Paper Citation Record · LEDGER

Adaptive feature capture method for solving partial differential equations with near singular solutions

As of 9 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 1 inbound Pith citation observation for arXiv:2507.12941.

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

pith.paper-citation-record.v1
2507.12941 v4

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:40:21.953052Z

measured 41 of 41 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 2026-08-04T10:45:10.678037Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

40 of 40 outbound references displayed

verified exact0
verified fuzzy17
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3b124e81-e0b1-434d-8d64-4cd3231239df · outbound

This paper cites Debnath, L.

Adaptive feature capture method for solving partial differential equations with near singular solutions Debnath, L

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:27.862888Z

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 eb936bde-81bf-452b-b964-04024eb09d36 · outbound

This paper cites Achdou, F.

Adaptive feature capture method for solving partial differential equations with near singular solutions Achdou, F

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:27.599554Z

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 ae266877-c008-4fb5-9eba-c172326d799b · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:27.425930Z

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 bc925476-ad33-4a16-99fd-eb097a3c57f4 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:27.242889Z

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 85195238-795e-486f-8b17-5206f4dff68b · outbound

This paper cites Moukalled, L.

Adaptive feature capture method for solving partial differential equations with near singular solutions Moukalled, L

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:27.036263Z

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 5f48162d-8e12-4033-9d72-b2c749616b41 · outbound

This paper cites Thom´ ee, Galerkin Finite Element Methods for Parabolic Problems, Vol.

Adaptive feature capture method for solving partial differential equations with near singular solutions Thom´ ee, Galerkin Finite Element Methods for Parabolic Problems, Vol

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:26.845335Z

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 0bedb54e-47aa-4c8f-a553-8ae39e47c156 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:26.646468Z

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 95cabee0-6779-43f5-b720-2daba03cc075 · outbound

This paper cites Rajendran, A technique to develop mesh-distortion immune finite elements, Computer Methods in Applied Mechanics and Engineering 199 (17-20) (2010) 1044–1063.

Adaptive feature capture method for solving partial differential equations with near singular solutions Rajendran, A technique to develop mesh-distortion immune finite elements, Computer Methods in Applied Mechanics and Engineering 199 (17-20) (2010) 1044–1063

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:26.467468Z

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 cc6ea842-2c6a-44a9-825d-0bdf53833e86 · outbound

This paper cites Blazek, Computational fluid dynamics: principles and applications, Butterworth-Heinemann, 2015.

Adaptive feature capture method for solving partial differential equations with near singular solutions Blazek, Computational fluid dynamics: principles and applications, Butterworth-Heinemann, 2015

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:26.309538Z

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 7ae1de1e-456e-41f0-b7fa-f11864b1a12f · outbound

This paper cites Goodfellow, Y.

Adaptive feature capture method for solving partial differential equations with near singular solutions Goodfellow, Y

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:26.119535Z

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 527e041e-1dc0-498b-93d5-0355192d643d · outbound

This paper cites Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems 2 (4) (1989) 303–314.

Adaptive feature capture method for solving partial differential equations with near singular solutions Cybenko, Approximation by superpositions of a sigmoidal function, Mathematics of control, signals and systems 2 (4) (1989) 303–314

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:19.257094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bfb491ed-33ec-49ef-8a2e-d2dc61604cbe · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:25.935611Z

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 7f59ad3e-8797-4fce-b57e-37288c019a42 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:25.722464Z

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 168061c1-307c-44fe-9be9-bd2bb8f0beb9 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:25.538563Z

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 ce266b7d-fb1a-49cc-9f39-7ad394cf5f2c · outbound

This paper cites Sirignano, K.

Adaptive feature capture method for solving partial differential equations with near singular solutions Sirignano, K

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:25.357395Z

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 2596b91c-161e-46ae-9216-87af75b0f86f · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:25.237963Z

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 f03cdcb0-69c6-43c4-bb41-8de2aa9da36e · outbound

This paper cites Raissi, P.

Adaptive feature capture method for solving partial differential equations with near singular solutions Raissi, P

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:19.847497Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a62efb6-a818-4a9f-b626-75f4c6b96e70 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:25.084124Z

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 5d2de342-b54f-406e-97c6-7a0cedee451d · outbound

This paper cites Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy.

Adaptive feature capture method for solving partial differential equations with near singular solutions Adaptive Neural Network Subspace Method for Solving Partial Differential Equations with High Accuracy

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:20.041526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7dcf7f32-5ff4-4933-baf1-8e6227af0181 · outbound

This paper cites Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects.

Adaptive feature capture method for solving partial differential equations with near singular solutions Physics Informed Neural Networks (PINNs) as intelligent computing technique for solving partial differential equations: Limitation and Future prospects

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:20.131830Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d9536b4-8f76-4377-9232-a8c0c904276e · outbound

This paper cites Huang, Q.-Y.

Adaptive feature capture method for solving partial differential equations with near singular solutions Huang, Q.-Y

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:24.925536Z

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 7a006eb3-3436-44fb-8d42-b5aea9d70ab8 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:20.349517Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3466414c-303f-4b89-94cc-60b7422b9da6 · outbound

This paper cites Rahimi, B.

Adaptive feature capture method for solving partial differential equations with near singular solutions Rahimi, B

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:24.730074Z

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 2f8a4b6a-c2e9-45f5-83f9-6ed5432aaed3 · outbound

This paper cites Huang, G.-B.

Adaptive feature capture method for solving partial differential equations with near singular solutions Huang, G.-B

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:24.552043Z

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 e3a9e450-fadc-4c37-bd51-a4559b7fb05d · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:24.398204Z

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 915cd7fb-b22b-4a2b-9b7d-4748c4dc18fb · outbound

This paper cites The Random Feature Method for Time-dependent Problems.

Adaptive feature capture method for solving partial differential equations with near singular solutions The Random Feature Method for Time-dependent Problems

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:20.718959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 306f71cb-025b-4d53-8b1a-13f85b0fc412 · outbound

This paper cites Huang, L.

Adaptive feature capture method for solving partial differential equations with near singular solutions Huang, L

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:24.183586Z

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 9df29857-70f0-4987-a81f-fed0757b73ee · outbound

This paper cites Dwivedi, B.

Adaptive feature capture method for solving partial differential equations with near singular solutions Dwivedi, B

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:24.000797Z

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 678d7622-5333-4df2-bc01-cd90c554d6b8 · outbound

This paper cites Calabr` o, G.

Adaptive feature capture method for solving partial differential equations with near singular solutions Calabr` o, G

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:23.812816Z

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 35a9083b-6340-4593-8dca-37c2de7a62f5 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:23.667883Z

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 b6076481-8122-40a8-b963-bd997fea2aae · outbound

This paper cites Fabiani, F.

Adaptive feature capture method for solving partial differential equations with near singular solutions Fabiani, F

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:23.515582Z

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 8ddffcbc-d3a0-43ed-856b-bcdde02f1386 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:23.324243Z

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 d5ac96ba-4a30-44cd-aae2-66216d2491ad · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:23.171424Z

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 d55ae63c-a52f-47f2-8944-eff73a0ba25b · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:21.475993Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc681fcb-e5ce-429b-897f-0ca3a70ce279 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:22.996164Z

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 ea9974b3-b50c-4018-8e44-5dc8db28e945 · outbound

This paper cites Adaptive neural network basis methods for partial differential equations with low-regular solutions.

Adaptive feature capture method for solving partial differential equations with near singular solutions Adaptive neural network basis methods for partial differential equations with low-regular solutions

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T16:40:21.641692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e02d6cbe-12ac-4ffa-8371-c84436d08c96 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:22.878233Z

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 4b6ebc26-665d-46c1-9012-8bd84a865c10 · outbound

This paper cites Huang, R.

Adaptive feature capture method for solving partial differential equations with near singular solutions Huang, R

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:22.723906Z

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 b297ca00-0aeb-49c8-8c9b-371f0eb6ec22 · outbound

This paper cites an unresolved cited work.

Adaptive feature capture method for solving partial differential equations with near singular solutions Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:40:22.565552Z

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 de2ba691-f7ff-4d98-ad09-f034caf6c1c5 · outbound

This paper cites Zhang, F.

Adaptive feature capture method for solving partial differential equations with near singular solutions Zhang, F

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:40:22.370438Z

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.

Pith citing papers

Observation e3347a32-3ee4-49a8-946f-0060dda0a692 · inbound

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation cites this paper.

A Morphology-Adaptive Random Feature Method for Inverse Source Problem of the Helmholtz Equation Adaptive feature capture method for solving partial differential equations with near singular solutions

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-04T10:45:10.678037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.