Paper Citation Record · LEDGER

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction

As of 14 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2507.05584.

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

pith.paper-citation-record.v1
2507.05584 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T19:27:46.673171Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

21 of 21 outbound references displayed

verified exact0
verified fuzzy12
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a0b74df1-4e97-464c-916a-61d0885016e0 · outbound

This paper cites Journal of Computational Physics378, 686–707 (2019) 11 Fig.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Journal of Computational Physics378, 686–707 (2019) 11 Fig

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.867524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3ed3a2a5-7507-4af2-bbad-c7bd89662ae1 · outbound

This paper cites Nature Reviews Physics3, 422–440 (2021).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Nature Reviews Physics3, 422–440 (2021)

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.614158Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9600901e-df25-4c5a-b9f8-6aa1b8fee57f · outbound

This paper cites Acta Mechanica Sinica 38(11), 1725–1737 (2022).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Acta Mechanica Sinica 38(11), 1725–1737 (2022)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.853106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 982d973b-9a85-424c-b70d-2eaee14a9293 · outbound

This paper cites Journal of Computational Physics404, 109136 (2020).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Journal of Computational Physics404, 109136 (2020)

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.843891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 930f36dc-f722-4612-8abf-39c0578bafee · outbound

This paper cites Science367(6481), 1026– 1030 (2020).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Science367(6481), 1026– 1030 (2020)

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.835974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dbd2b8ec-87cf-4ca7-98a3-d6ff7224c97e · outbound

This paper cites In: International Conference on Learning Representations (2021).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: International Conference on Learning Representations (2021)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.827401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bd1c353b-4b5e-4e80-8eb9-4bf21a13a155 · outbound

This paper cites In: International Conference on Learning Representations (2023).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: International Conference on Learning Representations (2023)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.819507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d6101c12-b348-480d-9d26-3dad458bf345 · outbound

This paper cites Nature Machine Intelligence3(3), 218–229 (2021).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Nature Machine Intelligence3(3), 218–229 (2021)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.811527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8628f2c4-4b2a-4d55-ba9c-bcc5db9f97c9 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.635789Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec2973c2-c63c-4f23-9b75-8f9b6b9383ce · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Neural Operator: Learning Maps Between Function Spaces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.639151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57736654-9431-48a0-976e-79023fcfe43e · outbound

This paper cites In: International Conference on Learning Representations (2022).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: International Conference on Learning Representations (2022)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.802738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 73b56ca5-8456-4b8a-906b-296f5ba7ac21 · outbound

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

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.645731Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 275ecb16-bc20-45fe-8a49-1d485e4883ac · outbound

This paper cites Physics-Informed Neural Operator for Learning Partial Differential Equations.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Physics-Informed Neural Operator for Learning Partial Differential Equations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.648801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7e47833-38d1-4aa7-9982-e4fe12197f44 · outbound

This paper cites Ask Me Anything: A simple strategy for prompting language models.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Ask Me Anything: A simple strategy for prompting language models

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.651835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46343a7c-3bfd-464a-b04f-cdc73aa48ccd · outbound

This paper cites In: Advances in Neural Information Processing Systems, pp.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: Advances in Neural Information Processing Systems, pp

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.794610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 16cd8631-b842-4dd7-8ba9-0d9d8b4787a0 · outbound

This paper cites In: Advances in Neural Information Processing Systems (2020).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: Advances in Neural Information Processing Systems (2020)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.786580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c98e4aa7-4bd9-43da-be68-c4160b65dcb3 · outbound

This paper cites The pairing symmetry in quasi-one-dimensional superconductor Rb2Mo3As3.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction The pairing symmetry in quasi-one-dimensional superconductor Rb2Mo3As3

Reference 17

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T19:27:46.718954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3e5be7e5-c89f-4652-b7ba-26e419b73a23 · outbound

This paper cites Acoustic Beamforming for Object-relative Distance Estimation and Control in Unmanned Air Vehicles using Propulsion System Noise.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Acoustic Beamforming for Object-relative Distance Estimation and Control in Unmanned Air Vehicles using Propulsion System Noise

Reference 18

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T19:27:46.706334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 39dfec57-eb54-4149-9c3a-0761c4223173 · outbound

This paper cites Offline RL for Natural Language Generation with Implicit Language Q Learning.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction Offline RL for Natural Language Generation with Implicit Language Q Learning

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T19:27:46.666843Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53c9a3c1-9112-42b5-aef4-c943f083f4b2 · outbound

This paper cites In: International Conference on Learning Representations (2023).

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: International Conference on Learning Representations (2023)

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.778285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8718293a-4a3c-4024-b8be-be0695239bb0 · outbound

This paper cites In: Advances in Neural Information Processing Systems, pp.

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction In: Advances in Neural Information Processing Systems, pp

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T19:27:46.766810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.