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Paper Citation Record · LEDGER

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

As of 17 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 5 inbound Pith citation observations for arXiv:2412.20183.

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

pith.paper-citation-record.v1
2412.20183 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:32:57.373671Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:13:09.644803Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T02:06:27.754353Z

Reference resolution

17 of 17 outbound references displayed

  • verified exact0
  • verified fuzzy5
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1e439a18-da30-40b1-a826-6773ba3f3ed4 · outbound

This paper cites Boull´ e, C.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Boull´ e, C

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:32:57.611593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.300076Z digest=sha256:89c3eecfb947fc9be9a73e1894458fb17991cff79fe85e39a8e119b6ecca2b6a

Observation 8674bff5-64ed-49aa-b6cc-2828beafdbf9 · outbound

This paper cites Boull´ e and A.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Boull´ e and A

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:32:57.600378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.304191Z digest=sha256:bd969c02262b4f7bac236da8b71374003aa2d0e23bf149f77e1c3d5c1b44e2f3

Observation adbcf2ed-8fa1-4d3d-a89c-ffd67adbfab2 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.589023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.308989Z digest=sha256:e790d8f1b2ac800e4997e6590d69132e17672a9941c4435a30d59d8ec58a7187

Observation 11ac1011-b28e-4036-a05d-f9b19ee57958 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.577609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.313414Z digest=sha256:1ce46366fb68a1a5ef3b8ec7c3cc9e1a8e38432a818dd003d8ce1462ba0e16cd

Observation 2f16614f-a4e5-41c9-b736-d997fc62d189 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.563130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.317792Z digest=sha256:a2f833bb2708c3b1a61d7e090215b7d9a944937c268ce73990d02e14b6d81b5c

Observation 37802d81-43ea-4655-8c9a-89c12b2203de · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.550864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.321871Z digest=sha256:94e827ef2dbcab755dddc0b141d010d7d32b667dfb588280a6211a148cfa50a2

Observation 0ead081a-b27e-41b9-ad65-55d7743adb72 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.538801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.326757Z digest=sha256:231b259e938d247e6402659f92eb351550938d781c75f5728a5f0ac39946372b

Observation 5cb7019b-7fb9-4be4-808c-380101695951 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.526470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.331251Z digest=sha256:ed6cda8b99b9fc45159e512bf8e45fa1b8e7ec49988e7038d3c2cc31f5b21441

Observation d1389d6a-9073-47b6-a82e-ecae50caece7 · outbound

This paper cites Mitigating spectral bias for the multiscale operator learning.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Mitigating spectral bias for the multiscale operator learning

Reference 9

Resolution
unresolved
no resolver link, observed 2026-08-10T23:32:57.335908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:32:57.335908Z digest=sha256:156500e8237f009e3977e0ef91b0e8f597be12e5eba5bee6b8b55055501c2837

Observation 5a1e9cb2-1e52-4dd8-8222-e6a48b7552a0 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.511534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.340911Z digest=sha256:dcc3ef0d1506e1192f336693f152051a5bfcd6448d53d6d9d86a58d485991b5a

Observation 2f5defb3-3b82-44da-9dff-a64df5299a36 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.499350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.345863Z digest=sha256:98fcd6e5f5d44429baeb5bffb05e5c256e295d4f1cbef6a7c8f955dbf1ec27cc

Observation b1dd858b-990f-475c-9c5e-7bbff280e302 · outbound

This paper cites Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Integrating Neural Operators with Diffusion Models Improves Spectral Representation in Turbulence Modeling

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-10T23:32:57.350901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T23:32:57.350901Z digest=sha256:4ca415787792b22cad31b01e6ae84a92749af42beca64b43d7d79eee23a2138b

Observation 5a48e88b-0086-4f5a-a055-cc29d58d4d3d · outbound

This paper cites Rahaman, A.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Rahaman, A

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:32:57.486737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.356513Z digest=sha256:15f7cd6609870d4042a8c1603c325ee455957aa43d53461c8d69874635557eb6

Observation b36ad373-953e-4557-9798-2b8d6c92d52c · outbound

This paper cites Ronneberger, P.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Ronneberger, P

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:32:57.475017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.361172Z digest=sha256:099eee6cebd45ea9edb1fd178cc43b796dbbf337c69b6de57d7b7ce246b06a06

Observation 3bc0ee69-426b-482e-b722-5bc1b54efa67 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.462199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.365168Z digest=sha256:b9e4305f8db1894134668ae68ad0d605f27dc6ed6531ee3edd8e93c4cce5bd19

Observation ce390347-c88b-417f-9eb2-c7a2ad2598d2 · outbound

This paper cites an unresolved cited work.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-10T23:32:57.449749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.369297Z digest=sha256:b187d790071582a2b2ccd9ae09528c5199bce596df17d0f871fef7bfcdc81189

Observation 47f1cc6c-f8c0-4353-8b8f-61d409bd1916 · outbound

This paper cites Zhang, W.

MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces Zhang, W

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T23:32:57.436025Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-10T23:32:57.373671Z digest=sha256:fb800da0e5245229de128870e9b6b245248a73ec82ada2e55d766a41abb5d9bf

Pith citing papers

Observation 02e0c6f9-570d-43aa-898d-1d0eb3fa0d8e · inbound

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs cites this paper.

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 124

Resolution
unresolved
no resolver link, observed 2026-08-10T19:32:41.811028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T19:32:41.811028Z digest=sha256:85da24f8e3b79f3e0a06bd89bb42cad3db1f09bfc15ca346ff1cf89aab685d7a

Observation 315ee48d-38eb-4ff6-9eaf-49a9f04c5ec1 · inbound

Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction cites this paper.

Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-15T16:13:09.644803Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T16:13:09.644803Z digest=sha256:028351d1f8f1aba5b3baa97723190ecbd0362d986160f5f20d900f87d4acaecc

Observation 577803ec-18d6-4f58-9dd2-73dfcbef53a1 · inbound

A Greedy PDE Router for Blending Neural Operators and Classical Methods cites this paper.

A Greedy PDE Router for Blending Neural Operators and Classical Methods MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 19

Resolution
verified exact
arxiv_id, observed 2026-05-18T12:32:36.228002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-05-18T12:32:13.577474Z digest=sha256:729bfb9030037f902b3b76b2e251bce95b24db820475467d602c96189317a660

Observation a027da67-ac21-459a-b38a-979c881ff182 · inbound

Generalized Spherical Neural Operators: Green's Function Formulation cites this paper.

Generalized Spherical Neural Operators: Green's Function Formulation MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 23

Resolution
verified exact
arxiv_id, observed 2026-05-16T23:08:40.073154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-05-16T23:05:33.582759Z digest=sha256:35751cf3a51fcfec14dfd9e3f44459d4903c78c778938c226de1b3e273e08868

Observation f0e4e2f2-34a3-48ca-a465-ecc893ce2fb5 · inbound

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations cites this paper.

Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations MscaleFNO: Multi-scale Fourier Neural Operator Learning for Oscillatory Function Spaces

Reference 17

Resolution
verified exact
arxiv_id, observed 2026-07-02T02:06:27.757130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-06-28T11:10:52.822919Z digest=sha256:9670143be4833446a17203b40e305fc4953968e1350d0eebb408af9201989020