Paper Citation Record · LEDGER

Symplectic Representation of Legendre Dynamics

As of 9 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2512.19409.

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

pith.paper-citation-record.v1
2512.19409 v2

Coverage vector

measured 38 of 38 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-03T14:48:00.784384Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

38 of 38 outbound references displayed

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Outbound references

Observation 63e123aa-c270-4b9f-b148-12422cad7e62 · outbound

This paper cites Methods of information geometry , volume 191.

Symplectic Representation of Legendre Dynamics Methods of information geometry , volume 191

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.684080Z

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Observation 4f5b66e8-eb8a-47ae-a405-5a895ef343a1 · outbound

This paper cites Mathematical methods of classical mechanics , volume 60.

Symplectic Representation of Legendre Dynamics Mathematical methods of classical mechanics , volume 60

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.689272Z

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Observation af854ae1-170f-40fd-8ede-b55c9678868d · outbound

This paper cites On invariance and selectivity in representation learning.

Symplectic Representation of Legendre Dynamics On invariance and selectivity in representation learning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.692148Z

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Observation f6cedc63-a0f1-4909-83f3-663fd88270bf · outbound

This paper cites Representation learning: A review and new perspectives.

Symplectic Representation of Legendre Dynamics Representation learning: A review and new perspectives

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.695021Z

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Observation b2e9f0c3-2204-43f3-84aa-ed7dc71d1a1c · outbound

This paper cites On explaining the surprising success of reservoir computing forecaster of chaos? the universal machine learning dynamical system with contrast to var and dmd.

Symplectic Representation of Legendre Dynamics On explaining the surprising success of reservoir computing forecaster of chaos? the universal machine learning dynamical system with contrast to var and dmd

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.698245Z

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Observation 23fa1969-6ad6-41b4-bc4c-25e35228846d · outbound

This paper cites Projecting the Fokker-Planck Equation onto a finite dimensional exponential family.

Symplectic Representation of Legendre Dynamics Projecting the Fokker-Planck Equation onto a finite dimensional exponential family

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.700916Z

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Observation 4c7e277f-a03d-479e-a6bc-7bc714118844 · outbound

This paper cites Lectures on the Geometry of Quantization , volume 8.

Symplectic Representation of Legendre Dynamics Lectures on the Geometry of Quantization , volume 8

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.704075Z

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Observation d2f91c74-ec02-4b67-89fb-a9cab773d7c7 · outbound

This paper cites Group equivariant convolutional networks.

Symplectic Representation of Legendre Dynamics Group equivariant convolutional networks

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.706560Z

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Observation 7183fcbf-5abd-4f89-a2a1-c0e4e43ab2ac · outbound

This paper cites Symplectic Recurrent Neural Networks.

Symplectic Representation of Legendre Dynamics Symplectic Recurrent Neural Networks

Reference 9

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Observation 259dcb13-d57f-47a8-bf0e-cc88fe9e441c · outbound

This paper cites Information processing capacity of dynamical systems.

Symplectic Representation of Legendre Dynamics Information processing capacity of dynamical systems

Reference 10

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Observation 1e0611c4-4643-4682-a8d1-956667cb559a · outbound

This paper cites Universality of real minimal complexity reservoir.

Symplectic Representation of Legendre Dynamics Universality of real minimal complexity reservoir

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.714502Z

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Observation 4b6595a0-1491-4165-9def-0f49e0780463 · outbound

This paper cites Linear simple cycle reservoirs at the edge of stability perform fourier decomposition of the input driving signals.

Symplectic Representation of Legendre Dynamics Linear simple cycle reservoirs at the edge of stability perform fourier decomposition of the input driving signals

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.717057Z

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Observation 33e8aa4c-ee5a-4984-963b-d0b97a0f47ac · outbound

This paper cites Euler state networks: Non-dissipative reservoir computing.

Symplectic Representation of Legendre Dynamics Euler state networks: Non-dissipative reservoir computing

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.719791Z

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Observation 7d66a134-dc5e-4e98-af48-a00bb3260443 · outbound

This paper cites Echo state networks are universal.

Symplectic Representation of Legendre Dynamics Echo state networks are universal

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.722274Z

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Observation 529f006c-4bd5-4186-b63c-d77a221489eb · outbound

This paper cites Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems.

Symplectic Representation of Legendre Dynamics Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.724824Z

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Observation 63b24ba1-33eb-446d-a0bf-33a972ed894d · outbound

This paper cites Reservoir computing universality with stochastic inputs.

Symplectic Representation of Legendre Dynamics Reservoir computing universality with stochastic inputs

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.727296Z

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Observation 62a93db4-3a8b-4399-b363-0d9107c660f3 · outbound

This paper cites Kalman filtering and smoothing solutions to temporal gaussian process regression models.

Symplectic Representation of Legendre Dynamics Kalman filtering and smoothing solutions to temporal gaussian process regression models

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.730004Z

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Observation aeb77a5f-c226-4ad1-b0fb-94bfc030514e · outbound

This paper cites Reservoir computing beyond memory-nonlinearity trade-off.

Symplectic Representation of Legendre Dynamics Reservoir computing beyond memory-nonlinearity trade-off

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.732515Z

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Observation 95c489a7-1333-410d-aadb-e268f364cf90 · outbound

This paper cites Short term memory in echo state networks.

Symplectic Representation of Legendre Dynamics Short term memory in echo state networks

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.734949Z

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Observation 4c942d37-ff81-45ac-b5d0-1dd0a2c2ba66 · outbound

This paper cites echo state.

Symplectic Representation of Legendre Dynamics echo state

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.737508Z

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Observation 60f16439-2a35-4c6a-8b8b-045930677ca2 · outbound

This paper cites Tutorial on training recurrent neural networks, covering bppt, rtrl, ekf and the echo state network approach.

Symplectic Representation of Legendre Dynamics Tutorial on training recurrent neural networks, covering bppt, rtrl, ekf and the echo state network approach

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.740257Z

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Observation 911cc78a-96e4-41d5-a325-19b974ee9106 · outbound

This paper cites Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication.

Symplectic Representation of Legendre Dynamics Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.742787Z

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Observation 045ea248-3a07-4fae-8b95-4d7c62053493 · outbound

This paper cites An introduction to probabilistic graphical models, 2003.

Symplectic Representation of Legendre Dynamics An introduction to probabilistic graphical models, 2003

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.745219Z

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Observation daa5b118-8768-4ae4-b11c-94dff37bc1cf · outbound

This paper cites Markov-modulated affine processes.

Symplectic Representation of Legendre Dynamics Markov-modulated affine processes

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.747652Z

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Observation 0f99b053-0bef-4caf-9f4f-249c9a2519c5 · outbound

This paper cites On translation invariance in cnns: Convolutional layers can exploit absolute spatial location.

Symplectic Representation of Legendre Dynamics On translation invariance in cnns: Convolutional layers can exploit absolute spatial location

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.750167Z

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Observation a400ea4e-bc67-49b1-a208-689b94082411 · outbound

This paper cites Metric learning: A survey.

Symplectic Representation of Legendre Dynamics Metric learning: A survey

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.752751Z

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Observation e7fb5cd0-8a8d-47ee-9034-68059427a4e6 · outbound

This paper cites Introduction to smooth manifolds.

Symplectic Representation of Legendre Dynamics Introduction to smooth manifolds

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.755317Z

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Observation 7b0158d2-8f93-4a72-ab66-9ca64af1fdfd · outbound

This paper cites Simple Cycle Reservoirs are Universal.

Symplectic Representation of Legendre Dynamics Simple Cycle Reservoirs are Universal

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.757868Z

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Observation 3d57361f-1247-46fe-a84d-f7884c534b0c · outbound

This paper cites Reservoir computing approaches to recurrent neural network training.

Symplectic Representation of Legendre Dynamics Reservoir computing approaches to recurrent neural network training

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.760500Z

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Observation 26e18586-2611-4d0e-9cce-170ac60d13a6 · outbound

This paper cites Real-time computing without stable states: A new framework for neural computation based on perturbations.

Symplectic Representation of Legendre Dynamics Real-time computing without stable states: A new framework for neural computation based on perturbations

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.763035Z

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Observation 01d6a0ac-ba56-4b1f-a4ce-d24fe683cd8c · outbound

This paper cites Stochastic processes and applications.

Symplectic Representation of Legendre Dynamics Stochastic processes and applications

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.765496Z

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Observation f611d4e0-74cb-44ad-90cf-f5a01ddc52af · outbound

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

Symplectic Representation of Legendre Dynamics Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.767962Z

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Observation 1a56b45c-7d6a-417c-8e88-06f69c041397 · outbound

This paper cites Minimum complexity echo state network.

Symplectic Representation of Legendre Dynamics Minimum complexity echo state network

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.770511Z

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Observation b99ceb4a-9ccc-4aef-b291-bc307e3384bf · outbound

This paper cites Bayesian filtering and smoothing , volume 17.

Symplectic Representation of Legendre Dynamics Bayesian filtering and smoothing , volume 17

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.773047Z

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Observation abfe06c8-4893-4b28-8abe-7eb0f1fd1ebc · outbound

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

Symplectic Representation of Legendre Dynamics Predicting the future of discrete sequences from fractal representations of the past

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.775752Z

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Observation 1f95d7ea-46eb-43c5-a4a8-ee313e66b603 · outbound

This paper cites Dynamical systems as temporal feature spaces.

Symplectic Representation of Legendre Dynamics Dynamical systems as temporal feature spaces

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.778611Z

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Observation 638aa0f6-ee47-4290-8e6c-59281f48d650 · outbound

This paper cites Universal Time-Series Representation Learning: A Survey.

Symplectic Representation of Legendre Dynamics Universal Time-Series Representation Learning: A Survey

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.781479Z

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Observation a7ab4038-d19a-42db-ab1f-be022f69dc8c · outbound

This paper cites Recent advances in physical reservoir computing: A review.

Symplectic Representation of Legendre Dynamics Recent advances in physical reservoir computing: A review

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-03T14:48:00.784384Z

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Pith citing papers

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