Paper Citation Record · LEDGER

Learning with Mandelbrot and Julia

As of 7 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.

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

48 of 48 outbound references displayed

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verified fuzzy45
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External citation measurements

No source-named external measurement is stored.

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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.942374Z

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 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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.935024Z

Source-reported events for the cited work

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Observation 1626d382-4a25-4527-a246-8e6b258cac31 · outbound

This paper cites Fractal-based methods in analysis.

Learning with Mandelbrot and Julia Fractal-based methods in analysis

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.927532Z

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 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

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.919848Z

Source-reported events for the cited work

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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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.912411Z

Source-reported events for the cited work

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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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.904800Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.897251Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.889358Z

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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.881797Z

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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.874102Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.865633Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.857878Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.849795Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.842201Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.834598Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.826920Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.818932Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.811248Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.803543Z

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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.795690Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.787778Z

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

This paper cites Disconnected Julia sets.

Learning with Mandelbrot and Julia Disconnected Julia sets

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.780114Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.772495Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.764793Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.757049Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.748844Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.741225Z

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 3f1babe9-5c99-481e-885d-997fdde06ce9 · outbound

This paper cites an unresolved cited work.

Learning with Mandelbrot and Julia Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:16:02.733117Z

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 fdcc90d7-5966-49cd-8299-898d5107932e · outbound

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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.725783Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.718228Z

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 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; raw_fallback, observed 2026-08-05T13:16:02.710209Z

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 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: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:02.701877Z

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 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; raw_fallback, observed 2026-08-05T13:16:02.693025Z

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 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; raw_fallback, observed 2026-08-05T13:16:02.685344Z

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 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 2026-08-07T06:34:17.273281+00:00.

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

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 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 2026-08-07T06:34:17.273281+00:00.

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; raw_fallback, observed 2026-08-05T13:16:02.653109Z

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 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

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 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 2026-08-07T06:34:17.273281+00:00.

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 2026-08-07T06:34:17.273281+00:00.

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 2026-08-07T06:34:17.273281+00:00.

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.

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 2026-08-07T06:34:17.273281+00:00.

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 2026-08-07T06:34:17.273281+00:00.

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.

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 2026-08-07T06:34:17.273281+00:00.

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 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.