Paper Citation Record · LEDGER

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System

As of 10 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2607.04993.

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

pith.paper-citation-record.v1
2607.04993 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T10:24:00.719150Z

measured 40 of 40 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.

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

40 of 40 outbound references displayed

verified exact0
verified fuzzy0
unresolved40
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1939fd6f-e6c9-4add-abe6-e5e589e3d1cb · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Unavailable: canonical work link unavailable.

Observation bc0975d9-d6cf-48eb-8cc4-7e5cea345189 · outbound

This paper cites and Whitley, David C.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System and Whitley, David C

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation d7915b95-b9bf-4a25-9941-2a07257c3ce9 · outbound

This paper cites International Conference on Learning Representations , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System International Conference on Learning Representations , year =

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 3836a7e4-b560-4479-87ba-9d7c095973f6 · outbound

This paper cites International Conference on Learning Representations , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System International Conference on Learning Representations , year =

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation f493191e-a531-4397-a888-f4114f4ffc61 · outbound

This paper cites International Conference on Learning Representations , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System International Conference on Learning Representations , year =

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 78ff5971-2196-4865-bc41-ae66854cfd0f · outbound

This paper cites From Stability to Chaos: Analyzing Gradient Descent Dynamics in Quadratic Regression.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System From Stability to Chaos: Analyzing Gradient Descent Dynamics in Quadratic Regression

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 2b7e6772-604c-468a-986b-b9a42367096e · outbound

This paper cites Journal of the Fisheries Research Board of Canada , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Journal of the Fisheries Research Board of Canada , volume =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 4e95604d-cd9d-4dcf-b4b8-4e91a0834c95 · outbound

This paper cites International Conference on Learning Representations , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System International Conference on Learning Representations , year =

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 8ed05444-e79c-417c-b07c-cc62055f153e · outbound

This paper cites The large learning rate phase of deep learning: the catapult mechanism.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System The large learning rate phase of deep learning: the catapult mechanism

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation df27c82f-7ade-425e-a0ef-0778f9f5fc0c · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 8dc59758-6114-4fce-aa30-68ad20163612 · outbound

This paper cites Experimental Mathematics , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Experimental Mathematics , volume =

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation b318f876-828c-424c-9e09-80588b524265 · outbound

This paper cites Proceedings of the 40th International Conference on Machine Learning (ICML) , series =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Proceedings of the 40th International Conference on Machine Learning (ICML) , series =

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation dd44d595-effd-46bf-865b-d094f6a5add1 · outbound

This paper cites The Twelfth International Conference on Learning Representations , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System The Twelfth International Conference on Learning Representations , year =

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation c5984571-ac88-4dab-ae78-75381588aa58 · outbound

This paper cites an unresolved cited work.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 7e654c6e-049b-4a6e-8c09-25c389077f81 · outbound

This paper cites Communications in Mathematical Physics , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Communications in Mathematical Physics , volume =

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation ab0722b7-9a6e-44b6-8173-0330bb09557e · outbound

This paper cites Absolutely continuous measures for certain maps of an interval , journal =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Absolutely continuous measures for certain maps of an interval , journal =

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 601d5cb6-0acb-4dc3-8f5a-b2d9769cf6c2 · outbound

This paper cites Annals of Mathematics , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Annals of Mathematics , volume =

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation a8c12b14-4583-4afe-b35a-3573b1736848 · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 45b7d9f9-a95e-47b9-90d2-43f8b09551d2 · outbound

This paper cites Journal de Physique Colloques , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Journal de Physique Colloques , volume =

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 098d28fe-133f-4b19-9347-6c99b8ec2365 · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 4d6fed78-5919-4b44-9e35-89dd947f9a4e · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

Source-reported events for the cited work

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Observation ca309a15-1861-4cc4-9aeb-a73ef3a72897 · outbound

This paper cites Annals of Mathematics , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Annals of Mathematics , volume =

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 7e540345-2980-404d-95d6-fa36af160e41 · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 1c870442-dc3c-4457-9981-6ee2ee8cfc75 · outbound

This paper cites SIAM Journal on Applied Mathematics , volume =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System SIAM Journal on Applied Mathematics , volume =

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 0adafefa-f671-45f1-bd7b-1b72c61888f7 · outbound

This paper cites Proceedings of the 42nd International Conference on Machine Learning , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Proceedings of the 42nd International Conference on Machine Learning , year =

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation a9b97f95-e20d-45a4-8492-2ac3f0536bbf · outbound

This paper cites Discourse on the Method , publisher =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Discourse on the Method , publisher =

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 680d410c-7aaf-4ea0-a865-94c256c6759f · outbound

This paper cites Proceedings of the 40th International Conference on Machine Learning , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Proceedings of the 40th International Conference on Machine Learning , year =

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 2437dbd6-60a2-46ec-80b9-d486f2fdcfb1 · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 1762c4aa-e730-42aa-a3cc-e387d8771b4c · outbound

This paper cites Advances in Neural Information Processing Systems , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Advances in Neural Information Processing Systems , year =

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 836f5e9f-7b6e-48be-bd24-23f3fae9fcf1 · outbound

This paper cites Proceedings of the 39th International Conference on Machine Learning , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Proceedings of the 39th International Conference on Machine Learning , year =

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 37448de2-ba3c-4c37-bf7f-7663bab6acdc · outbound

This paper cites International Conference on Learning Representations , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System International Conference on Learning Representations , year =

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 0d86bea7-8ba7-47d5-bc4e-1812733c835a · outbound

This paper cites Proceedings of the 40th International Conference on Machine Learning , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Proceedings of the 40th International Conference on Machine Learning , year =

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 11c0a225-06a6-428e-8211-6120a1530ecd · outbound

This paper cites and Hu, Wei and Lee, Jason D.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System and Hu, Wei and Lee, Jason D

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation dd4d3c71-7aa9-4d6d-920a-19842e0b52d0 · outbound

This paper cites Proceedings of the 35th International Conference on Machine Learning , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Proceedings of the 35th International Conference on Machine Learning , year =

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation a46fb03b-2fe2-4d9b-8330-43dda949c452 · outbound

This paper cites Conference on Learning Theory , year =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Conference on Learning Theory , year =

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 67c78ab8-ad1b-45d7-b5d1-2671afda8d64 · outbound

This paper cites , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System , title =

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation ecd4e1df-4393-4682-bdea-6493f132ac72 · outbound

This paper cites and Nauenberg, Michael and Rudnick, Joseph , title =.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System and Nauenberg, Michael and Rudnick, Joseph , title =

Reference 37

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation a78c6933-138e-4d37-a103-c99f47d19bb8 · outbound

This paper cites Eugene and Martin, Paul C.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Eugene and Martin, Paul C

Reference 38

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 7428a34f-4b0e-4694-9dce-baadea88429d · outbound

This paper cites High dimensional analysis reveals conservative sharpening and a stochastic edge of stability.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System High dimensional analysis reveals conservative sharpening and a stochastic edge of stability

Reference 39

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Observation 8fc7cb80-1a3c-44a9-b455-23815fc39d53 · outbound

This paper cites Dying ReLU and Initialization: Theory and Numerical Examples.

The Map Behind the Flow: Finite-Step Gradient Descent as a Dynamical System Dying ReLU and Initialization: Theory and Numerical Examples

Reference 40

Resolution: unresolved; no resolver link, observed 2026-07-11T10:24:00.719150Z

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Pith citing papers

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