Paper Citation Record · LEDGER

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems

As of 20 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 2 inbound Pith citation observations for arXiv:2505.07363.

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

pith.paper-citation-record.v1
2505.07363 v3

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T22:24:58.822869Z

measured 26 of 26 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:59:58.733800Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-22T06:34:40.970558Z

Reference resolution

24 of 24 outbound references displayed

verified exact0
verified fuzzy10
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 338c0356-7487-47e9-b6c6-c9d9a1976a04 · outbound

This paper cites an unresolved cited work.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-15T22:24:59.263753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 495f69fe-4141-4c0f-bf64-75efd5e4c278 · outbound

This paper cites The momentum is defined by pi(x, ˙x,t ) = ∂L(x, ˙x,t ) ∂ ˙xi.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems The momentum is defined by pi(x, ˙x,t ) = ∂L(x, ˙x,t ) ∂ ˙xi

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.248248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 733ad0f1-bde5-482d-9fb9-1910bcf1416c · outbound

This paper cites an unresolved cited work.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T22:24:59.233891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9512b18a-54d2-4ed4-aebb-5dd979c3a27d · outbound

This paper cites Nakajima and I.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Nakajima and I

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.730315Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 931b62b2-6379-4d98-aa43-071e48ff7a60 · outbound

This paper cites an unresolved cited work.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.735526Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86164ed2-336c-44d6-bb47-7b1bb177aa5a · outbound

This paper cites Weinan, A proposal on machine learning via dynamical systems, Communications in Mathematics and Statistics 5, 1 (2017).

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Weinan, A proposal on machine learning via dynamical systems, Communications in Mathematics and Statistics 5, 1 (2017)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.209649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e9ec5722-7247-47b0-bf7a-ff6fe27a802d · outbound

This paper cites Ruiz-Balet and E.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Ruiz-Balet and E

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.744981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0280863-eefa-438c-8859-e2b51f0d8314 · outbound

This paper cites Hermans, M.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Hermans, M

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.195172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 2ea22125-cdb7-4122-923f-fe81778a9ccc · outbound

This paper cites L´ opez-Pastor and F.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems L´ opez-Pastor and F

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.180505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 170324e0-22f6-49fe-b6c0-e74641ea270e · outbound

This paper cites Scellier and Y.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Scellier and Y

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.758913Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f8df864-de83-451a-8175-303f4f714de8 · outbound

This paper cites A deep learning theory for neural networks grounded in physics.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems A deep learning theory for neural networks grounded in physics

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.763362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05e94eed-4573-454a-98aa-669c7e45ea0e · outbound

This paper cites Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.768029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3adf84b7-1137-44aa-a713-f036a446a23c · outbound

This paper cites Equilibrium Propagation for Dissipative Dynamics.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Equilibrium Propagation for Dissipative Dynamics

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.773189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c2c65a3-41c6-4580-8847-4dcdbe0e1986 · outbound

This paper cites Massar and B.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Massar and B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.155412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d40cf6c1-0707-4ebf-88fc-94aa5389a6e6 · outbound

This paper cites Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Quantum Equilibrium Propagation: Gradient-Descent Training of Quantum Systems

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.782085Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 709e66b6-80ae-49c4-b4f4-9ecef203298e · outbound

This paper cites Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Quantum Equilibrium Propagation for efficient training of quantum systems based on Onsager reciprocity

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.786722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07707467-5f0f-4d90-98eb-da2a4f03ee15 · outbound

This paper cites Laborieux, M.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Laborieux, M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.140246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e77656b9-0fc8-471a-9604-7cb1341e0f17 · outbound

This paper cites Generalization of Equilibrium Propagation to Vector Field Dynamics.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Generalization of Equilibrium Propagation to Vector Field Dynamics

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.795519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef043e41-294f-432e-934c-ab3b1f068ce0 · outbound

This paper cites Equilibrium Propagation with Continual Weight Updates.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Equilibrium Propagation with Continual Weight Updates

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T22:24:58.800572Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2259c450-cc80-4825-ae26-5518384210d2 · outbound

This paper cites Martin, M.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Martin, M

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.124001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9bdb5693-9ea8-4d49-a355-8c731dd61e9c · outbound

This paper cites Laborieux and F.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Laborieux and F

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.107890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c789097f-2d7c-492c-9a2c-f968aa5c7b8c · outbound

This paper cites Scellier, M.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Scellier, M

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.092262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation fd63dc82-1813-4692-a87b-64b51f4414e1 · outbound

This paper cites an unresolved cited work.

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T22:24:59.075890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8418f607-fda8-4133-afc8-28c895d03f00 · outbound

This paper cites Riewe, Nonconservative lagrangian and hamiltonian mechanics, Physical Review E 53, 1890 (1996).

Equilibrium Propagation for Learning in Lagrangian Dynamical Systems Riewe, Nonconservative lagrangian and hamiltonian mechanics, Physical Review E 53, 1890 (1996)

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T22:24:59.059442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 41e5f171-bbd6-4fc1-ba41-920a99369c7a · inbound

Equilibrium Propagation for Dissipative Dynamics cites this paper.

Equilibrium Propagation for Dissipative Dynamics Equilibrium Propagation for Learning in Lagrangian Dynamical Systems

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T22:59:58.733800Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57c80f67-d2d4-4085-bdbb-8d85e8449c0e · inbound

Efficient Agentic Reasoning Through Self-Regulated Simulative Planning cites this paper.

Efficient Agentic Reasoning Through Self-Regulated Simulative Planning Equilibrium Propagation for Learning in Lagrangian Dynamical Systems

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-22T06:34:40.972621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.