Paper Citation Record · LEDGER

Data-driven inference of Hopf normal form representations from oscillatory time series

As of 20 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2606.26847.

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

pith.paper-citation-record.v1
2606.26847 v1

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T01:50:41.758200Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-12T12:10:09.266586Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

59 of 59 outbound references displayed

verified exact1
verified fuzzy0
unresolved58
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External citation measurements

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Outbound references

Observation 26ec0733-693c-4cad-bedc-1efc5d1c9c52 · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 2dc25a31-4e10-47d0-a92f-eb07e0859c2a · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 2

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Observation beed158e-fce5-4441-b97a-7885aebd144c · outbound

This paper cites The remainder of this article is organized as follows.

Data-driven inference of Hopf normal form representations from oscillatory time series The remainder of this article is organized as follows

Reference 3

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Observation 1538f667-6d0b-4845-a9e8-9e989cd03def · outbound

This paper cites Our goal 4 is to computep(x t |y 1:t,Θ) fromp(x t−1|y1:t−1,Θ).

Data-driven inference of Hopf normal form representations from oscillatory time series Our goal 4 is to computep(x t |y 1:t,Θ) fromp(x t−1|y1:t−1,Θ)

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 4237c2bd-bfc7-4a46-b5d3-026b0e794675 · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation b8def41a-ba9d-4bc7-a070-7b2ba504060f · outbound

This paper cites Given the esti- mated parameters ˆΘ, the latent states{µ s t }for each time series are inferred by forward–backward smoothing (see Subsection III B for details).

Data-driven inference of Hopf normal form representations from oscillatory time series Given the esti- mated parameters ˆΘ, the latent states{µ s t }for each time series are inferred by forward–backward smoothing (see Subsection III B for details)

Reference 6

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Observation 2a958444-3484-4f76-94b5-14bd7567e365 · outbound

This paper cites The resulting estimated limit-cycle orbit is subsequently used in (21) and (22) to estimate the PSF and ASF, respectively.

Data-driven inference of Hopf normal form representations from oscillatory time series The resulting estimated limit-cycle orbit is subsequently used in (21) and (22) to estimate the PSF and ASF, respectively

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 2101409f-d617-4051-b38f-deab9a8af611 · outbound

This paper cites First, a moving average with window width 0.07 is applied to reduce observation noise.

Data-driven inference of Hopf normal form representations from oscillatory time series First, a moving average with window width 0.07 is applied to reduce observation noise

Reference 8

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Observation ab04ae77-ad2c-44af-9966-504af87f2a2a · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 9

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Observation 3f8ebe9e-2475-4821-bf98-90d9948f83e8 · outbound

This paper cites To compute the mean and covariance of the filtering density (11), we approximate the joint densityp(x t,y t | y1:t−1,Θ) =p(y t |x t,Θ)p(x t |y 1:t−1,Θ) by a Gaussian.

Data-driven inference of Hopf normal form representations from oscillatory time series To compute the mean and covariance of the filtering density (11), we approximate the joint densityp(x t,y t | y1:t−1,Θ) =p(y t |x t,Θ)p(x t |y 1:t−1,Θ) by a Gaussian

Reference 10

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Observation e3b8a507-2870-46d2-8def-3fb277fce909 · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation bb0fe18c-5139-43d7-a6d4-c92c6a3dbeed · outbound

This paper cites Buzsaki and A.

Data-driven inference of Hopf normal form representations from oscillatory time series Buzsaki and A

Reference 12

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Observation c7f208e7-a3a5-4ef7-ada6-4e620f7129fb · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 13

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Observation c6d4187e-7833-4d06-a5c9-5c615763e9eb · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 14

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Observation dbaafe80-880f-4d62-b94d-94690dd7cabc · outbound

This paper cites Sch¨ afer, M.

Data-driven inference of Hopf normal form representations from oscillatory time series Sch¨ afer, M

Reference 15

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Observation 3f1aed92-8792-479c-97a6-84e1c6aab255 · outbound

This paper cites Kralemann, M.

Data-driven inference of Hopf normal form representations from oscillatory time series Kralemann, M

Reference 16

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Observation 9b904076-9926-46bc-aa42-7eb205f02032 · outbound

This paper cites Kobayashi, H.

Data-driven inference of Hopf normal form representations from oscillatory time series Kobayashi, H

Reference 17

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Observation 61c853ad-a73a-4d14-abf4-499ab8ef1ba3 · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 18

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Observation 14cd028f-1707-49d9-a7e4-41415a4670f4 · outbound

This paper cites Kiehn, Locomotor circuits in the mammalian spinal cord, Annu.

Data-driven inference of Hopf normal form representations from oscillatory time series Kiehn, Locomotor circuits in the mammalian spinal cord, Annu

Reference 19

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Observation ba218da2-6047-48d3-9b96-bc8cc39af6ce · outbound

This paper cites Funato, Y.

Data-driven inference of Hopf normal form representations from oscillatory time series Funato, Y

Reference 20

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Observation 1371ac6c-1bd6-4dbb-98ce-8e09f8d703fd · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 21

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Observation 761894cd-2f11-4344-b4b1-ca6eb18d697c · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 22

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Observation 24d48a0d-6560-4c50-b9df-ee82647bf4f2 · outbound

This paper cites Guckenheimer and P.

Data-driven inference of Hopf normal form representations from oscillatory time series Guckenheimer and P

Reference 23

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Observation c042a54f-4139-4c87-a38a-099c5ae6a915 · outbound

This paper cites Wiggins,Introduction to Applied Nonlinear Dynamical Systems and Chaos(Springer, New York, 2003).

Data-driven inference of Hopf normal form representations from oscillatory time series Wiggins,Introduction to Applied Nonlinear Dynamical Systems and Chaos(Springer, New York, 2003)

Reference 24

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Observation 91a3a752-cadc-4109-9e0c-88c302a9c1e9 · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation b2e67ffd-b9ca-434a-b9d8-8b9289dda150 · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 5de82121-58fe-4a6f-91c3-1884e36505e1 · outbound

This paper cites Wilson, Data-driven model identification near a super- critical Hopf bifurcation using phase-based approaches, Physica D476, 134635 (2025).

Data-driven inference of Hopf normal form representations from oscillatory time series Wilson, Data-driven model identification near a super- critical Hopf bifurcation using phase-based approaches, Physica D476, 134635 (2025)

Reference 27

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Observation 4ce5a5c6-d8b6-411b-ab0a-90dac8ba7114 · outbound

This paper cites Durbin and S.

Data-driven inference of Hopf normal form representations from oscillatory time series Durbin and S

Reference 28

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Observation 837149e9-d1e1-4dfb-b687-978d0ceedc5c · outbound

This paper cites Kitagawa,Introduction to Time Series Modeling (Chapman and Hall/CRC, Boca Raton, FL , USA, 2010).

Data-driven inference of Hopf normal form representations from oscillatory time series Kitagawa,Introduction to Time Series Modeling (Chapman and Hall/CRC, Boca Raton, FL , USA, 2010)

Reference 29

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Observation 81e80a2c-f25e-4562-825d-b14db21bfd58 · outbound

This paper cites Kuramoto,Chemical Oscillations, Waves and Turbu- lence(Springer, Berlin, 1984).

Data-driven inference of Hopf normal form representations from oscillatory time series Kuramoto,Chemical Oscillations, Waves and Turbu- lence(Springer, Berlin, 1984)

Reference 30

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Observation dd4b94da-f140-4605-86d1-9c8b910f46e3 · outbound

This paper cites Nakao, Phase reduction approach to synchronisation of nonlinear oscillators, Contemporary Physics57, 188 (2016).

Data-driven inference of Hopf normal form representations from oscillatory time series Nakao, Phase reduction approach to synchronisation of nonlinear oscillators, Contemporary Physics57, 188 (2016)

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 86f54977-8a0d-4717-9d5e-b6fea7c91483 · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 32

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Observation 6a2760d4-f9b4-4fa3-8994-674cf88f8c25 · outbound

This paper cites Shirasaka, W.

Data-driven inference of Hopf normal form representations from oscillatory time series Shirasaka, W

Reference 33

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Observation 618552d1-a9dd-4a4b-a28d-3ece75d5dd99 · outbound

This paper cites Shirasaka, W.

Data-driven inference of Hopf normal form representations from oscillatory time series Shirasaka, W

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation bb37cce4-054e-40be-9ea3-8db60d56dc8f · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 35

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Observation 2e124e50-6a2d-48b6-9392-31725e0b0e2e · outbound

This paper cites Turner, M.

Data-driven inference of Hopf normal form representations from oscillatory time series Turner, M

Reference 36

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Observation f77f44f1-65e9-45b8-a099-d8f5977242b5 · outbound

This paper cites Donner, A.

Data-driven inference of Hopf normal form representations from oscillatory time series Donner, A

Reference 37

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Observation 98b3b23d-f673-42e3-834c-08884f141cdb · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 38

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Observation 9f2d0959-7b4d-40b7-bfd3-c92d85819bd9 · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation cecc5865-8b55-4db0-a8a2-8dee6c2922ce · outbound

This paper cites Boloix-Tortosa, J.

Data-driven inference of Hopf normal form representations from oscillatory time series Boloix-Tortosa, J

Reference 40

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Observation 3169f9a1-3dbd-4daf-b0ae-606d928eac4f · outbound

This paper cites Namura, S.

Data-driven inference of Hopf normal form representations from oscillatory time series Namura, S

Reference 41

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Observation be07989b-b34c-449c-bd6d-728f071ff2e9 · outbound

This paper cites Yamamoto, H.

Data-driven inference of Hopf normal form representations from oscillatory time series Yamamoto, H

Reference 42

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Observation 85363b24-4ee1-4c71-84ed-a5dc4cca1e73 · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation ffd553e6-7cd6-462d-a8b7-90fd79f7c337 · outbound

This paper cites Takata, Y.

Data-driven inference of Hopf normal form representations from oscillatory time series Takata, Y

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 893d54ef-08b5-4499-b9c9-d20e1324edf4 · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 45

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Observation 92f05c21-0cc4-40b0-86a6-8e85a2cbb177 · outbound

This paper cites Wilson, A direct method approach for data-driven in- ference of high accuracy adaptive phase-isostable reduced order models, Physica D446, 133675 (2023).

Data-driven inference of Hopf normal form representations from oscillatory time series Wilson, A direct method approach for data-driven in- ference of high accuracy adaptive phase-isostable reduced order models, Physica D446, 133675 (2023)

Reference 46

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Observation a140a217-a2e3-42eb-8b3d-c326425831ae · outbound

This paper cites an unresolved cited work.

Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 5b0f40a4-8d80-44b9-88d0-5b0407f38997 · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 48

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Observation 28cf1dd8-9f82-4e8c-8903-ea7a89e1fc9c · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 49

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Observation 923c6d43-9316-452e-a056-4ad5c6dfc6d3 · outbound

This paper cites Yawata, K.

Data-driven inference of Hopf normal form representations from oscillatory time series Yawata, K

Reference 50

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Observation 800430f7-695c-4549-aa5f-97d79cea1fd0 · outbound

This paper cites Wilson, A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems, Chaos30, 013121 (2020).

Data-driven inference of Hopf normal form representations from oscillatory time series Wilson, A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems, Chaos30, 013121 (2020)

Reference 51

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation cca983c4-1580-4c5c-b005-77530325a87c · outbound

This paper cites Wilson, Data-driven inference of high-accuracy isostable-based dynamical models in response to exter- nal inputs, Chaos31, 063137 (2021).

Data-driven inference of Hopf normal form representations from oscillatory time series Wilson, Data-driven inference of high-accuracy isostable-based dynamical models in response to exter- nal inputs, Chaos31, 063137 (2021)

Reference 52

Resolution: unresolved; no resolver link, observed 2026-06-26T01:50:41.758200Z

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Observation 1a5a6942-1271-4484-894c-3e789d2609f0 · outbound

This paper cites Tanaka, S.

Data-driven inference of Hopf normal form representations from oscillatory time series Tanaka, S

Reference 53

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Observation 14e3dea6-c448-494a-8f6b-9ff402a97368 · outbound

This paper cites Araya, H.

Data-driven inference of Hopf normal form representations from oscillatory time series Araya, H

Reference 54

Resolution: verified exact; arxiv_id, observed 2026-07-04T15:09:55.373606Z

Source-reported events for the cited work

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Observation 9aa2cc6d-39ae-47c6-8988-6d3870450abc · outbound

This paper cites Roweis and Z.

Data-driven inference of Hopf normal form representations from oscillatory time series Roweis and Z

Reference 55

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Observation bd342439-3379-4f57-9f6e-0e0c73b30ae6 · outbound

This paper cites Qui˜ nonero-Candela and C.

Data-driven inference of Hopf normal form representations from oscillatory time series Qui˜ nonero-Candela and C

Reference 56

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Observation 34514b89-fc03-4669-8e3c-ec87355bab5c · outbound

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Data-driven inference of Hopf normal form representations from oscillatory time series Unresolved cited work

Reference 57

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Observation 55e016ea-7aaa-4ceb-8218-a08842a6ed0d · outbound

This paper cites Solin and S.

Data-driven inference of Hopf normal form representations from oscillatory time series Solin and S

Reference 58

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Observation 3ee77a6a-48b4-4515-aea8-75bb8f47179d · outbound

This paper cites S¨ arkk¨ a, A.

Data-driven inference of Hopf normal form representations from oscillatory time series S¨ arkk¨ a, A

Reference 59

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Pith citing papers

Observation 3933abaf-4cd2-48e3-b360-dfe9d572efce · inbound

An Isochron-Free Framework for Phase Reduction and Coupling Inference cites this paper.

An Isochron-Free Framework for Phase Reduction and Coupling Inference Data-driven inference of Hopf normal form representations from oscillatory time series

Reference 11

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