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Paper Citation Record · LEDGER

Learning with Mandelbrot and Julia

As of 9 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2509.00903.

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

pith.paper-citation-record.v1
2509.00903 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T13:16:02.540786Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

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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

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External citation measurements

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Outbound references

Observation 5aaa3718-b2d1-46cc-872f-2f6631da66ee · outbound

This paper cites Physics and Fractal Structures.

Learning with Mandelbrot and Julia Physics and Fractal Structures

Reference 1

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Observation 900d84fc-2d10-4a0e-a594-6f4e139e6ac2 · outbound

This paper cites The Fractal Geometry of Nature , volume 1.

Learning with Mandelbrot and Julia The Fractal Geometry of Nature , volume 1

Reference 2

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This paper cites Fractal-based methods in analysis.

Learning with Mandelbrot and Julia Fractal-based methods in analysis

Reference 3

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Observation ae9a2445-ef12-4eed-b109-a8bc5c3c206b · outbound

This paper cites Introduction to the Modern Theory of Dynamical Systems , volume 54 of Encyclopedia of Mathematics and its Applications.

Learning with Mandelbrot and Julia Introduction to the Modern Theory of Dynamical Systems , volume 54 of Encyclopedia of Mathematics and its Applications

Reference 4

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Observation 434f83fc-7913-447d-96fd-4e18be8ea3ea · outbound

This paper cites A first course in chaotic dynamical systems: Theory and experiment.

Learning with Mandelbrot and Julia A first course in chaotic dynamical systems: Theory and experiment

Reference 5

Resolution
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Observation 9ebc8221-9cc4-4a20-8f98-247a55c9b83a · outbound

This paper cites Mandelbrot set and Julia sets of fractional order.

Learning with Mandelbrot and Julia Mandelbrot set and Julia sets of fractional order

Reference 6

Resolution
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Observation 08c380de-d345-4224-a530-ec97e80d3e34 · outbound

This paper cites Zalcman functions and similarity be- tween the Mandelbrot set, Julia sets, and the tricorn.

Learning with Mandelbrot and Julia Zalcman functions and similarity be- tween the Mandelbrot set, Julia sets, and the tricorn

Reference 7

Resolution
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Source-reported events for the cited work

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Observation cbfd4323-cdf0-4422-802f-a5a3b5b1c459 · outbound

This paper cites Similarity between the Mandelbrot set and Julia sets.

Learning with Mandelbrot and Julia Similarity between the Mandelbrot set and Julia sets

Reference 8

Resolution
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Source-reported events for the cited work

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Observation 8045109b-fa73-4cbf-a1e0-e9d0c87fcb52 · outbound

This paper cites Haus- dorff dimension of Julia sets in the logistic family.

Learning with Mandelbrot and Julia Haus- dorff dimension of Julia sets in the logistic family

Reference 9

Resolution
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Source-reported events for the cited work

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Observation 8170af59-9c62-451a-825d-d976f7be2bfc · outbound

This paper cites On the directional derivative of the Hausdorff dimension of quadratic polynomial Julia sets at-2.

Learning with Mandelbrot and Julia On the directional derivative of the Hausdorff dimension of quadratic polynomial Julia sets at-2

Reference 10

Resolution
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Source-reported events for the cited work

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Observation 699b9e37-6bf7-418d-92b4-c24d2b5905f3 · outbound

This paper cites Automatic prediction of tumour malignancy in breast cancer with fractal di- mension.

Learning with Mandelbrot and Julia Automatic prediction of tumour malignancy in breast cancer with fractal di- mension

Reference 11

Resolution
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Observation c2fe9c4f-c6fd-4373-9291-03ca37de459e · outbound

This paper cites A machine learning approach to auto- matic detection of irregularity in skin lesion border using dermoscopic images.

Learning with Mandelbrot and Julia A machine learning approach to auto- matic detection of irregularity in skin lesion border using dermoscopic images

Reference 12

Resolution
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Source-reported events for the cited work

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Observation 96d7e224-4766-43f3-af70-bfc790d15281 · outbound

This paper cites Ma- chine learning and fractal theory models for landslide sus- ceptibility mapping: Case study from the Jinsha River Basin.

Learning with Mandelbrot and Julia Ma- chine learning and fractal theory models for landslide sus- ceptibility mapping: Case study from the Jinsha River Basin

Reference 13

Resolution
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Observation 0ebcd4fc-9e8c-4603-9797-a9d970f2a195 · outbound

This paper cites Predicting the future of discrete sequences from fractal representations of the past.

Learning with Mandelbrot and Julia Predicting the future of discrete sequences from fractal representations of the past

Reference 14

Resolution
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Observation bedf52d6-a413-444a-bf23-3c8949b10b5c · outbound

This paper cites Schema genetic algorithm for fractal image compres- sion.

Learning with Mandelbrot and Julia Schema genetic algorithm for fractal image compres- sion

Reference 15

Resolution
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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.

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Observation 46ce99c4-d848-4c0a-814f-1d6ea4469567 · outbound

This paper cites Pre-training without natural images.

Learning with Mandelbrot and Julia Pre-training without natural images

Reference 16

Resolution
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Source-reported events for the cited work

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Observation d9b4fb0e-0ff4-4109-a988-514ab4a4b5d3 · outbound

This paper cites Improving fractal pre-training.

Learning with Mandelbrot and Julia Improving fractal pre-training

Reference 17

Resolution
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Source-reported events for the cited work

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Observation 35af878a-e2e1-41bd-a7c6-1a9138eda838 · outbound

This paper cites Learning fractals by gradient descent.

Learning with Mandelbrot and Julia Learning fractals by gradient descent

Reference 18

Resolution
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Source-reported events for the cited work

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Observation c52975a6-92c9-4cab-b4e4-36bc1577f32a · outbound

This paper cites Machine learning and fractal geometry.

Learning with Mandelbrot and Julia Machine learning and fractal geometry

Reference 19

Resolution
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Source-reported events for the cited work

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Observation bac45c01-59e4-45e9-967a-b280d8c5506a · outbound

This paper cites What do deep neural networks under- stand of fractals?, 2017.

Learning with Mandelbrot and Julia What do deep neural networks under- stand of fractals?, 2017

Reference 20

Resolution
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Source-reported events for the cited work

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Observation 54ad643f-6c2b-464f-ba7b-16e420e1ded2 · outbound

This paper cites On the quadratic mapping z → z2 − µ for complex µ and z: the fractal structure of its M set, and scaling.

Learning with Mandelbrot and Julia On the quadratic mapping z → z2 − µ for complex µ and z: the fractal structure of its M set, and scaling

Reference 21

Resolution
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Source-reported events for the cited work

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Observation 1b9b36ce-b663-4621-9b2e-ab1b3df87331 · outbound

This paper cites Disconnected Julia sets.

Learning with Mandelbrot and Julia Disconnected Julia sets

Reference 22

Resolution
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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.

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Observation 5b3eed04-aed1-4fca-bf95-31d098518026 · outbound

This paper cites Clinical time series pre - diction: Toward a hierarchical dynamical system frame- work.

Learning with Mandelbrot and Julia Clinical time series pre - diction: Toward a hierarchical dynamical system frame- work

Reference 23

Resolution
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Source-reported events for the cited work

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Observation 6cb07779-af03-458b-9db1-e4f3a2bfe3a7 · outbound

This paper cites An intelligent syste m for financial time series prediction combining dynamical systems theory, fractal theory, and statistical methods.

Learning with Mandelbrot and Julia An intelligent syste m for financial time series prediction combining dynamical systems theory, fractal theory, and statistical methods

Reference 24

Resolution
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Source-reported events for the cited work

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Observation 43498efc-05fa-446b-8cef-65d7222eb2cb · outbound

This paper cites Classification of chaotic time series with deep learning.

Learning with Mandelbrot and Julia Classification of chaotic time series with deep learning

Reference 25

Resolution
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Source-reported events for the cited work

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Observation 16a2e115-53f5-4c76-bba4-dd62ca5fd463 · outbound

This paper cites Deep learning for time series classification: a review.

Learning with Mandelbrot and Julia Deep learning for time series classification: a review

Reference 26

Resolution
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Source-reported events for the cited work

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Observation b4621607-9319-4d3c-99b7-fd7a29566063 · outbound

This paper cites Inception- time: Finding alexnet for time series classification.

Learning with Mandelbrot and Julia Inception- time: Finding alexnet for time series classification

Reference 27

Resolution
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Source-reported events for the cited work

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Learning with Mandelbrot and Julia Unresolved cited work

Reference 28

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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.

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This paper cites Solving high-dimensional partial differential equations using dee p learning.

Learning with Mandelbrot and Julia Solving high-dimensional partial differential equations using dee p learning

Reference 29

Resolution
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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.

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Observation 41974756-86d9-4ed0-9f1f-8740c8e46b9a · outbound

This paper cites Solving differential equations using deep neural networks.

Learning with Mandelbrot and Julia Solving differential equations using deep neural networks

Reference 30

Resolution
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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.

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Observation 7be3adcc-f256-4d86-b2d1-32ea6386a527 · outbound

This paper cites A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic par- tial differential equations.

Learning with Mandelbrot and Julia A deep-genetic algorithm (deep-GA) approach for high-dimensional nonlinear parabolic par- tial differential equations

Reference 31

Resolution
verified fuzzy
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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.

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Observation abdf36da-9b38-4524-b1c5-5297ad505451 · outbound

This paper cites Deep hidden physics models: Deep learn- ing of nonlinear partial differential equations.

Learning with Mandelbrot and Julia Deep hidden physics models: Deep learn- ing of nonlinear partial differential equations

Reference 32

Resolution
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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.

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Observation f6e03cd3-607f-4d1a-bf28-f5d21651742f · outbound

This paper cites Hidden physics models: Machine learning of nonlinear partial dif- ferential equations.

Learning with Mandelbrot and Julia Hidden physics models: Machine learning of nonlinear partial dif- ferential equations

Reference 33

Resolution
verified fuzzy
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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.

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Observation 28bec9b7-6869-42aa-8d90-f08a62db9249 · outbound

This paper cites Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse problems involving nonlinear partial differential equations.

Learning with Mandelbrot and Julia Physics-informed neural networks: A deep learn- ing framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 34

Resolution
verified fuzzy
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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.

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Observation 20ea30d5-b774-4166-878c-f2f5f1c4349a · outbound

This paper cites Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations.

Learning with Mandelbrot and Julia Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.677521Z

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.

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Observation 8a4c631b-9bd0-4e36-ac2a-a36574d40bf2 · outbound

This paper cites Neural networks for bifurcation and linear sta- bility analysis of steady states in partial differential equ a- tions.

Learning with Mandelbrot and Julia Neural networks for bifurcation and linear sta- bility analysis of steady states in partial differential equ a- tions

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.669408Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation 6e590c72-ba94-4a2e-843e-c6c0313bd845 · outbound

This paper cites Neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices.

Learning with Mandelbrot and Julia Neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.661075Z

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.

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Observation 1240cd16-9b0d-4ebc-b907-f749661f9982 · outbound

This paper cites Un- derstanding and mitigating gradient flow pathologies in physics-informed neural networks.

Learning with Mandelbrot and Julia Un- derstanding and mitigating gradient flow pathologies in physics-informed neural networks

Reference 38

Resolution
verified fuzzy
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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.

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Observation e4614f56-e8e9-4c85-8c7f-ecbb0e120ccf · outbound

This paper cites Extended physics-informed neural networks (XPINNs): A general- ized space-time domain decomposition based deep learn- ing framework for nonlinear partial differential equations.

Learning with Mandelbrot and Julia Extended physics-informed neural networks (XPINNs): A general- ized space-time domain decomposition based deep learn- ing framework for nonlinear partial differential equations

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.644522Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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Observation bb7ef3f6-fd42-40ea-96dc-d9da16819f12 · outbound

This paper cites A composite neural network that learns from multi-fidelity data: Appli- cation to function approximation and inverse PDE prob- lems.

Learning with Mandelbrot and Julia A composite neural network that learns from multi-fidelity data: Appli- cation to function approximation and inverse PDE prob- lems

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.636233Z

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.

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Observation 6021d8a7-97c3-4f55-95c6-6f9ca4e170a9 · outbound

This paper cites Transfer learning on physics-informed neural networks for tracking the hemo- dynamics in the evolving false lumen of dissected aorta.

Learning with Mandelbrot and Julia Transfer learning on physics-informed neural networks for tracking the hemo- dynamics in the evolving false lumen of dissected aorta

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.627549Z

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.

source=pdf_text observed=2026-08-05T13:16:02.522885Z digest=sha256:a9a9dc1edc8c6a230b3409ef0c4b547e4c1b63c8a7cff7d97561865fbd6b1df2

Observation 84e58a8e-7e0a-40c2-950d-8268e0beef28 · outbound

This paper cites Physics guided neural networks for modelling of non- linear dynamics.

Learning with Mandelbrot and Julia Physics guided neural networks for modelling of non- linear dynamics

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.618441Z

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.

source=pdf_text observed=2026-08-05T13:16:02.525434Z digest=sha256:f70fcbd7d38a3294eb9b1b66c8cf9700c96bcefa5b1ecc1924d87fd152ce918b

Observation 2c1dde14-4551-4790-ae0b-2d6dd40e841d · outbound

This paper cites Zero-shot forecasting of chaotic systems.

Learning with Mandelbrot and Julia Zero-shot forecasting of chaotic systems

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-05T13:16:02.527907Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T13:16:02.527907Z digest=sha256:0baf3371ac92b985706401d3011e19c955f399c301f5c83156c75372c8a6013c

Observation 24a10306-2bf5-4178-8899-ab83400d1774 · outbound

This paper cites Discovering governing equations from data by sparse iden- tification of nonlinear dynamical systems.

Learning with Mandelbrot and Julia Discovering governing equations from data by sparse iden- tification of nonlinear dynamical systems

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.610273Z

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.

source=pdf_text observed=2026-08-05T13:16:02.530639Z digest=sha256:ddfaca8137fb04f08bf8a90406026f5e6e6701cdb3dc2e2e54c7622dd90485e9

Observation 21c81cb4-f032-481a-bf38-fd2eb226711e · outbound

This paper cites Data-driven discovery of coordinates and governing equations.

Learning with Mandelbrot and Julia Data-driven discovery of coordinates and governing equations

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.601765Z

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.

source=pdf_text observed=2026-08-05T13:16:02.533240Z digest=sha256:4d9bfb7ff251f71b0d13f271a5477cd5e36e9cc4cfd3ae66f4cb15b7dd02aae5

Observation 4ae16cca-d8fc-4c37-b1eb-4bcc7dbf3744 · outbound

This paper cites Chaos as an interpretable benchmark for forecasting and data-driven modelling.

Learning with Mandelbrot and Julia Chaos as an interpretable benchmark for forecasting and data-driven modelling

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-05T13:16:02.535689Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T13:16:02.535689Z digest=sha256:948b66d4625d07cce7d192eca935381ff4bcc32e33269cb7c900e0935f17d39d

Observation 5ace688c-cddb-473c-9d76-3527c3cf7e4b · outbound

This paper cites Tjahjono.

Learning with Mandelbrot and Julia Tjahjono

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.593392Z

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.

source=pdf_text observed=2026-08-05T13:16:02.538490Z digest=sha256:ce6dfd767be69a582ad6fbcbe3cefa97f507f664633667177c74f5ab11f28919

Observation eea37404-a433-485a-9636-31bb4e9094b8 · outbound

This paper cites Discovering physical concepts with neural networks.

Learning with Mandelbrot and Julia Discovering physical concepts with neural networks

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:16:02.584959Z

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.

source=pdf_text observed=2026-08-05T13:16:02.540786Z digest=sha256:4e553fe6ac6f35bef9f570be557109cb9f99339ab14167207b257e501aa0107c

Pith citing papers

No inbound Pith citation observations are available.