Pith. sign in

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.

source=pdf_text observed=2026-08-11T00:43:52.133937Z digest=sha256:5cd489346f2cd1325bddb0dd56e987ee615616e15d4315ffaf49ef24afc6d86b

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=sha256:9e5aa71055ed6e8d1494277e26eaa73e520af2e3a3a84470e48e76cfaa6ee59d

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.

source=pdf_text observed=2026-08-11T00:43:52.145093Z digest=sha256:ff4edd3e366bedff133caf751b57787f71cc96edeac160b509d293c1c4c9d5d5

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=sha256:154de80280997fc3a755819891f6133cacf6b25cf455e991eca878d5a32056e0

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:e5eac3bd4699c85d572adda7cc03f3fe93b38220bed3d606ac7da030951c0205

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.

source=pdf_text observed=2026-08-11T00:43:52.160787Z digest=sha256:d182e6423d60cb7b3e0607b1cb387c9329887b47733f7c0b98bef26cffb7a4d5

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:c161f50089cc9e36e41ee88fe08e3c8769add9624011e87301ee36b692e1175e

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=sha256:411402c116901054e767562839f259a789793251d09f908cc42e6ffa0ca4dc28

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:b51067e3c30d704b8151867e16008c8134872f838c15bdf52d6995248886ffe2

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=sha256:941aa3ec999cad7508ab11d0a2c453a9166f07e5c96a197940f6cea1baaf09a9

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=sha256:7270f09b63532ff4ac6be26e5f38476c50e548a5e0bea5bcf60824516894b49d

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=sha256:9f1d9c15104f172870c13ce180f318a204f968932ec14a098ca977fb2d8bddb4

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=sha256:2679f50af9b30a1b59fb79481da3d8ab6ebca4d62cb6713143912558d3e0d813

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=sha256:07fa2d044e710a215394da460c9190126b8d0327b3b38269135e2da661d68a19

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:b1161fde0b7745f612660bdaaff840f4493e2b80cfc991e717534bf29d762692

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:d2c863ea1cd1835816115abb96c79eccca1cee09a16442ac542438609eae136d

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=sha256:27f0ecfe8a051e84780f7d33d3d35305c8e26ffb208c9ffa107a7866872cfe55

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=sha256:3509385c637f936bcd8bdf50d4072dbf905907aa20c6afefcfc3983151ef05f5

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:e837df99649f9161981e51e19c03ad4e612087b8cef9458a083b3ded1f51ca3e

Pith citing papers

No inbound Pith citation observations are available.