Paper Citation Record · LEDGER

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs

As of 18 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2507.15137.

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

pith.paper-citation-record.v1
2507.15137 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:57:54.100500Z

measured 42 of 42 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

42 of 42 outbound references displayed

verified exact1
verified fuzzy33
unresolved8
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4c402a98-d465-4fad-be8c-7b3099b952d6 · outbound

This paper cites An extension of a bound for functions in sobolev spaces, with applications to (m, s)-spline interpolation and smoothing.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs An extension of a bound for functions in sobolev spaces, with applications to (m, s)-spline interpolation and smoothing

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.438839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 64b85157-09bb-45fe-9d24-0dc5968bace3 · outbound

This paper cites A Generalized Randomized Rank-Revealing Factorization.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs A Generalized Randomized Rank-Revealing Factorization

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:57:54.136661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f268c18a-5c12-47b3-8b2d-74ef434cd1bc · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.431343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d87ea003-423c-41ad-a561-7c5132187aef · outbound

This paper cites On selecting a maximum volume sub-matrix of a matrix and related problems.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs On selecting a maximum volume sub-matrix of a matrix and related problems

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.424146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 92e8d024-af97-490c-bbba-4a3c4b25cb67 · outbound

This paper cites Extrinsic meshless collocation methods for PDEs on manifolds.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Extrinsic meshless collocation methods for PDEs on manifolds

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.416482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4a8d789e-6118-4b53-b4bd-203a8ac72aa1 · outbound

This paper cites Proving the stability estimates of variational least-squares kernel-based methods.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Proving the stability estimates of variational least-squares kernel-based methods

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.408950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4078a561-965a-48d6-aed1-fc3b64fc70cb · outbound

This paper cites A kernel-based embedding method and convergence analysis for surfaces PDEs.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs A kernel-based embedding method and convergence analysis for surfaces PDEs

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.401522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4fddcc6c-21f6-4f21-b24b-8a88bc1bac49 · outbound

This paper cites H 2-convergence of least-squares kernel collocation methods.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs H 2-convergence of least-squares kernel collocation methods

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.394350Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f5f58ce0-668e-42e9-9b81-5a334b2b6b12 · outbound

This paper cites Kernel-Based Galerkin Methods on Compact Manifolds Without Boundary, with an Em- phasis on SO(3).

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Kernel-Based Galerkin Methods on Compact Manifolds Without Boundary, with an Em- phasis on SO(3)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.386968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f5c22386-647a-4056-8579-6a6bc8063154 · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.379276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 27634088-e914-41d0-bc4f-f9174e25ce84 · outbound

This paper cites Error bounds for a least squares meshless finite difference method on closed manifolds.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Error bounds for a least squares meshless finite difference method on closed manifolds

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.372108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1df93bdf-8a27-4a3d-aaf3-f9d1c740b9d5 · outbound

This paper cites Duersch and Ming Gu.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Duersch and Ming Gu

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.363532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 942fab55-0e0a-4dbc-b359-9258d86ca5fb · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.356002Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2a7c5683-4247-4f11-9de9-51b43f4094cd · outbound

This paper cites Fasshauer.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Fasshauer

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.348531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b64713e0-eddd-44eb-a80c-65bc78b53894 · outbound

This paper cites Fasshauer.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Fasshauer

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.340845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a93edcee-8e19-45a8-b5a2-4bfef2f4acb0 · outbound

This paper cites Fuselier, T.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Fuselier, T

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.332902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 40a7b748-317e-4440-844a-75277a519665 · outbound

This paper cites Gonzalez.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Gonzalez

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.324521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b4a2b7a6-c564-46e0-827c-e962771eddcb · outbound

This paper cites Gonzalez.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Gonzalez

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.316859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c3e2f61d-a96b-42e1-ba19-9541da5d60ee · outbound

This paper cites Bounding homotopy types by geometry.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Bounding homotopy types by geometry

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.309397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3ee8e4e0-ba8b-48e7-b01d-aad591a1a5c4 · outbound

This paper cites Eisenstat.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Eisenstat

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.301399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bc62ec94-5e7c-4661-a577-a1ed6be7dc14 · outbound

This paper cites Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Kernel-based Greedy Approximation of Parametric Elliptic Boundary Value Problems

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T15:57:54.051933Z

Source-reported events for the cited work

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Observation 20ed39bf-2336-41d3-809b-55eac4d589cf · outbound

This paper cites Hangelbroek, F.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Hangelbroek, F

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.293552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bafe2c7b-fe8e-4871-a08d-b36766820c30 · outbound

This paper cites Hangelbroek, F.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Hangelbroek, F

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.285934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8cf99a22-1b1f-4d71-9bc2-a150abcd1e49 · outbound

This paper cites Hangelbroek, C.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Hangelbroek, C

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.278650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ebdcc388-4a8b-405e-a648-c8fc8940f26e · outbound

This paper cites Narcowich, Christian Rieger, and Joseph D.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Narcowich, Christian Rieger, and Joseph D

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.271658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a548626f-f7a7-4fad-8bf3-a73d0139bc8d · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.264230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 198cb546-0151-4417-a8fa-aeeffda5d5d1 · outbound

This paper cites Limonova Kashin, B.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Limonova Kashin, B

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.256867Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e1b1f6ab-4bc3-4e79-8b22-b089e1848f97 · outbound

This paper cites On sampling discretization in l2.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs On sampling discretization in l2

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.249769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 818e17d0-af86-4d3e-ae7a-585d77e52b95 · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.242740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c4fa5d61-29f6-47c8-9fb6-c2849b6a04e3 · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.235344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e29de454-2160-455f-9529-77a4becc5c16 · outbound

This paper cites Efficient algorithms for computing a strong rank-revealing QR factor- ization.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Efficient algorithms for computing a strong rank-revealing QR factor- ization

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.227662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 123305f1-0724-4922-9ac4-c76397bbf32d · outbound

This paper cites Springer-Verlag, Berlin- New York, 1966.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Springer-Verlag, Berlin- New York, 1966

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.220302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a770c6c2-c316-407a-82c7-1f4465f3fb65 · outbound

This paper cites Narcowich.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Narcowich

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.213268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 60e5c5f3-46e0-4600-8cfd-6d0b8db0eda7 · outbound

This paper cites Narcowich, Stephen T.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Narcowich, Stephen T

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.206311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6d75b18f-6866-456e-b43b-14c49389d0f8 · outbound

This paper cites Narcowich, Xinping Sun, and Joseph D.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Narcowich, Xinping Sun, and Joseph D

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.199037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 14b3510d-7af2-466a-b6e5-392a59160c43 · outbound

This paper cites Stein and Guido Weiss.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Stein and Guido Weiss

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.191405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 43a46cdc-816b-4b55-8aab-233299fb0dd6 · outbound

This paper cites Strichartz.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Strichartz

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.184154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 594b19da-dd5e-43a7-87a7-df82d9ad0ee3 · outbound

This paper cites A least squares radial basis function finite difference method with improved stability properties.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs A least squares radial basis function finite difference method with improved stability properties

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.176071Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4390d3b9-0051-4cb2-8692-9bfdcfb4073f · outbound

This paper cites Theory of function spaces.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Theory of function spaces

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.168140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5fc6d4c0-8c8a-4ee2-a6d0-8d1921452c94 · outbound

This paper cites an unresolved cited work.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:57:54.160481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d4c01a82-c56c-4cde-bf88-ae48879393d4 · outbound

This paper cites Wendland.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Wendland

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.152809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dd674d79-84d2-4888-9c8d-c57084868914 · outbound

This paper cites Sharp inverse estimates for radial basis function interpolation: One-to-one correspondence between smoothness and approximation rates.

Extending Data to Improve Stability and Error Estimates Using Asymmetric Kansa-like Methods to Solve PDEs Sharp inverse estimates for radial basis function interpolation: One-to-one correspondence between smoothness and approximation rates

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:57:54.145190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

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