e853487802b471c6a7f217261ee

Observation 184d9800-10b8-407c-9311-ec694d774d97 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:22.496034Z

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=2026-08-06T10:49:13.939280Z digest=sha256:1a75a869f08078e0129514d0828dcefc495deec391ae9cb319067dd6613ee60f

Observation da502665-fbcd-4c79-b084-cc1487463793 · outbound

This paper cites Demeter and S.

Linear dependence of time-frequency shifts of a Schwartz function Demeter and S

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:22.160812Z

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=2026-08-06T10:49:14.077814Z digest=sha256:23d1e95e6c4a1782b9a7afdecd9aafb152ea2107c6af52722197594407e0330a

Observation 40997113-e33d-449c-b053-50f3da2e178d · outbound

This paper cites Demeter and A.

Linear dependence of time-frequency shifts of a Schwartz function Demeter and A

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:21.968478Z

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=2026-08-06T10:49:14.301015Z digest=sha256:8ce002d7e097b91196a763da92fc810f90bdaef7793cea17035cfc64400ba491

Observation 0ad25bfb-0634-4bea-860d-c1096f3b69b2 · outbound

This paper cites Enstad and J.

Linear dependence of time-frequency shifts of a Schwartz function Enstad and J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:21.704667Z

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=2026-08-06T10:49:14.421076Z digest=sha256:4b23ca913d647149c946e6f35c36eef1d8348b011b8886586a1f27fcc4d5cfbd

Observation ba741b17-827a-4219-b762-e1d1f8f00d65 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-06T10:49:14.576136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T10:49:14.576136Z digest=sha256:328fa08f6409a040ed9313f78a749c7ce19dceb781e0bf47972bb430b0f38203

Observation 8627786b-ce85-4d35-9327-a1603da16b06 · outbound

This paper cites Grafakos.Classical Fourier analysis, volume 249 ofGraduate Texts in Mathematics.

Linear dependence of time-frequency shifts of a Schwartz function Grafakos.Classical Fourier analysis, volume 249 ofGraduate Texts in Mathematics

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-06T10:49:14.737954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-06T10:49:14.737954Z digest=sha256:58249f13f0a103ee0869328f471fd211b2cc3ae5abcc1da2bfe07db9b020b4eb

Observation c8cc1120-637d-4396-9174-cc18d81e3646 · outbound

This paper cites Gröchenig.Foundations of time-frequency analysis.

Linear dependence of time-frequency shifts of a Schwartz function Gröchenig.Foundations of time-frequency analysis

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:21.405380Z

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=2026-08-06T10:49:14.873871Z digest=sha256:0166427b1c0e5a61ffc78059b09ffc57c3d90129de39ce0fbaaf22760dd98998

Observation ac9b6989-addb-4bf2-9f71-0ce77f80a234 · outbound

This paper cites Gröchenig.

Linear dependence of time-frequency shifts of a Schwartz function Gröchenig

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:21.081223Z

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=2026-08-06T10:49:15.037124Z digest=sha256:4abff343e637eda62d5ef2e54b0f02b771f93eac253ad21fa80404849ae2df45

Observation 08f12ac0-757d-44a8-b313-539e91f3ba65 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:20.825783Z

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=2026-08-06T10:49:15.189704Z digest=sha256:b2082b5e4d9c7884a317ebb66fd08370b5dc015b26813733c92454369e1007cb

Observation f79e36e1-5846-4b15-88f8-4a2cbccf0122 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:20.587916Z

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=2026-08-06T10:49:15.331870Z digest=sha256:9fcac25b1887a69f8af0b2a15ee57cfe0e8311aeb0dbd27020897392473b2a5b

Observation 0aa89bbd-a369-4a0e-a94e-e1c96f100ff2 · outbound

This paper cites Heil and D.

Linear dependence of time-frequency shifts of a Schwartz function Heil and D

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:20.381418Z

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=2026-08-06T10:49:15.515556Z digest=sha256:2fdb9ccc6b71a474a4f0c66f5027a1760c190d21ed970181ee79382c4f69a1fa

Observation 22b26fda-ecac-4cb0-a62c-cb32cea565ae · outbound

This paper cites Comput., 66(8):1281–1292, 2017.

Linear dependence of time-frequency shifts of a Schwartz function Comput., 66(8):1281–1292, 2017

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:20.123019Z

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=2026-08-06T10:49:15.666595Z digest=sha256:aa441a6976b88a7ff9d64195efc5dc94e49ce193136f12252c94898a21ba508d

Observation 1862c880-2f85-4061-9f42-8e4258bd7b25 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:19.854649Z

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=2026-08-06T10:49:15.837696Z digest=sha256:804aa88f2d4e1bc994435943c7100c964c9a4646b01ed2d4800ad0928a92ffd7

Observation 969c1cd2-04ea-456d-8a6d-e1e8ebe4ed1c · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:19.599463Z

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=2026-08-06T10:49:15.993690Z digest=sha256:a1025b25cd417ae71a7b35990a62d1e162a5daab9f7a5aecc5692b931c683b93

Observation 12b88534-1ee2-4f20-81a0-dc118eacfbdb · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:19.363607Z

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=2026-08-06T10:49:16.164668Z digest=sha256:620a1d8351e5acd56e0cfd9594b397a68a13a18ce6ad138f13d98c82590a2726

Observation 17a9c308-49c0-4bd1-898d-e133197dc7d5 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:19.111975Z

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=2026-08-06T10:49:16.333116Z digest=sha256:292e46f332e2c8a8a4c0eab13497794d475a84c4e78895b47b8acc2e3e0e1903

Observation 8679a0aa-d2c9-4aa2-bbde-c3a8959b8173 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:18.893084Z

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=2026-08-06T10:49:16.492158Z digest=sha256:9fe7c8e4eb54636ddcfe512e0aada3c955863a48e5eadc63471fa56da32e6b6b

Observation fa11a5d0-b1ec-481a-bc82-b26743d2bf81 · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:18.547067Z

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=2026-08-06T10:49:16.578412Z digest=sha256:afc681a42f6295b47b8651615c33b77be12e50deebc85e96f436f83d73222311

Observation 45777ab9-56c0-41e5-ab5c-60843dd0b1ea · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:18.312812Z

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=2026-08-06T10:49:16.758399Z digest=sha256:f398136577f1cb115ad9677b5c374047a543525bc71e6017e2593f2dc0aa1bd2

Observation 5d943d69-f014-4d6c-9e18-f851575fbc1b · outbound

This paper cites an unresolved cited work.

Linear dependence of time-frequency shifts of a Schwartz function Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-06T10:49:17.943455Z

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=2026-08-06T10:49:16.915097Z digest=sha256:ec1594ff72cdac811af6c347c2e1b3c4345e86427c3eb047ca37544f0addf01d

Observation 98e93f18-1da6-4ba4-a4c2-3ddbe304ef9f · outbound

This paper cites Tucker.Validated numerics.

Linear dependence of time-frequency shifts of a Schwartz function Tucker.Validated numerics

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:17.632734Z

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=2026-08-06T10:49:17.033368Z digest=sha256:613c175c54381b7e16f3452272f7c94265c05585a0fc66c5443df76f134b48ea

Observation 20eaefd8-14dd-4b54-b9a7-343e2b254463 · outbound

This paper cites Zibulski and Y.

Linear dependence of time-frequency shifts of a Schwartz function Zibulski and Y

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-06T10:49:17.471941Z

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=2026-08-06T10:49:17.198226Z digest=sha256:e9f8c86782f4c8f9c36614e2ebb4a47fcfe31269697f4607f5448a9d0d0a7fa9

Pith citing papers

Observation d829b681-dae2-434a-98c4-16e82fa4ff1c · inbound

An intrinsically subcritical four-point counterexample cites this paper.

An intrinsically subcritical four-point counterexample Linear dependence of time-frequency shifts of a Schwartz function

Reference 5

Resolution
metadata mismatch
local_arxiv, observed 2026-08-11T00:43:52.302532Z

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=2026-08-11T00:43:52.155248Z digest=sha256:07a3fe281702bd18cdc18515187d49ef9c4ad1c5b4ba847282411ef4099a379f

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

The Minimum Cardinality of a Dependent Finite Gabor System Is Four cites this paper.

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.

source=pdf_text observed=2026-08-12T00:29:35.546201Z digest=sha256:df87dbe90d92fc6c9489bd13cf55ab04ac2a6d4c33768f504c8690cb9b66a50d