Paper Citation Record · LEDGER

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO)

As of 9 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 1 inbound Pith citation observation for arXiv:2507.18731.

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

pith.paper-citation-record.v1
2507.18731 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T14:36:35.246713Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T11:54:43.085071Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy3
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a2c91d00-b496-43f7-8e4f-55319f49725e · outbound

This paper cites , " * write output.state after.block = add.period write newline.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) , " * write output.state after.block = add.period write newline

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T14:36:35.182322Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dee973b1-1ceb-4e46-9931-a5bea77a619b · outbound

This paper cites write newline.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) write newline

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T14:36:35.186055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f50ee114-16f6-4811-b049-51b0370f62c2 · outbound

This paper cites M.; and Cahn, J.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) M.; and Cahn, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:36:35.443764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4e33f655-5ec5-4836-9a27-21a29f42a18b · outbound

This paper cites W.; Blowey, J.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) W.; Blowey, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:36:35.428698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f28d43c0-43b9-4741-a64a-370fcf3031e8 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.417337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c594cb49-0196-449c-8cac-0023fd41169d · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.404277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e6d5b2a4-0ac3-4d43-b3c8-fcb13014591a · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.394438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 16836794-2c22-4770-8263-c8cd2bf1cb4d · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Fourier Neural Operator for Parametric Partial Differential Equations

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T14:36:35.204743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdc8793f-306b-45ea-b9a1-3b338b3cc0a9 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.387980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2ad155ca-15e6-4ce8-9df8-2ec436bae232 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.381820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation da3de676-2357-475e-bbff-c7b2ad3d8019 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.375003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f34a3705-fced-4652-a816-c451d836eb56 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.368269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a0c0b0a1-2165-4b26-8018-1843967bee9d · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T14:36:35.231043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8930ea06-b4b5-4a24-b63d-ef398893862d · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T14:36:35.233519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1776149-00a5-46b6-a9b2-aa68ac77c055 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.344746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 878e18fc-0dda-4acd-b7c6-fe5c370a3e53 · outbound

This paper cites G.; Al Majed, H.; and Huerta, E.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) G.; Al Majed, H.; and Huerta, E

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T14:36:35.334734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 172acc16-87c4-4980-a4fd-74d8195a7ddb · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.308973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 24478f49-8643-4e8e-8f11-247f272915d7 · outbound

This paper cites an unresolved cited work.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T14:36:35.297027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bd29fe44-6862-4b4e-8b66-c0d507d80783 · outbound

This paper cites Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks.

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO) Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T14:36:35.246713Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 24288437-52d1-44db-82a8-dd49d8c6f5fb · inbound

A joint voxel flow-phase field framework for ultra-long microstructure evolution prediction with physical regularization cites this paper.

A joint voxel flow-phase field framework for ultra-long microstructure evolution prediction with physical regularization Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO)

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T11:54:43.085071Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.