Paper Citation Record · LEDGER

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks

As of 7 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2508.00247.

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

pith.paper-citation-record.v1
2508.00247 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T10:22:36.015100Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

36 of 36 outbound references displayed

verified exact0
verified fuzzy23
unresolved13
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External citation measurements

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Outbound references

Observation 0782c68f-8c93-4f93-bbe2-0a8a3cd9bbb7 · outbound

This paper cites fkan: Fractional kolmogorov-arnold networks with trainable jacobi basis functions, 2024.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks fkan: Fractional kolmogorov-arnold networks with trainable jacobi basis functions, 2024

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.434013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation aae34488-3ff3-44c8-8cbf-c40d02b9fe15 · outbound

This paper cites rkan: Rational kolmogorov-arnold networks, 2024.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks rkan: Rational kolmogorov-arnold networks, 2024

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.423116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 245822e9-df73-42ce-ba7b-3a1e6e98c3ae · outbound

This paper cites A theory of adaptive pattern classifiers.IEEE Transactions on Elec- tronic Computers, (3):299–307, 2006.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks A theory of adaptive pattern classifiers.IEEE Transactions on Elec- tronic Computers, (3):299–307, 2006

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.410917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 813b0d34-b668-4438-8f43-6bf6a3f09507 · outbound

This paper cites Wav-kan: Wavelet kolmogorov-arnold networks, 2024.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Wav-kan: Wavelet kolmogorov-arnold networks, 2024

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:35.898795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9cad226b-0824-4fc5-bd8b-518df92d1dbf · outbound

This paper cites Coleman and Yuying Li.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Coleman and Yuying Li

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.390184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 13942aac-32f1-45ba-9d21-a1bbfb1c81f4 · outbound

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

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Approximation by superpositions of a sigmoidal function.Mathemat- ics of control, signals and systems, 2(4):303–314, 1989

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.380502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 997ef08d-94f6-4114-930d-d06a84f57059 · outbound

This paper cites The weierstrass approximation theorem.Journal of Mathematics and Physics, 4(1-4):148–152, 1925.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks The weierstrass approximation theorem.Journal of Mathematics and Physics, 4(1-4):148–152, 1925

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.371091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 966320f6-812a-46f1-b3b4-5fb19701527b · outbound

This paper cites Representation properties of networks: Kol- mogorov’s theorem is irrelevant.Neural Computation, 1(4):465–469, 1989.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Representation properties of networks: Kol- mogorov’s theorem is irrelevant.Neural Computation, 1(4):465–469, 1989

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.359809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 569a5a36-9cd3-423c-a198-6003656ed484 · outbound

This paper cites Kolmogorov’s mapping neural network existence theorem.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Kolmogorov’s mapping neural network existence theorem

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.348653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ebdcc51b-c212-4e91-9671-a73c393e6208 · outbound

This paper cites Addison-Wesley Longman Publishing Co., Inc., 1989.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Addison-Wesley Longman Publishing Co., Inc., 1989

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.336148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0b72fed7-5db3-48e6-af7d-35d609547bd8 · outbound

This paper cites an unresolved cited work.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:22:36.325528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 889780ea-1769-4fa0-beee-34a91e5c9fa7 · outbound

This paper cites Multilayer feedforward net- works are universal approximators.Neural networks, 2(5):359–366, 1989.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Multilayer feedforward net- works are universal approximators.Neural networks, 2(5):359–366, 1989

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.314944Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f0011aff-1c52-4af3-9080-16e9da313f67 · outbound

This paper cites an unresolved cited work.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:22:36.304987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5141c854-ffed-43aa-8f8b-fccbfd34be0c · outbound

This paper cites On the representations of continuous functions of many variables by superposition of continuous functions of one variable and addition.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks On the representations of continuous functions of many variables by superposition of continuous functions of one variable and addition

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.293009Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cd946f17-a2bc-439f-b1fc-605871c3c8e8 · outbound

This paper cites American Mathematical Society, 1961.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks American Mathematical Society, 1961

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.281791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 36234b14-c511-4c16-b1fa-a13491762a7d · outbound

This paper cites Kolmogorov’s theorem is relevant.Neural Computation, 3(4):617–622, 1991.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Kolmogorov’s theorem is relevant.Neural Computation, 3(4):617–622, 1991

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.269429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 33caf5b6-eb5a-4a8d-9128-af3f2c40d4d1 · outbound

This paper cites Kolmogorov’s theorem and multilayer neural networks.Neural Networks, 5(3):501–506, 1992.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Kolmogorov’s theorem and multilayer neural networks.Neural Networks, 5(3):501–506, 1992

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.258116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f8e44a88-436c-43d8-9ecf-777207506d22 · outbound

This paper cites Kolmogorov-Arnold Networks are Radial Basis Function Networks.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Kolmogorov-Arnold Networks are Radial Basis Function Networks

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:35.949097Z

Source-reported events for the cited work

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Observation 75616422-fc30-406f-8351-53ac3afabc9e · outbound

This paper cites KAN 2.0: Kolmogorov-Arnold Networks Meet Science.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks KAN 2.0: Kolmogorov-Arnold Networks Meet Science

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:35.953387Z

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Unavailable: canonical work link unavailable.

Observation 7a9905b3-1e15-4dcb-852d-60cdba9be6fb · outbound

This paper cites KAN: Kolmogorov-Arnold Networks.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks KAN: Kolmogorov-Arnold Networks

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:35.957334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0fc408e-d93c-4345-9cf4-e18aa937da30 · outbound

This paper cites Approximation of functions, athena series.Selected Topics in Mathematics, 1966.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Approximation of functions, athena series.Selected Topics in Mathematics, 1966

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.245824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b600c162-4011-4b7d-8131-9580a83b3570 · outbound

This paper cites MIT press, 2017.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks MIT press, 2017

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.235133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation aff49614-3e8d-4ef3-8320-accb55048504 · outbound

This paper cites ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLU

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:35.968460Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 977d68dd-862c-4c58-bc7e-fd45e3672dc5 · outbound

This paper cites Sinekan: Kolmogorov- arnold networks using sinusoidal activation functions.Frontiers in Artificial Intelligence, Volume 7 - 2024, 2025.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Sinekan: Kolmogorov- arnold networks using sinusoidal activation functions.Frontiers in Artificial Intelligence, Volume 7 - 2024, 2025

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.225085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b7ba7ea4-1cc8-452c-a425-005d94160529 · outbound

This paper cites The perceptron: a probabilistic model for information storage and organization in the brain.Psychological review, 65(6):386, 1958.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks The perceptron: a probabilistic model for information storage and organization in the brain.Psychological review, 65(6):386, 1958

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:35.975868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ffbcda8f-7c25-4562-bf87-9bc5b5e8ed57 · outbound

This paper cites Rumelhart, Geoffrey E.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Rumelhart, Geoffrey E

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.205093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5de53efb-5177-404b-b8e5-535c89fe1381 · outbound

This paper cites Learning representa- tions by back-propagating errors.nature, 323(6088):533–536, 1986.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Learning representa- tions by back-propagating errors.nature, 323(6088):533–536, 1986

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.194050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0585a3f9-e42e-4789-8f1a-4c300fcf1fda · outbound

This paper cites an unresolved cited work.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:22:36.183386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 48ccc8df-ae32-4437-bd03-ddef7fba3194 · outbound

This paper cites A comprehensive and fair comparison between mlp and kan representations for differential equations and operator networks, 2024.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks A comprehensive and fair comparison between mlp and kan representations for differential equations and operator networks, 2024

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.170940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e4dd546c-fef0-45fc-b836-346984e38050 · outbound

This paper cites an unresolved cited work.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:22:36.159546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9d295a87-99f1-45b0-a408-9629f986037c · outbound

This paper cites On the structure of continuous functions of several variables.Trans- actions of the American Mathematical Society, 115:340–355, 1965.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks On the structure of continuous functions of several variables.Trans- actions of the American Mathematical Society, 115:340–355, 1965

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.146747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 41b32f68-3a17-4895-ba31-3d78a875de44 · outbound

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

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximation

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:36.000359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a377140-17a8-45b5-b1bb-c80040193542 · outbound

This paper cites Chebyshev polynomial-based kolmogorov-arnold networks: An efficient architecture for nonlinear function approxi- mation, 2024.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Chebyshev polynomial-based kolmogorov-arnold networks: An efficient architecture for nonlinear function approxi- mation, 2024

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.133568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 36db5f1d-3081-4190-86c5-66067a85c439 · outbound

This paper cites Bsrbf-kan: A combination of b-splines and radial basic functions in kolmogorov-arnold networks, 2024.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Bsrbf-kan: A combination of b-splines and radial basic functions in kolmogorov-arnold networks, 2024

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:22:36.121115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c600179b-0b1e-43df-bff1-d33fd72e7b7c · outbound

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

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformation

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:36.011666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1bf6fc30-20e3-4c9e-b95b-1463b01c2a95 · outbound

This paper cites KAN or MLP: A Fairer Comparison.

Sinusoidal Approximation Theorem for Kolmogorov-Arnold Networks KAN or MLP: A Fairer Comparison

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T10:22:36.015100Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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