Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T13:16:02.540786Z
Paper Citation Record · LEDGER
Learning with Mandelbrot and Julia
As of 18 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
48 of 48 outbound references displayed
- verified exact0
- verified fuzzy45
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
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 2026-08-18T06:34:40.430872+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
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
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 2026-08-18T06:34:40.430872+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
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
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
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
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
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
No inbound Pith citation observations are available.