Paper Citation Record · LEDGER

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces

As of 19 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2509.08168.

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

pith.paper-citation-record.v1
2509.08168 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:30:18.211999Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

25 of 25 outbound references displayed

verified exact3
verified fuzzy13
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cbe4202a-bebd-4beb-8e5c-ee46f9d78da7 · outbound

This paper cites Albritton, E.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Albritton, E

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.064633Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55a0f5b9-bd63-432f-8a12-1d0d3de6bae5 · outbound

This paper cites Albritton, E.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Albritton, E

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.711177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 945ec76f-a6f5-4ca2-a078-8aa3b8118a9a · outbound

This paper cites Bru´ e and M.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Bru´ e and M

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.691331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fbc87dcd-fd6c-40a5-b299-46d2caa3eb3a · outbound

This paper cites Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Flexibility of Two-Dimensional Euler Flows with Integrable Vorticity

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.089076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 400075c4-2e9a-4527-a269-4837f552e625 · outbound

This paper cites Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Compactly supported anomalous weak solutions for 2D Euler equations with vorticity in Hardy spaces

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:30:18.395886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 006a0b0d-6798-40b3-9c73-99549a9ea244 · outbound

This paper cites Buck and S.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Buck and S

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.672313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation de9dcc41-2e09-4ae1-8c37-d2fd97ff63cc · outbound

This paper cites Buckmaster, M.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Buckmaster, M

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.110194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 25e7113c-64af-40d4-8d8e-48cb19169bff · outbound

This paper cites Buckmaster and V.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Buckmaster and V

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.642844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9c2ad596-1b3a-402c-befd-279e93efdded · outbound

This paper cites Buckmaster and V.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Buckmaster and V

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.624408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ac7a65fb-ba7d-4e23-b259-a528bc19de92 · outbound

This paper cites Burczak, S.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Burczak, S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.607061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 72ef72d2-c8f8-4f9c-9fae-8da94a710425 · outbound

This paper cites A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces A proof of Vishik's nonuniqueness Theorem for the forced 2D Euler equation

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.132532Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf24a9ad-d2c4-4986-baa3-82117d2ac571 · outbound

This paper cites Cheskidov and X.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Cheskidov and X

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.589761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7090ad10-8c18-4034-bfca-faafc94d40e1 · outbound

This paper cites Cheskidov and X.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Cheskidov and X

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.571565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5e505b67-579d-4cee-bc42-fda9aeb6026c · outbound

This paper cites an unresolved cited work.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Unresolved cited work

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-08-04T21:30:18.349362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a84878f1-d8b7-4abf-a01a-7c1d810825f5 · outbound

This paper cites De Lellis and L.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces De Lellis and L

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.552870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 40ffd4c4-7746-4320-80c0-146fb2ed7f43 · outbound

This paper cites De Lellis and L.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces De Lellis and L

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.537506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ddad1d1a-1138-42f3-b801-6f3a167ab5cd · outbound

This paper cites Wellposedness and singularity formation beyond the Yudovich class.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Wellposedness and singularity formation beyond the Yudovich class

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-04T21:30:18.316017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6ca8a509-241d-4c17-940d-c12727a5040a · outbound

This paper cites Fan and S.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Fan and S

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.519786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8ce37c2d-d252-47c8-9b22-b808575b42f3 · outbound

This paper cites an unresolved cited work.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:30:18.500967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 86421748-d4a7-4b96-bf23-7cf557849fc8 · outbound

This paper cites Goldberg.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Goldberg

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.485058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4cde84af-520d-4d38-85a8-ada89874bcb2 · outbound

This paper cites an unresolved cited work.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.191418Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1b56437-3850-40cd-a10c-abdc65fe763e · outbound

This paper cites Jia and V.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Jia and V

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T21:30:18.451577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d1607f0f-6113-4b73-a1ae-3abf368ce3a4 · outbound

This paper cites an unresolved cited work.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-04T21:30:18.432876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c5fb4d4b-b5b9-4705-b88e-21a1ba122500 · outbound

This paper cites Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part I.

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part I

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.205484Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 533e9b40-ba28-406a-8d02-04f23dbcd3c4 · outbound

This paper cites Instability and non-uniqueness in the Cauchy problem for the Euler equations of an ideal incompressible fluid. Part II.

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-04T21:30:18.211999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.