Paper Citation Record · LEDGER

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability

As of 12 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 2 inbound Pith citation observations for arXiv:2501.09283.

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

pith.paper-citation-record.v1
2501.09283 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:12:17.262300Z

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T04:08:26.888691Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T22:30:54.116211Z

Reference resolution

14 of 14 outbound references displayed

verified exact1
verified fuzzy1
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 375427ff-1ba8-460c-b03d-66ffab91922b · outbound

This paper cites Mad Max: Affine Spline Insights into Deep Learning.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Mad Max: Affine Spline Insights into Deep Learning

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.199716Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4005d72-a4a0-4ebd-99a1-2b1265c4031e · outbound

This paper cites The Upper Bound on Knots in Neural Networks.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability The Upper Bound on Knots in Neural Networks

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-10T20:12:17.394927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 53c852ba-c914-473b-997e-b0390f4f1241 · outbound

This paper cites P., Lyu, Y ., Fan, X., Wu, Z., Cheng, Y ., Wu, J., Chen, L., Wu, P., Lee, M.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability P., Lyu, Y ., Fan, X., Wu, Z., Cheng, Y ., Wu, J., Chen, L., Wu, P., Lee, M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T20:12:17.446689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 032dcfe6-87b3-4f59-83c0-f1134b065d9a · outbound

This paper cites Kolmogorov-Arnold Transformer.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Kolmogorov-Arnold Transformer

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.252758Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b0ac904-6d32-4437-ace1-3a3ecaaf86c7 · outbound

This paper cites GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networks.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.258136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b8d2500-fe6a-4cd9-ab3e-c43e1ce38bdf · outbound

This paper cites Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Reference 2002

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.243245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b720e65-4846-4fdd-a947-5e17198034d1 · outbound

This paper cites A Temporal Kolmogorov-Arnold Transformer for Time Series Forecasting.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability A Temporal Kolmogorov-Arnold Transformer for Time Series Forecasting

Reference 2011

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.220278Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e28e43c-0350-4f00-aaf3-f63a7f5a1966 · outbound

This paper cites U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability U-KAN Makes Strong Backbone for Medical Image Segmentation and Generation

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.229828Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eaf9ba4a-5361-496a-8651-53023cf7883c · outbound

This paper cites Character-level Convolutional Networks for Text Classification.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Character-level Convolutional Networks for Text Classification

Reference 2016

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.262300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0f2f347-074a-4b0e-9df3-28c760443daa · outbound

This paper cites Convolutional Kolmogorov-Arnold Networks.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Convolutional Kolmogorov-Arnold Networks

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.205136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d633b439-727e-4e1e-b614-01fd8357d079 · outbound

This paper cites doi: 10.1038/ s41597-019-0103-9.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability doi: 10.1038/ s41597-019-0103-9

Reference 2019

Resolution: malformed identifier; raw_fallback, observed 2026-08-10T20:12:17.459290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5262f442-6979-4c08-b9d4-31178e679c7f · outbound

This paper cites Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.247615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a934f2b-a630-4373-a993-92e1e787128a · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability KAN: Kolmogorov-Arnold Networks

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.238545Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33cbf494-66d1-4d09-a765-77fa4f6f02f4 · outbound

This paper cites Wav-KAN: Wavelet Kolmogorov-Arnold Networks.

Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability Wav-KAN: Wavelet Kolmogorov-Arnold Networks

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-10T20:12:17.209986Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 1f915e35-6d1d-4a64-8e77-3fbdb4ea687a · inbound

Clifford Kolmogorov-Arnold Networks cites this paper.

Clifford Kolmogorov-Arnold Networks Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T04:08:26.888691Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f8e0b1b-5f3f-43a4-afb8-0460304bca12 · inbound

From Uniform to Learned Knots: A Study of Spline-Based Numerical Encodings for Tabular Deep Learning cites this paper.

From Uniform to Learned Knots: A Study of Spline-Based Numerical Encodings for Tabular Deep Learning Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-10T22:30:54.120342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.