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Paper Citation Record · LEDGER

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators

As of 5 August 2026, this Paper Citation Record lists 63 of 63 outbound references and 0 inbound Pith citation observations for arXiv:2607.00320.

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

pith.paper-citation-record.v1
2607.00320 v1

Coverage vector

measured 63 of 63 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-02T00:53:52.334280Z

measured 63 of 63 standing notices

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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

63 of 63 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fd3a7cf9-d8e7-43a8-a4c8-68a8b94e99f2 · outbound

This paper cites Adcock, N.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Adcock, N

Reference 1

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This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 2

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Observation 54205eca-6279-489c-a0e2-f4cdb8537a47 · outbound

This paper cites The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators The Sample Complexity of Learning Lipschitz Operators with respect to Gaussian Measures

Reference 3

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Observation 41c13474-222c-4f40-bebc-4a11d16dfc3c · outbound

This paper cites Adrian, D.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Adrian, D

Reference 4

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 5

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Observation f07dbb7c-ca8e-4b38-911d-0d43d94b3ff3 · outbound

This paper cites Bonev, T.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Bonev, T

Reference 6

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Observation 95fa8b35-800a-4302-a398-a808b48040ae · outbound

This paper cites Boullé, D.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Boullé, D

Reference 7

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Observation 306c57b5-782a-405c-a0ae-b9cfb8e012cf · outbound

This paper cites Boullé, S.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Boullé, S

Reference 8

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Observation 81f9f5f2-364a-4752-8625-7cbdfdcacd88 · outbound

This paper cites Boullé and A.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Boullé and A

Reference 9

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Observation 2877436d-561c-4729-a777-a475143fa6a9 · outbound

This paper cites Bourgain and D.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Bourgain and D

Reference 10

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Observation 461ea3ff-e20b-419e-8974-3d736b82ad88 · outbound

This paper cites Chen and D.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Chen and D

Reference 11

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 12

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This paper cites Error analysis for learning the time-stepping operator of evolutionary PDEs.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Error analysis for learning the time-stepping operator of evolutionary PDEs

Reference 13

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 14

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

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This paper cites Cheng,Energy stable semi-implicit schemes for the 2D Allen–Cahn and fractional Cahn–Hilliard equations, IMA Journal of Numerical Analysis, (2025), p.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Cheng,Energy stable semi-implicit schemes for the 2D Allen–Cahn and fractional Cahn–Hilliard equations, IMA Journal of Numerical Analysis, (2025), p

Reference 16

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 17

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 18

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Observation 74c7f654-0364-4cac-89df-f11789044ed4 · outbound

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators De Ryck and S

Reference 19

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Observation e902d29d-7995-4c66-93a5-b1bb2d7a2dd4 · outbound

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Elbrächter, D

Reference 20

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Furuya, K

Reference 23

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Fourier Neural Operator for Plasma Modelling

Reference 24

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Grohs and F

Reference 25

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators 2097–2124

Reference 27

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators He and Y

Reference 28

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Reference 29

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Kim and M

Reference 30

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This paper cites Korolev,Two-layer neural networks with values in a Banach space, SIAM Journal on Mathe- matical Analysis, 54 (2022), pp.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Korolev,Two-layer neural networks with values in a Banach space, SIAM Journal on Mathe- matical Analysis, 54 (2022), pp

Reference 31

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Kotsuki, K

Reference 32

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Kovachki, S

Reference 33

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This paper cites Data Complexity Estimates for Operator Learning.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Data Complexity Estimates for Operator Learning

Reference 34

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From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 35

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Observation 77efa005-6a69-47c8-8b94-fcec78838c49 · outbound

This paper cites Lanthaler and N.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Lanthaler and N

Reference 36

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 428be095-9722-4472-baba-872116cb30ce · outbound

This paper cites Stuart, and Margaret Trautner.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Stuart, and Margaret Trautner

Reference 37

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.123778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation f33717ec-dc03-4910-a833-46a4bf024323 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.246924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:19314f12a3f0304744f2534bce97a0b916ebfc5d0ae9675b769aa6ac0c5732bb

Observation e329e185-7009-477e-8b4a-341585531cbe · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.242705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:ed8f044f359ae5fdc84a18ca9eb9fb1c0aa642670d9598dd27474618b0b8f374

Observation d2511b1b-cf57-437d-a802-3ac14f5d3bc6 · outbound

This paper cites Li and T.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Li and T

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-07-06T10:02:15.242946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:2916af71fbbfdada9d3db5af2cf9cafef281116e36cda2fb8f77975422907edf

Observation 246d2180-31f9-4e36-84db-3bada2ed9ff5 · outbound

This paper cites Continuous Data Assimilation with Learned Surrogate Dynamics.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Continuous Data Assimilation with Learned Surrogate Dynamics

Reference 41

Resolution
verified exact
local_arxiv, observed 2026-07-02T00:56:24.131092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:be354d52d1a6392f4bfe78023de9884b8469f9e6b3e2d33871122f9018061195

Observation c8116cd3-53b8-4b47-9c81-d45b720a009d · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.233766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:4819354fe685b94ecf8ba413e2731a6f46f09301720cf6381743c92d2334b5ac

Observation bdb7a62d-08e3-4f1b-8e1d-b8d3da6a5778 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.235131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:eb939048c2810c0bfa6a63afd6a51f391fb1cf09e104cc164363e143e61ec369

Observation 7000bc0a-7f98-4f72-9cbf-f5c7e0557a41 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.237476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:6a7a4b9931d9bedce88c291b8b97fd0497eefebf2e23774eff8de283417eb9c4

Observation ea31474a-a0ed-4610-a708-224df08f2287 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 45

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.229971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:b8bf3a8410ca11bbaac4763d821a77e536a6bf125f60ade5568c925d1f714678

Observation 567e5142-b5ab-4744-a9c1-d31f1dfb7020 · outbound

This paper cites Nelsen and Yunan Yang.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Nelsen and Yunan Yang

Reference 46

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.084804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:357d75249dc37182d0d1142704c6420759429d3c2a792088b5f6e9a88031dc18

Observation 4f30e4d8-3c27-44d0-8b2f-c5615f90ed96 · outbound

This paper cites FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Reference 47

Resolution
verified exact
local_arxiv, observed 2026-07-02T00:56:24.135211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:bd5bb3dba5b55be0439cb64f06036bbaeef8b7753b3453e10b9f59d9af6caa12

Observation 85d4779b-2b61-4eef-b554-fc3a0b31bca9 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.219400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:0a476fb95fe58951bb1ce86f9006c98c1ad7f4a4497046b7ce706e03b214ed7d

Observation 2cd27549-814f-4ca2-8fb4-6b1361dff3f0 · outbound

This paper cites Sanz-Alonso and N.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Sanz-Alonso and N

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-07-06T10:02:15.221622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:0f0ac859c1976d4cedf8f17774e044e1d78c6a6103ea8617466ea627bda39214

Observation 2140ba8f-384c-4399-a5bc-47786d5789b2 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 50

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.226045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:546348e2ef99234fa50d30ef0a503390e74ae756ee58abdc465a17345fcc06ec

Observation 8c56bd7a-82d4-4434-bac2-689e836f208d · outbound

This paper cites Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Controlling Statistical, Discretization, and Truncation Errors in Learning Fourier Linear Operators

Reference 51

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.103106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:c433297834ab03a2f11d45278d98a8db6b5e47f877514517d5d7f731e3c940bc

Observation 80a0a5b5-f96b-46ed-897e-c4abd7a33a67 · outbound

This paper cites Operator Learning: A Statistical Perspective.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Operator Learning: A Statistical Perspective

Reference 52

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.127678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:10328bf2d18e4e187cbcd2fd12caa25ebac4d984723b03de5f804145e2ca1e8e

Observation 26d919e0-fcfd-4e00-a745-d5afec3b4d86 · outbound

This paper cites Temam,Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Temam,Infinite-Dimensional Dynamical Systems in Mechanics and Physics, vol

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-07-06T10:02:15.239384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation af86f163-72e6-46a7-88af-50dc9ba4844c · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.172493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:279871bfe4864eb9b4a8bef2d1ae9c5fa62da439cf3cc2f39fdda473345355f6

Observation 18d9263d-568e-41b4-99b6-8a37999a0225 · outbound

This paper cites W ang and A.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators W ang and A

Reference 55

Resolution
verified exact
arxiv_id, observed 2026-07-02T00:56:24.142199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:32796f36ea277c5f8ecb9668d676faaf3148ca48c5c4cd81de7b1524c61041ac

Observation a73fa8e4-1f2c-4c89-abed-635803e30616 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.165541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:302c8edefb403f8ab4c1eb2536a9f0194939cac1c4a9582285f940bd78fd21da

Observation b6c04ce2-f011-4cd6-964c-2369b6178d01 · outbound

This paper cites Yarotsky,Error bounds for approximations with deep ReLU networks, Neural Networks, 94 (2017), pp.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Yarotsky,Error bounds for approximations with deep ReLU networks, Neural Networks, 94 (2017), pp

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-07-06T10:02:15.182817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:f7cf7c7b644354c940214f04db16f6d0b5d76668cdf5a95f77e9cdebebc07374

Observation 4fd82948-20ce-4654-9b25-cc91ef0011a8 · outbound

This paper cites de-aliasing.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators de-aliasing

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-07-06T10:02:15.198962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:fc513539ff5b610428b28817cef68ce156b39d76179678eee39144ec18a01728

Observation a00d3bc7-4f9d-42d7-adb2-3ccb2f0a5a55 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 59

Resolution
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raw_fallback, observed 2026-07-06T10:02:15.154540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:5dcdeed94eb8940bf0703449cd592b5f62bf827b6e72ec05d6093ee4a8f4d3e5

Observation da554c8a-936a-476d-bb3d-d07f38467379 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.229792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:849872fd66fcec2cb62f2046e10af8ebcb1a9fb986239afc2f0287b2c7c92ecf

Observation 7c436c2f-43ee-4810-8dd5-44b7c97693a5 · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 61

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.159701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:f7bb5bc77964dbe32304235f2da8392640c353accad23f9c4b90888b6e268087

Observation 38f4c3d3-7d3d-417d-bc62-37980d783d6f · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 62

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.142671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:79abb4c3cafb6207c38fbcbe1f9a2c0cea29c397f08295ef384cbd1235a37431

Observation bbedffc1-81dd-4389-bef2-be80ab998c4d · outbound

This paper cites an unresolved cited work.

From Spectral Methods to Sample Complexity Bounds for Fourier Neural Operators Unresolved cited work

Reference 63

Resolution
unresolved
raw_fallback, observed 2026-07-06T10:02:15.144889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-07-02T00:53:52.334280Z digest=sha256:4e2e2075df2852bd80cd3a8091b4618a5c3a3f0ff1b326e4733bc079483c5fe7

Pith citing papers

No inbound Pith citation observations are available.