Paper Citation Record · LEDGER

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series

As of 20 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 1 inbound Pith citation observation for arXiv:2412.18515.

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

pith.paper-citation-record.v1
2412.18515 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T04:47:38.438070Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-31T09:10:14.145303Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

verified exact16
verified fuzzy13
unresolved16
parse uncertain0
malformed identifier3
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7201aa1f-668b-460a-b510-6be3a715be54 · outbound

This paper cites On the concept of space in neuroscience.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series On the concept of space in neuroscience

Reference 1

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.595749Z

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Observation e346aecd-98c7-4ec4-a248-050563e7944b · outbound

This paper cites Towards a theoretical foundation for Laplacian-based manifold methods.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Towards a theoretical foundation for Laplacian-based manifold methods

Reference 2

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Observation 8c93aa87-a565-4a5d-a005-846a1b41b9e9 · outbound

This paper cites Density estimation on an unknown submanifold.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Density estimation on an unknown submanifold

Reference 3

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Observation 38cc745b-fe2c-4ab7-af59-a0e190e3386d · outbound

This paper cites Orthogonal Procrustes rotation for two or more matri- ces.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Orthogonal Procrustes rotation for two or more matri- ces

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T04:47:39.303498Z

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Observation 614fcca8-e815-48be-aa8c-b8cb1df4f11a · outbound

This paper cites Graph Approximations to Geodesics on Embedded Manifolds.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Graph Approximations to Geodesics on Embedded Manifolds

Reference 5

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Observation a5ed8dda-5eb0-4d90-9de2-58371ee4d2e6 · outbound

This paper cites A weightedk-nearest neighbor density estimate for geometric inference.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series A weightedk-nearest neighbor density estimate for geometric inference

Reference 6

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.581993Z

Source-reported events for the cited work

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Observation f3d35c2c-6f51-4883-baa4-132f3c70f2c0 · outbound

This paper cites Resampling and averaging coordinates on data.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Resampling and averaging coordinates on data

Reference 7

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Source-reported events for the cited work

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Observation a7538a51-2c07-460a-86e6-6d81b3e05ec6 · outbound

This paper cites The reach, metric distortion, geodesic convexity and the variation of tangent spaces.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series The reach, metric distortion, geodesic convexity and the variation of tangent spaces

Reference 8

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.573241Z

Source-reported events for the cited work

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Observation a1336270-b4c7-4dad-8c98-746de3b5f0e7 · outbound

This paper cites One dimensional approximations of neuronal dynamics reveal computation strategy.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series One dimensional approximations of neuronal dynamics reveal computation strategy

Reference 9

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Source-reported events for the cited work

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Observation 2ccde89e-c28f-495c-8d4a-3ea39fca3035 · outbound

This paper cites A quantitative model of conserved macroscopic dynamics predicts future motor commands.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series A quantitative model of conserved macroscopic dynamics predicts future motor commands

Reference 10

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.564682Z

Source-reported events for the cited work

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Observation 2d31fe72-0ed8-44f2-a56f-10b7f6828967 · outbound

This paper cites Topological methods for data modelling.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Topological methods for data modelling

Reference 11

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Source-reported events for the cited work

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Observation 24e21887-26b5-4752-800f-dc04f52c2fe7 · outbound

This paper cites Geometric in- ference for probability measures.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Geometric in- ference for probability measures

Reference 12

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Source-reported events for the cited work

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Observation becd3a4a-f3fe-4868-9889-2f93722bfd7a · outbound

This paper cites The structure and stability of persistence modules.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series The structure and stability of persistence modules

Reference 13

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Source-reported events for the cited work

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Observation 9e743aa5-1a5e-42b4-9ccb-cb5d23095e1d · outbound

This paper cites Adaptive, locally linear models of complex dynamics.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Adaptive, locally linear models of complex dynamics

Reference 14

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.552183Z

Source-reported events for the cited work

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Observation 83c7ad6f-df03-420e-a085-76bbfa890223 · outbound

This paper cites A Course in Density Estimation.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series A Course in Density Estimation

Reference 15

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Observation 1ff503f9-95a0-4209-bc63-6b27cb216160 · outbound

This paper cites Computational topology: an introduc- tion.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Computational topology: an introduc- tion

Reference 16

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Source-reported events for the cited work

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Observation 26655d8e-54f5-4430-b935-c771058ec3ae · outbound

This paper cites Unsupervised learn- ing of control signals and their encodings in Caenorhabditis elegans whole- brain recordings.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Unsupervised learn- ing of control signals and their encodings in Caenorhabditis elegans whole- brain recordings

Reference 17

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Source-reported events for the cited work

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Observation 0c31dabc-f75f-4282-adeb-5ced15a30653 · outbound

This paper cites Discriminatory Analysis. Nonparametric Dis- crimination: Consistency Properties.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Discriminatory Analysis. Nonparametric Dis- crimination: Consistency Properties

Reference 18

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Source-reported events for the cited work

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Observation 1eabecc5-b74d-41ac-b3a3-41effd097e37 · outbound

This paper cites Toroidal topology of population activity in grid cells.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Toroidal topology of population activity in grid cells

Reference 19

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Observation 156e5465-0896-4093-9ec5-25b3c095dcd9 · outbound

This paper cites Barcodes: The persistent topology of data.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Barcodes: The persistent topology of data

Reference 20

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Observation 611ba793-c426-4fd2-97cc-2a4dba58215a · outbound

This paper cites A Family of Density-Scaled Filtered Complexes.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series A Family of Density-Scaled Filtered Complexes

Reference 21

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Source-reported events for the cited work

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Observation 4f850c0d-1314-4477-8e4f-f92864578532 · outbound

This paper cites Global Brain Dynamics Embed the Motor Command Sequence of Caenorhabditis elegans.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Global Brain Dynamics Embed the Motor Command Sequence of Caenorhabditis elegans

Reference 22

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.540471Z

Source-reported events for the cited work

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Observation 63da22fc-cb3c-40b4-9173-228ed9b25da5 · outbound

This paper cites Estimating mutual information.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Estimating mutual information

Reference 23

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Observation 3dd97a12-9072-4e3b-9420-3dcb948bed39 · outbound

This paper cites Studying the Shape of Data Using Topology.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Studying the Shape of Data Using Topology

Reference 24

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Observation 00aaecb4-4e9c-45ea-b628-fb5ad15f3275 · outbound

This paper cites Hierarchical recurrent state space models reveal discrete and con- tinuous dynamics of neural activity in C. elegans.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Hierarchical recurrent state space models reveal discrete and con- tinuous dynamics of neural activity in C. elegans

Reference 25

Resolution: verified exact; doi, observed 2026-08-11T04:47:38.531813Z

Source-reported events for the cited work

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Observation 73ac8455-26e0-4b3b-9d70-1467b940fe04 · outbound

This paper cites A Nonparametric Estimate of a Multivariate Density Function.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series A Nonparametric Estimate of a Multivariate Density Function

Reference 26

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Observation ebd49631-ebfe-495d-a1a3-27174574aeea · outbound

This paper cites Zigzag persis- tent homology in matrix multiplication time.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Zigzag persis- tent homology in matrix multiplication time

Reference 27

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Source-reported events for the cited work

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Observation bfd650ec-3152-4f3e-87de-c37e81e4c3b8 · outbound

This paper cites Persistent (Co)Homology in Matrix Multiplication Time.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Persistent (Co)Homology in Matrix Multiplication Time

Reference 28

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Observation b791dbb4-ff0f-4e35-81cf-cb9f2159fbf9 · outbound

This paper cites Nonlinear Control in the Nematode C. elegans.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Nonlinear Control in the Nematode C. elegans

Reference 29

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Observation 8052a1b8-d4c5-4977-be17-e9312f36a685 · outbound

This paper cites Accurate estimation of the normalized mutual information of multidimensional data.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Accurate estimation of the normalized mutual information of multidimensional data

Reference 30

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Observation 9c0563a6-293c-43e1-8f93-8a04bbeacdda · outbound

This paper cites Distributed Computation of Persistent Cohomology.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Distributed Computation of Persistent Cohomology

Reference 31

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Observation ac84447f-cf88-4152-9860-0170ac06b1dc · outbound

This paper cites Persistence theory: from quiver representations to data analysis.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Persistence theory: from quiver representations to data analysis

Reference 32

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Observation 82084a2e-e4d2-4910-adf3-230b4ff9a733 · outbound

This paper cites Circular Coordinates for Density-Robust Analysis.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Circular Coordinates for Density-Robust Analysis

Reference 33

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Observation b2c12bf6-6239-4c1b-92e5-0bb4457c51d9 · outbound

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series On Estimation of a Probability Density Function and Mode

Reference 34

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Observation 528a23be-7fa1-4725-b4f4-bd1a75528557 · outbound

This paper cites Multiscale Projective Coordinates via Persistent Cohomol- ogy of Sparse Filtrations.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Multiscale Projective Coordinates via Persistent Cohomol- ogy of Sparse Filtrations

Reference 35

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This paper cites Sparse Circular Coordinates via Principal Z-Bundles.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Sparse Circular Coordinates via Principal Z-Bundles

Reference 36

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Blumberg

Reference 37

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This paper cites Remarks on Some Nonparametric Estimates of a Desnity Function.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Remarks on Some Nonparametric Estimates of a Desnity Function

Reference 38

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This paper cites Decoding of Neural Data Using Cohomological Feature Extraction.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Decoding of Neural Data Using Cohomological Feature Extraction

Reference 39

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This paper cites Spherical coordinates from persistent cohomology.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Spherical coordinates from persistent cohomology

Reference 40

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Unresolved cited work

Reference 41

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This paper cites Persistent Cohomology of Circular Coordinates.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Persistent Cohomology of Circular Coordinates

Reference 42

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This paper cites From Geometry to Topology: Inverse Theorems for Distributed Persistence.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series From Geometry to Topology: Inverse Theorems for Distributed Persistence

Reference 43

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Detecting strange attractors in turbulence

Reference 44

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Cohomological learning of periodic motion

Reference 45

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This paper cites NeuroPAL: A Multicolor Atlas for Whole-Brain Neuronal Identification in C. elegans.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series NeuroPAL: A Multicolor Atlas for Whole-Brain Neuronal Identification in C. elegans

Reference 46

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This paper cites Revealing neural dynamical struc- ture of C. elegans with deep learning.

Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Revealing neural dynamical struc- ture of C. elegans with deep learning

Reference 47

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Unresolved cited work

Reference 837

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Subsampling, aligning, and averaging to find circular coordinates in recurrent time series Unresolved cited work

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Pith citing papers

Observation af573574-ba39-42c6-9222-011235260bde · inbound

Density-Robust Spherical Coordinates from Persistent Cohomology cites this paper.

Density-Robust Spherical Coordinates from Persistent Cohomology Subsampling, aligning, and averaging to find circular coordinates in recurrent time series

Reference 4

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