Paper Citation Record · LEDGER

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices

As of 14 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2507.09782.

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

pith.paper-citation-record.v1
2507.09782 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:55:26.829795Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

48 of 48 outbound references displayed

verified exact0
verified fuzzy21
unresolved27
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 16562853-a889-47fb-88a4-5e2a5c870abb · outbound

This paper cites Cuomo, V.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Cuomo, V

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.721542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3530957d-bbf0-4b76-a675-8cbcacf2d678 · outbound

This paper cites Hornik, M.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Hornik, M

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.705499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6188ecfb-f504-422a-8f5f-0deed1d67375 · outbound

This paper cites Dissanayake, N.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Dissanayake, N

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.689438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a682db93-993f-4129-b3ca-c328cfd01da1 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:23.101701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48558530-191e-429d-81dc-90835232b0a8 · outbound

This paper cites Raissi, P.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Raissi, P

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:23.157168Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:23.222358Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71b9f521-9433-4540-9d2f-f448f912bda7 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.640557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b0ec3f21-f28d-421f-a179-84a2603e298c · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.624535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c3223734-e67c-4a96-b937-71dd9ca60d66 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.609044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation fbf1271d-fe4a-4917-930c-22773fa598f8 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.591796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d9bb1c0a-f0b3-43a4-9890-74f1b0ed627f · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.575824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d731e264-6164-4499-a862-2d59118d8cd2 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.558422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b25ef71d-44e8-477f-8ba0-24456b5b4b9c · outbound

This paper cites Zhou, X.-Y.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Zhou, X.-Y

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.541475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ad16626d-4ce3-42a2-a5d9-da44aa703d1a · outbound

This paper cites Saqlain, W.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Saqlain, W

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.523640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 95c7eff7-f55b-4eb7-acfa-0f28057a8917 · outbound

This paper cites Opala, S.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Opala, S

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.507575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 45958ef1-2ef3-4519-962d-36631435b606 · outbound

This paper cites Stokes, J.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Stokes, J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.491837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2c62dce0-21ee-4a40-9d1b-d9775052c7f3 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.476365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bf9855df-3691-4d53-ba70-40c01c0ffdfb · outbound

This paper cites Taylor, J.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Taylor, J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.460066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 20dff1dd-d492-4e65-9772-28d33e8d6a92 · outbound

This paper cites Kusdiantara, H.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Kusdiantara, H

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.445072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f1c3e032-4490-4314-968e-8e304b162d7e · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.430182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation b8c490ca-f341-41f6-a257-70b0bac87b0c · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.414889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 6c01e99f-38cd-4d11-912f-4232136f22e7 · outbound

This paper cites Fabiani, F.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Fabiani, F

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.399723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3217a08c-2a58-4342-9dd0-3508358eb52a · outbound

This paper cites Galaris, G.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Galaris, G

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.384241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 97f32492-e2f2-4abc-b191-26e56b88d837 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.367015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37b0567c-10f3-4cef-a343-7cb8b44d4bcc · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.349448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d971b99c-0394-4451-9081-1cbf42fb58e2 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.333393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 58769003-d4bc-47fe-a9b6-6534627ba97c · outbound

This paper cites Liao, Homotopy analysis method in non-linear differential equations (2012).

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Liao, Homotopy analysis method in non-linear differential equations (2012)

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.317796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5fcd390a-5dea-4af9-bbdf-3d6e902b983f · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.301563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation cef5b2bf-ab1d-42fb-9d2f-b1f23c878d1e · outbound

This paper cites Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics 2 (2) (1944) 164–168.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Levenberg, A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics 2 (2) (1944) 164–168

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.286480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 305d1fab-de53-4bb0-859d-e4d6c80f52fb · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.269511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation df74937b-7467-4a94-921d-af299226f7ca · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.252282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 33abcb53-8886-471a-962e-eac7cd61d49b · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Adam: A Method for Stochastic Optimization

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:25.662804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bca2ba0-8d86-4667-a2b0-265d5128b81d · outbound

This paper cites Moseley, A.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Moseley, A

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.235058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a7b77b47-58fe-49a1-80a4-ffdd427c3019 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.219026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c697b172-90bc-4435-a046-63a974806d23 · outbound

This paper cites Heinlein, A.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Heinlein, A

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.202698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 248eaac7-d0b7-40e3-b02f-354ac39f9809 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.187753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4cb58792-c88c-419c-b240-d7a754e210de · outbound

This paper cites Pedregosa, G.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Pedregosa, G

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.172041Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9d4e4cfd-25c1-4663-8020-8484a8f8b8b7 · outbound

This paper cites Abadi, P.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Abadi, P

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.155803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2303a175-bf34-4fb8-9857-b964c1f95378 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.139975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 37ca6854-e071-41f7-8aa9-e17a03f67ac8 · outbound

This paper cites Stochastic Newton and Cubic Newton Methods with Simple Local Linear-Quadratic Rates.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Stochastic Newton and Cubic Newton Methods with Simple Local Linear-Quadratic Rates

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-06T17:55:26.674995Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57c1b421-08ba-426b-bfa3-92cad7b411c3 · outbound

This paper cites Burke, E.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Burke, E

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.124175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 8a93cd92-c1f6-4a87-83fc-33c388ca0b64 · outbound

This paper cites Kusdiantara, H.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Kusdiantara, H

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.109311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation dc04a5b1-3c2d-489c-b15f-8b657eea30dd · outbound

This paper cites Kusdiantara, F.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Kusdiantara, F

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.093206Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 31d96fd0-945b-4d91-8621-0c95d9560ec4 · outbound

This paper cites Kusdiantara, H.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Kusdiantara, H

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T17:55:27.074451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 481abbc8-1d3f-4327-a977-647e83cea37d · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:27.058310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2c0cb414-9345-4012-a60c-7a6fafeeb588 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:26.942016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a84cc53f-10b0-49ca-a7c5-abb8f5daf693 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:26.925205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 403fc38a-1992-4a01-b97b-dc4ebbc18194 · outbound

This paper cites an unresolved cited work.

Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:55:26.908081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.