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Paper Citation Record · LEDGER

An intrinsically subcritical four-point counterexample

As of 12 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2608.07604.

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

pith.paper-citation-record.v1
2608.07604 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:43:52.228986Z

measured 19 of 19 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

19 of 19 outbound references displayed

  • verified exact1
  • verified fuzzy9
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0ef964f8-4fc4-4876-84c7-3a0636b58ffa · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.584974Z

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.

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Observation ed041cbd-9b75-45cb-af80-28b72835c2b7 · outbound

This paper cites 12699, Springer, 2021, pp.

An intrinsically subcritical four-point counterexample 12699, Springer, 2021, pp

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.569171Z

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=2026-08-11T00:43:52.140332Z digest=sha256:5277985338f090f34d8df6f5f302babbfdead2851fc1c1bfe5e83bb5c29f9cb5

Observation 8e413871-2795-4173-a2f6-e5eca4bca9b0 · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.553198Z

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.

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Observation b35d349c-0eca-49c8-a8b2-b23d07517e4a · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.536959Z

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=2026-08-11T00:43:52.149827Z digest=sha256:65447ba9ccd7f1daef04bdf28142dddc6e7daab8138c324edb93f9106e0b6973

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

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

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=sha256:85d1c289acc0f77be5200d036bb8ad7fca1390d662621cb5a7efe6045d5e0daf

Observation 861b397d-f4ed-43d8-8f00-b6eba881417a · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.520745Z

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.

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Observation 8cc84277-64bc-4199-bf2d-a44f057dd258 · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.505197Z

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=2026-08-11T00:43:52.166335Z digest=sha256:23b0fa58af33cf895f002c33d51033362f8b68cab892dffdcf0a54054f498776

Observation 8e241402-07e6-4eba-995a-ae8cd8e6e864 · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.485159Z

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=2026-08-11T00:43:52.171276Z digest=sha256:5abf5a07c23f52ee0bb5501ec8decdf0d64e8e89f0965e150af2308705076a43

Observation ff9515dc-72b7-412b-9be2-32002ab196fb · outbound

This paper cites Hirsch, Charles C.

An intrinsically subcritical four-point counterexample Hirsch, Charles C

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.471168Z

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=2026-08-11T00:43:52.176483Z digest=sha256:ee3d6365ce86e67186ea6ec2dd6130ed92b4c6f925605a7c1e48af81fab96682

Observation 1761bd15-8e37-4d48-85e2-ad4b17823710 · outbound

This paper cites Comput.66(2017), no.

An intrinsically subcritical four-point counterexample Comput.66(2017), no

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.455215Z

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=2026-08-11T00:43:52.181628Z digest=sha256:412895b649b90989b21f166007fe8e74a11e3f4e1a79281690c71a4b09a44851

Observation 2b2e964f-556d-4535-ba4b-49b80edb3450 · outbound

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

An intrinsically subcritical four-point counterexample Linnell,Von Neumann algebras and linear independence of translates, Proc

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.439438Z

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=2026-08-11T00:43:52.186830Z digest=sha256:798fcee30325e8fa76c5471d3f83ac4ead8d75e0c53c0e27f7f67d9783fe0319

Observation a53e93ff-0723-40a0-9a06-ea5391bbc420 · outbound

This paper cites Fourier Anal.

An intrinsically subcritical four-point counterexample Fourier Anal

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.423321Z

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=2026-08-11T00:43:52.191734Z digest=sha256:e20d70d36e8b7cc3b79442dd0ca703db26eb8260c0eb0d0e1051c5772ab88281

Observation d3eb4578-94c4-4e6c-bd44-7ee18cb53e05 · outbound

This paper cites Moore, R.

An intrinsically subcritical four-point counterexample Moore, R

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.406358Z

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=2026-08-11T00:43:52.197060Z digest=sha256:f5569e658b25f32989dc8c4bad559a9562ba1ca94a5b3b60813dd93ca4a9a349

Observation fa3ac72c-8d84-44e0-85c5-9dda99da748c · outbound

This paper cites Okoudjou and Vignon Oussa,Letter to the editor: On a special configuration for the HRT conjecture, J.

An intrinsically subcritical four-point counterexample Okoudjou and Vignon Oussa,Letter to the editor: On a special configuration for the HRT conjecture, J

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.387883Z

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=2026-08-11T00:43:52.202881Z digest=sha256:f0ba7909e92ca65c18307bdd4a13964bc5f3ecdc5c14e35c6bf84193a2fe57af

Observation ac3f4a21-18e8-4d30-bd19-bee17a44f01b · outbound

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

An intrinsically subcritical four-point counterexample Lean-certified four-point HRT results for three lattice points and one off-lattice point

Reference 15

Resolution
verified exact
local_arxiv, observed 2026-08-11T00:43:52.277521Z

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=2026-08-11T00:43:52.208057Z digest=sha256:68263cbb4d30b0a7c8f418f6e5d5109b294d467ebf285185ef106b155cd23466

Observation b562f10f-d72e-405e-8d34-a0403d97149f · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.370199Z

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=2026-08-11T00:43:52.213971Z digest=sha256:4caa509e840211dddf85d517319d7cd6f5b8aed28c876ca70801441c0793fc14

Observation 92815346-d622-4d9a-a281-65368a7a1be0 · outbound

This paper cites Rump,Verification methods: Rigorous results using floating-point arith- metic, Acta Numer.19(2010), 287–449.

An intrinsically subcritical four-point counterexample Rump,Verification methods: Rigorous results using floating-point arith- metic, Acta Numer.19(2010), 287–449

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.353885Z

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=2026-08-11T00:43:52.219180Z digest=sha256:c587bd4589557443756b9e32505861b672d45e886e55742f02cadfdb5d7e96d1

Observation bf6926e2-d27c-4370-94b0-28c69607a206 · outbound

This paper cites an unresolved cited work.

An intrinsically subcritical four-point counterexample Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:43:52.337730Z

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=2026-08-11T00:43:52.223807Z digest=sha256:adb40f72e139cafe034d9af8e9211ef2c62b9260d1c303b65545cf3eccdce84d

Observation bf365ab3-6f7b-4086-8f07-cdd60aa9a0d4 · outbound

This paper cites Zeevi,Analysis of multiwindow Gabor-type schemes by frame methods, Appl.

An intrinsically subcritical four-point counterexample Zeevi,Analysis of multiwindow Gabor-type schemes by frame methods, Appl

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:43:52.320347Z

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=2026-08-11T00:43:52.228986Z digest=sha256:734aeda6f2d92326cd887c688688e6c51aba04d615db61fcb2b0c0f28726ef1c

Pith citing papers

No inbound Pith citation observations are available.