Paper Citation Record · LEDGER

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting

As of 5 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2509.21196.

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pith.paper-citation-record.v1
2509.21196 v3

Coverage vector

measured 47 of 47 reference resolution

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One-hop event checks from named stored sources.

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Pith citing papers itemized under the disclosed page cap.

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Source: cited_works

Reference resolution

47 of 47 outbound references displayed

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verified fuzzy38
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External citation measurements

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Outbound references

Observation 4ca69921-4827-4ce2-bbf3-1fc6dfb8d126 · outbound

This paper cites write newline.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting write newline

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.617847Z

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Observation d94349d9-0533-4f7b-ace6-0396aa869106 · outbound

This paper cites Accurate medium-range global weather forecasting with 3d neural networks.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Accurate medium-range global weather forecasting with 3d neural networks

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.624728Z

Source-reported events for the cited work

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Observation dd9cf7ad-ff74-4f05-ae3e-a8081e504098 · outbound

This paper cites Spherical fourier neural operators: Learning stable dynamics on the sphere.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Spherical fourier neural operators: Learning stable dynamics on the sphere

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.635491Z

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Observation d6d63703-7f80-460f-ad95-321d29064d3f · outbound

This paper cites Frequency spectrum of the flicker phenomenon in erythrocytes.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Frequency spectrum of the flicker phenomenon in erythrocytes

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.628947Z

Source-reported events for the cited work

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Observation f9a4cca7-b27f-4232-a906-397eb1836764 · outbound

This paper cites Physics-informed neural networks (pinns) for fluid mechanics: A review.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Physics-informed neural networks (pinns) for fluid mechanics: A review

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.637813Z

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Observation df9185b7-065c-47b4-a27e-3f8ab8d86963 · outbound

This paper cites Measuring and relieving the over-smoothing problem for graph neural networks from the topological view.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Measuring and relieving the over-smoothing problem for graph neural networks from the topological view

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.690574Z

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.

Observation 7b867bb5-ae8d-4597-8c8f-ea92b6695a4f · outbound

This paper cites Diffusion models in vision: A survey.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Diffusion models in vision: A survey

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.657595Z

Source-reported events for the cited work

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Observation b0f38b38-3eba-4711-bcc2-84533a139ffb · outbound

This paper cites An image is worth 16x16 words: Transformers for image recognition at scale.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting An image is worth 16x16 words: Transformers for image recognition at scale

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.647844Z

Source-reported events for the cited work

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Observation 3943da9f-01fa-4d27-994d-6532e8cecb40 · outbound

This paper cites Long-term 3d mhd simulations of black hole accretion discs formed in neutron star mergers.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Long-term 3d mhd simulations of black hole accretion discs formed in neutron star mergers

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.666596Z

Source-reported events for the cited work

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Observation 205e0f7a-6ef8-4e34-a075-673ba907ef67 · outbound

This paper cites Long-term prediction of chaotic systems with machine learning.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Long-term prediction of chaotic systems with machine learning

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.688283Z

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.

Observation ad575c95-f668-472f-b042-db27d3878770 · outbound

This paper cites Oneforecast: A universal framework for global and regional weather forecasting.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Oneforecast: A universal framework for global and regional weather forecasting

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.049077Z

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.

Observation 12070759-0a70-4986-9409-93529b6c73c8 · outbound

This paper cites Simvp: Simpler yet better video prediction.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Simvp: Simpler yet better video prediction

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.683924Z

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.

Observation 5003615c-18f2-438a-b803-ee647b1dfaf8 · outbound

This paper cites Hamiltonian neural networks.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Hamiltonian neural networks

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.655307Z

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.

Observation 1d5247d3-97a2-49c5-8f61-b6a2506827f8 · outbound

This paper cites Deep residual learning for image recognition.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Deep residual learning for image recognition

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.653078Z

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.

Observation 91cffa2f-8864-4958-aac1-be7a9cab69b2 · outbound

This paper cites Physically constrained generative adversarial networks for improving precipitation fields from earth system models.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Physically constrained generative adversarial networks for improving precipitation fields from earth system models

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.679540Z

Source-reported events for the cited work

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Observation da8b9c3e-c5e8-4afb-ad65-22c5bd2a2c56 · outbound

This paper cites Numerical simulations of non-spherical bubble collapse.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Numerical simulations of non-spherical bubble collapse

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.681561Z

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.

Observation 08103301-7097-4bb3-8172-9b0365ae18d5 · outbound

This paper cites Physics-informed machine learning.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Physics-informed machine learning

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.686066Z

Source-reported events for the cited work

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Observation 3864e8cf-9720-45ae-9e60-cb3bac306628 · outbound

This paper cites Learning skillful medium-range global weather forecasting.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Learning skillful medium-range global weather forecasting

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.660069Z

Source-reported events for the cited work

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Observation fe0ce181-1f26-4994-a651-188801c2b9cf · outbound

This paper cites Fourier neural operator for parametric partial differential equations.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Fourier neural operator for parametric partial differential equations

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.650462Z

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.

Observation 7a0c843c-9864-4b8b-989a-400d24949401 · outbound

This paper cites Fourier neural operator with learned deformations for pdes on general geometries.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Fourier neural operator with learned deformations for pdes on general geometries

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.671098Z

Source-reported events for the cited work

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Observation 1cbb250f-4463-4f9b-acab-d9ae896b5c65 · outbound

This paper cites Pde-refiner: Achieving accurate long rollouts with neural pde solvers.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Pde-refiner: Achieving accurate long rollouts with neural pde solvers

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.640134Z

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.

Observation 2867a37d-f324-4d45-9ecf-1f67355b0bcb · outbound

This paper cites Neural Operators with Localized Integral and Differential Kernels.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Neural Operators with Localized Integral and Differential Kernels

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.052923Z

Source-reported events for the cited work

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Observation d2fb8430-0903-42c0-8ae6-27bcf6b36850 · outbound

This paper cites Energy cascade and spatial fluxes in wall turbulence.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Energy cascade and spatial fluxes in wall turbulence

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.668858Z

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.

Observation 7699fbaf-ba3c-4fe2-a3f4-adf474f693bf · outbound

This paper cites Direct numerical simulation: a tool in turbulence research.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Direct numerical simulation: a tool in turbulence research

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.673150Z

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.

Observation ffdaa1cc-fdb0-4723-b051-e346addafdd6 · outbound

This paper cites How reliable are climate models? Tellus A: Dynamic Meteorology and Oceanography, 59 0 (1): 0 2--29.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting How reliable are climate models? Tellus A: Dynamic Meteorology and Oceanography, 59 0 (1): 0 2--29

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.664351Z

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.

Observation 2453378a-3d10-482e-b6a5-15e0c269cb90 · outbound

This paper cites Convolutional neural operators for robust and accurate learning of PDE s.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Convolutional neural operators for robust and accurate learning of PDE s

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.677182Z

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.

Observation 014eb934-fe58-4737-927e-1e4c8a31c4b7 · outbound

This paper cites U-net: Convolutional networks for biomedical image segmentation.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting U-net: Convolutional networks for biomedical image segmentation

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.644947Z

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.

Observation fd273110-7b7e-4b3f-b880-e969de4673f0 · outbound

This paper cites Direct numerical simulation of free-surface and interfacial flow.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Direct numerical simulation of free-surface and interfacial flow

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.642640Z

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.

Observation b98a4069-5085-491f-8720-4fc86edf26b5 · outbound

This paper cites Toward data-driven weather and climate forecasting: Approximating a simple general circulation model with deep learning.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Toward data-driven weather and climate forecasting: Approximating a simple general circulation model with deep learning

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.675153Z

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.

Observation b0c7a907-9077-4834-b8c6-37fe102b6ead · outbound

This paper cites Lagrangian approach to structural collapse simulation.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Lagrangian approach to structural collapse simulation

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.626853Z

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.

Observation c588d029-11e5-44f3-8f50-f3a60e649a36 · outbound

This paper cites The frequency spectrum of pulse width modulated signals.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting The frequency spectrum of pulse width modulated signals

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.631027Z

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.

Observation f29b99cb-6e99-48b9-9713-004258dbc64f · outbound

This paper cites Methodology for long-term prediction of time series.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Methodology for long-term prediction of time series

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.633373Z

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.

Observation e8bc1ce2-7b33-416f-ba45-ae21e4743b2d · outbound

This paper cites An estimate of the lorenz energy cycle for the world ocean based on the storm/ncep simulation.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting An estimate of the lorenz energy cycle for the world ocean based on the storm/ncep simulation

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.609568Z

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.

Observation ed090aee-e14e-4fa5-81b6-2783d8b331d0 · outbound

This paper cites Pdebench: An extensive benchmark for scientific machine learning.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Pdebench: An extensive benchmark for scientific machine learning

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.614843Z

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.

Observation b6577552-5d2e-4a62-b650-ea2f05cc20dc · outbound

This paper cites Hamiltonian Generative Networks.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Hamiltonian Generative Networks

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.032927Z

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.

Observation 669e4cd5-930a-4d54-b325-9430d6c70db3 · outbound

This paper cites Attention is all you need.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Attention is all you need

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.582684Z

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.

Observation 80661905-8e62-4cdc-bc0d-f1f1ae9d18e0 · outbound

This paper cites Solving High-Dimensional PDEs with Latent Spectral Models.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Solving High-Dimensional PDEs with Latent Spectral Models

Reference 37

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.045118Z

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.

Observation 44aeb5eb-f87d-4cd2-b2db-a283f38d960f · outbound

This paper cites Pure: Prompt evolution with graph ode for out-of-distribution fluid dynamics modeling.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Pure: Prompt evolution with graph ode for out-of-distribution fluid dynamics modeling

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.580416Z

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.

Observation 4b7589bb-a3c2-462b-bb81-9ed61db7fb7f · outbound

This paper cites Prometheus: Out-of-distribution fluid dynamics modeling with disentangled graph ode.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Prometheus: Out-of-distribution fluid dynamics modeling with disentangled graph ode

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.622556Z

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.

Observation aa3b0f97-6897-4497-84c7-039e44ed0669 · outbound

This paper cites Pastnet: Introducing physical inductive biases for spatio-temporal video prediction.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Pastnet: Introducing physical inductive biases for spatio-temporal video prediction

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.612467Z

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.

Observation af0e9d3b-1f76-4002-9d3b-24ac051d22a2 · outbound

This paper cites Neural manifold operators for learning the evolution of physical dynamics, 2024 d.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Neural manifold operators for learning the evolution of physical dynamics, 2024 d

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.577875Z

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.

Observation c06ca15c-f00f-41e8-b159-ef423e5aecb1 · outbound

This paper cites Advanced long-term earth system forecasting by learning the small-scale nature.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Advanced long-term earth system forecasting by learning the small-scale nature

Reference 42

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.028151Z

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.

Observation 505f3339-52f1-4612-9f26-23148b9397fe · outbound

This paper cites Breaking the discretization barrier of continuous physics simulation learning.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Breaking the discretization barrier of continuous physics simulation learning

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.041362Z

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.

Observation 19f55843-dcc4-4bae-8a6f-c36c3db45374 · outbound

This paper cites Revisiting Over-smoothing in Deep GCNs.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Revisiting Over-smoothing in Deep GCNs

Reference 44

Resolution: verified exact; arxiv_id, observed 2026-05-21T22:20:42.037278Z

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.

Observation 714c584c-8c6f-41a9-a67b-fed46cb02dd8 · outbound

This paper cites @esa (Ref.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting @esa (Ref

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-05-21T22:20:42.605592Z

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.

Observation 4bc01ebe-adb1-49dc-bda4-7af1d68b0da9 · outbound

This paper cites an unresolved cited work.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-05-21T22:20:42.620268Z

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.

Observation 4a0695b6-588f-47b8-adc4-7d5043448462 · outbound

This paper cites an unresolved cited work.

Differential-Integral Neural Operator for Long-Term Turbulence Forecasting Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-05-21T22:20:42.585435Z

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.

Pith citing papers

No inbound Pith citation observations are available.