Paper Citation Record · LEDGER

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains

As of 17 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2608.06660.

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

pith.paper-citation-record.v1
2608.06660 v1

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measured 38 of 38 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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38 of 38 outbound references displayed

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External citation measurements

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Outbound references

Observation 8382c8df-2b28-4457-8b80-b1f70458e1c4 · outbound

This paper cites an unresolved cited work.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Unresolved cited work

Reference 1

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This paper cites an unresolved cited work.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Unresolved cited work

Reference 2

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Observation efcf94e9-4087-4a71-826c-e0c0016f4cff · outbound

This paper cites Numerical Mathematics (2nd ed.).

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Numerical Mathematics (2nd ed.)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:50.037188Z

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Observation e31a5014-eade-4bde-9174-403da2e0bace · outbound

This paper cites C., Taylor, R.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains C., Taylor, R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:50.026278Z

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Observation 0e1e110b-b09b-4c90-9828-bce1658bcce3 · outbound

This paper cites H., & Peri, M.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains H., & Peri, M

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:50.015611Z

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Observation 5c15678c-39c4-4929-8598-efb3e1f5695c · outbound

This paper cites F., Soni, B.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains F., Soni, B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:50.005073Z

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Observation 8597f63b-ebaa-4095-ac10-0ce72e53b29a · outbound

This paper cites an unresolved cited work.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Unresolved cited work

Reference 7

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Observation ffd9d3af-b0f5-4dd2-98f2-d9645dfd0807 · outbound

This paper cites E., Kevrekidis, I.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains E., Kevrekidis, I

Reference 8

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Observation f30b682c-87fd-4713-ae45-9b7b1cc33268 · outbound

This paper cites Understanding and mitigating gradient ﬂow pathologies in physics-informed neural networks.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Understanding and mitigating gradient ﬂow pathologies in physics-informed neural networks

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.976589Z

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Observation 85be662f-db27-4515-90d4-d1ac65d33c41 · outbound

This paper cites S., Gholami, A., Zhe, S., Kirby, R.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains S., Gholami, A., Zhe, S., Kirby, R

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.967283Z

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Observation 14fc6739-99a3-4b7b-8c73-353bb49bf633 · outbound

This paper cites Respecting causality is all you need for train- ing physics-informed neural networks.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Respecting causality is all you need for train- ing physics-informed neural networks

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.957463Z

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Observation 652da60c-56f2-4575-91a4-b9f12d2c0789 · outbound

This paper cites Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.947133Z

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Observation 5e2f3d77-e0f8-4d97-9884-ca9e9f9c0b23 · outbound

This paper cites Finite Basis Physics-Informed Neural Networks (FBPINNs): A scalable domain decomposition approach for solving diﬀerential equations.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Finite Basis Physics-Informed Neural Networks (FBPINNs): A scalable domain decomposition approach for solving diﬀerential equations

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.937142Z

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Observation 3f8585e4-31e8-40cf-9450-63fdd0557ff0 · outbound

This paper cites Y., & Tegmark, M.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Y., & Tegmark, M

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.926633Z

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Observation 07dce702-e804-48bf-b76e-15c8197a4735 · outbound

This paper cites S., Zhuang, X., Rabczuk, T., & Liu, Y.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains S., Zhuang, X., Rabczuk, T., & Liu, Y

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.915845Z

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.

Observation 2f218296-0b70-4aff-8782-530836e7b255 · outbound

This paper cites A., & Stinis, P.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains A., & Stinis, P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.905515Z

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Observation cfb1753e-b6e5-4ccf-bffe-b3ffadb79ed3 · outbound

This paper cites A physics-informed deep learn- ing framework for solving forward and inverse problems based on KolmogorovArnold Networks.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains A physics-informed deep learn- ing framework for solving forward and inverse problems based on KolmogorovArnold Networks

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.894074Z

Source-reported events for the cited work

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Observation 5a337336-38e1-43e8-ad35-bb7d174d4944 · outbound

This paper cites KAN-ODEs: KolmogorovArnold net- work ordinary diﬀerential equations for learning dynamical systems and hidden physics.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains KAN-ODEs: KolmogorovArnold net- work ordinary diﬀerential equations for learning dynamical systems and hidden physics

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.883038Z

Source-reported events for the cited work

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Observation 95617f78-4aff-4683-8910-e2a14e4ee9aa · outbound

This paper cites Adaptive training of grid-dependent physics-informed kolmogorov-arnold networks.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Adaptive training of grid-dependent physics-informed kolmogorov-arnold networks

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.871475Z

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.

Observation 4fb61ead-b7ba-4769-b415-6622c5bc6449 · outbound

This paper cites Physics-informed kolmogorov-arnold networks for power system dynamics.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Physics-informed kolmogorov-arnold networks for power system dynamics

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.861620Z

Source-reported events for the cited work

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Observation 18daa108-5d91-4434-b5f7-beccf2058750 · outbound

This paper cites D., & Karniadakis, G.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains D., & Karniadakis, G

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.851231Z

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Observation 698439f6-da42-428b-a57c-597ea0f18fce · outbound

This paper cites PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irreg- ular Domain.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irreg- ular Domain

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.841181Z

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Observation 0c16d701-2aaf-4b55-86f7-515d37b9af0d · outbound

This paper cites S., Son, S., Kim, Y., & Seok, J.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains S., Son, S., Kim, Y., & Seok, J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.829863Z

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Observation 3a8ff26d-0999-444a-a36d-3253bc8de289 · outbound

This paper cites Pearlmutter, Alexey Andreyevich Radul, and Jeﬀrey Mark Siskind.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Pearlmutter, Alexey Andreyevich Radul, and Jeﬀrey Mark Siskind

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.820235Z

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.

Observation 1bdc8a6a-86ec-4c7a-88c6-42bfc1ffbb18 · outbound

This paper cites A mathematical model for automatic diﬀerentia- tion in machine learning.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains A mathematical model for automatic diﬀerentia- tion in machine learning

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.809506Z

Source-reported events for the cited work

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Observation d9bea659-2320-46c5-9bd6-a8588606d4a2 · outbound

This paper cites Auto- matic diﬀerentiation in ML: Where we are and where we should be going.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Auto- matic diﬀerentiation in ML: Where we are and where we should be going

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.798959Z

Source-reported events for the cited work

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Observation c5a6e074-4390-4589-a4e1-ed4c6714bab9 · outbound

This paper cites Nodal integral methods for heat and mass transfer in curvilinear coordinates.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Nodal integral methods for heat and mass transfer in curvilinear coordinates

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.788376Z

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.

Observation be56cecf-6d0d-439a-81be-95853dfb2dd7 · outbound

This paper cites Pseudo-Spectral Methods for Linear Advection and Dispersive Problems.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Pseudo-Spectral Methods for Linear Advection and Dispersive Problems

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.776780Z

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.

Observation cedf73f4-d85a-43e6-97ba-30bd737c722d · outbound

This paper cites A residual- based artiﬁcial viscosity ﬁnite diﬀerence method for scalar conservation laws.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains A residual- based artiﬁcial viscosity ﬁnite diﬀerence method for scalar conservation laws

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.765445Z

Source-reported events for the cited work

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Observation ef0163b6-090f-461c-86c4-c8f095dfed06 · outbound

This paper cites Numerical study of 1D and 2D advection-diﬀusion-reaction equations using Lucas and Fibonacci polynomials.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Numerical study of 1D and 2D advection-diﬀusion-reaction equations using Lucas and Fibonacci polynomials

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.754498Z

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.

Observation a9683cf5-8df0-4dc6-9ffd-7423bfd3bf81 · outbound

This paper cites Numerical Solution of TwoDimensional Nonlinear Unsteady AdvectionDiﬀusionReaction Equations with Variable Coeﬃcients.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Numerical Solution of TwoDimensional Nonlinear Unsteady AdvectionDiﬀusionReaction Equations with Variable Coeﬃcients

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.743248Z

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.

Observation aa56c5a4-6db1-4eff-813a-fb986c0f5ab1 · outbound

This paper cites Nodal integral method for convection- diﬀusion transport using linear and higher order quadrilateral elements.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Nodal integral method for convection- diﬀusion transport using linear and higher order quadrilateral elements

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.732715Z

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.

Observation d7d0c15d-0591-4cbf-bfc7-1f7c1664ea75 · outbound

This paper cites High-order accurate methods for unsteady vortical ﬂows on curvilinear meshes.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains High-order accurate methods for unsteady vortical ﬂows on curvilinear meshes

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.720908Z

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.

Observation dd64e460-026c-44e2-baa4-2347c57710a6 · outbound

This paper cites On the use of higher-order ﬁnite-diﬀerence schemes on curvilinear and deforming meshes.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains On the use of higher-order ﬁnite-diﬀerence schemes on curvilinear and deforming meshes

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.710643Z

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.

Observation 0143cba7-15e8-4e1d-9322-434355b7d357 · outbound

This paper cites A spectral diﬀerence lattice Boltzmann method for solution of inviscid compressible ﬂows on structured grids.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains A spectral diﬀerence lattice Boltzmann method for solution of inviscid compressible ﬂows on structured grids

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.700116Z

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.

Observation 9b4728bd-bba6-4265-83dd-3eeb2bd2819d · outbound

This paper cites Galerkin approach for estimating boundary data in Poisson equation on annular domain with application to heat transfer coeﬃcient estimation in coiled tubes.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Galerkin approach for estimating boundary data in Poisson equation on annular domain with application to heat transfer coeﬃcient estimation in coiled tubes

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.689247Z

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.

Observation 42e6ba05-d038-46ec-b010-8e78646be9f1 · outbound

This paper cites Chebyshev Spectral Neural Networks for Solving Partial Differential Equations.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Chebyshev Spectral Neural Networks for Solving Partial Differential Equations

Reference 37

Resolution: verified exact; local_arxiv, observed 2026-08-10T23:02:49.668250Z

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.

Observation 89a45dbf-5cf0-4328-9284-f17b0cb3b681 · outbound

This paper cites Solution to the Problem of Convective Heat Transfer in a Toroidal Channel Using a Curvilinear Coordinate System.

CT-PIKAN: Coordinate-Transformed Physics-Informed Kolmogorov-Arnold Network with Autograd-Based Metric Evaluation for Solving PDEs in Curvilinear Domains Solution to the Problem of Convective Heat Transfer in a Toroidal Channel Using a Curvilinear Coordinate System

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:02:49.679229Z

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.

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