Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T12:48:34.698218Z
Paper Citation Record · LEDGER
As of 7 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 2 inbound Pith citation observations for arXiv:2509.01293.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T12:48:34.698218Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-13T08:47:34.631129Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-11T00:20:51.556917Z
53 of 53 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation f67b93d3-00f7-43cc-8385-a4add1b5eaa9 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Anderson, G.B
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d8ea54ea-9097-45e2-a44d-5a3e945cf158 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f9ad1f7a-099e-4cdb-974f-1fb08e68f922 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
Reference 3
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f1b8d73f-b8b2-41d3-aca0-ab29e8a1021c · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5b13bc19-8a08-4159-bc34-e74d2656f35e · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cahn and J.E
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f47c928c-9ffa-45df-9d09-aa73dc5d9ac2 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Gurtin, D
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7265d98e-b76c-4ee3-93f7-ab9bb23cd0db · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Lowengrub and L
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ae719275-ac3f-41d3-8e7c-bbcfadab4c6b · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model ten Eikelder, K.G
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 753cb57e-6448-4995-b28a-d9793d9e6bd3 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Abels, H
Reference 9
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1397c44a-58f0-40eb-a2b1-09b8bc485ee9 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model AunifiedframeworkforN-phaseNavier–StokesCahn–HilliardAllen–Cahnmixture models with non-matching densities.Journal of Fluid Mechanics, 1013:A26, 2025
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 8dd42cf5-99ca-4063-8838-45df348fd602 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model A Thermodynamically Consistent Free Boundary Model for Two-Phase Flows in an Evolving Domain with Bulk-Surface Interaction
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 123bcad3-15b8-4508-aa83-ec5bee696881 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Compressible N-phase fluid mixture models
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4b7784b6-41b0-41ba-b6d2-a4a4eb1696f2 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Kay and R
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e7dd942f-8d6d-486c-ace6-e0c8703b35c7 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Minjeaud
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6b25536b-731f-43b2-9976-c42ee74194c6 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model ten Eikelder and D
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ce40a024-5926-472d-9c96-86bc70e97ed6 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Garcke and S
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b225edfc-8fc4-49fe-a339-5e8d7537c875 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Ebenbeck and H
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 94cca9d3-1e4b-4ed4-bf90-c3e9d35268b3 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Bertozzi, S
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9f3c3b8b-28f1-4a09-959f-1cfae4a78a11 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Khain and L.M
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5a9e26cb-9f53-4626-abfa-12d9d3beebc3 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Elson, E
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9f8a4b66-76ff-4328-9e26-cc0bb09352a9 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Berry, C.P
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 74ea4108-5227-448c-b400-a5fd32224e14 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Brown, B
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ba098b36-3cd7-4f8b-80a1-b8bc22055260 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Voulodimos, N
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation fb1a18d8-a17c-4d3c-a5fa-245e1881e1cb · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Ding.Data-driven design of fault diagnosis and fault-tolerant control systems
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation a3c1b4c1-0454-410b-b29d-bf4515b49c5e · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Brunton, B.R
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 242eacce-bbad-4457-a6ec-3d0b39f785fb · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Karniadakis, I.G
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f3c543af-3920-4773-aa1d-2afd02c56a24 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cheng, M
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation ae72998c-6827-419d-aa7b-37f25c9de35a · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 88926a09-ae18-4c74-a27e-fb61fa7f9e73 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Fukami, Y
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 73431e09-d46e-4b44-8747-f6f75311c9e4 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Xue, H.-D
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 45749cfb-9e62-422d-93d2-f0c56bede874 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 80bf934f-3b74-4067-914b-4c95fd290cdb · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7d6e9afe-640f-4215-9f2f-a92b8bf7264a · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cheng, F
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation c5cd1b54-2e09-4128-a3ed-ff107c0f3827 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e17a21ef-a4db-467b-af25-bd681439a145 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f083d83c-b0f1-4357-a104-2291fae6c4a6 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Shen, J.-J
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 6cd419b3-0541-4d5e-b2fd-0fdd521769fb · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7c48df84-0b2f-4c81-8888-399841a9dee9 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Teichert, A.R
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f6c3c5d7-4599-4840-a283-c9eebf00f33a · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Oommen, K
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation bd2cfa5f-7153-4ada-8d4d-064cadadeb74 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Cohen and M
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4861859c-ede4-4fb9-84a9-b768368ab89f · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4986a902-066c-4722-b035-265a176ba45a · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Schütt, O
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 9bea5b38-1e8c-4365-9093-849e4db3fee6 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Novick-Cohen
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 893b6e77-311d-4930-8cb8-04058ad4671b · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Kovachki, Z
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 22dc69ec-cd7c-4233-b43e-c4d952fb6378 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Evans.Partial differential equations, volume 19
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 71d6254c-2694-44b8-b59e-741783dd23f3 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Fourier Neural Operator for Parametric Partial Differential Equations
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 618a5d3d-34f3-48bc-b4b9-6649bf27cf22 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f56c4c2e-a7e7-4d67-8d41-e82c7a699d4f · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Multi-componentCahn–Hilliardsystemwithdifferentboundaryconditions in complex domains.Journal of Computational Physics, 323:1–16, 2016
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4a684a4c-5dae-4684-8efa-675bf1ce728c · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model ten Eikelder, K.G
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d4b26926-8ec5-45d9-9d8e-1de671e379b7 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Unresolved cited work
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b9b31c82-5801-41e1-be74-aafd4bb90e32 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Phase-field modeling of elastic microphase separation
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 1a48f3b7-095f-4ad7-ae73-55664325fc55 · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Golovin, S.H
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation d3e0a9b4-2d1c-48af-8429-83ee521247af · outbound
Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model Balakrishna and W.C
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 276f193e-f885-4c4e-858f-3938b0d6af5f · inbound
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5b9d301e-df5f-484c-a005-170d7180515c · inbound
MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems Equivariant U-Shaped Neural Operators for the Cahn-Hilliard Phase-Field Model
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.