Paper Citation Record · LEDGER

Expansive Natural Neural Gradient Flows for Energy Minimization

As of 9 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 2 inbound Pith citation observations for arXiv:2507.13475.

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

pith.paper-citation-record.v1
2507.13475 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:30:10.046202Z

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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T15:15:06.430599Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T15:23:32.774247Z

Reference resolution

38 of 38 outbound references displayed

verified exact5
verified fuzzy16
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9de8e338-3cdd-4cfb-a19e-bff303f0ad09 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.565837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0f96b530-01c9-403c-a6df-75607b2e4e7a · outbound

This paper cites Ambrosio, N.

Expansive Natural Neural Gradient Flows for Energy Minimization Ambrosio, N

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.558963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 611d780a-04ec-46c1-859b-972bb865d202 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.551835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0c7d431a-0af3-4965-9a0e-f27533a9092d · outbound

This paper cites Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy.

Expansive Natural Neural Gradient Flows for Energy Minimization Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:09.943952Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2bfd01c-444e-4f34-b0c4-394800b20fdc · outbound

This paper cites Barron, A.

Expansive Natural Neural Gradient Flows for Energy Minimization Barron, A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.544816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6be23b3e-dbde-43cd-8188-1426836dbd3d · outbound

This paper cites Bruna, B.

Expansive Natural Neural Gradient Flows for Energy Minimization Bruna, B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.537869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 07273a16-e864-4ca5-a41b-a912576f5a10 · outbound

This paper cites Berman, B.

Expansive Natural Neural Gradient Flows for Energy Minimization Berman, B

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.529998Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f938a8ae-12db-4318-bbdd-98bc62b57f75 · outbound

This paper cites Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs.

Expansive Natural Neural Gradient Flows for Energy Minimization Best approximation results and essential boundary conditions for novel types of weak adversarial network discretizations for PDEs

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:30:10.365337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f226a209-ea86-4bb4-90bd-01b03c7ebbfa · outbound

This paper cites Binev, A.

Expansive Natural Neural Gradient Flows for Energy Minimization Binev, A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.522696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6e10577a-ac35-4bc4-adac-d9efcb6c9d75 · outbound

This paper cites Binev, A.

Expansive Natural Neural Gradient Flows for Energy Minimization Binev, A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.515424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a87f965f-83b2-4ccb-8544-add97cf1c24b · outbound

This paper cites Bao and X.

Expansive Natural Neural Gradient Flows for Energy Minimization Bao and X

Reference 11

Resolution: verified exact; doi, observed 2026-08-06T16:30:10.093398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bc11dfa1-2e8c-4b98-9d64-9735f700ddec · outbound

This paper cites Berrone and C.

Expansive Natural Neural Gradient Flows for Energy Minimization Berrone and C

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:09.976539Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62b09580-0eb7-47ef-b13e-54c118d5373b · outbound

This paper cites Cayci, Gauss-newton dynamics for neural networks: A Riemannian optimization perspective, arXiv:2412.14031v3 [math.OC], December 2024.

Expansive Natural Neural Gradient Flows for Energy Minimization Cayci, Gauss-newton dynamics for neural networks: A Riemannian optimization perspective, arXiv:2412.14031v3 [math.OC], December 2024

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:09.979510Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2fcda47-5200-470b-801d-f1b2f12382bb · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.508001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 37e6fc22-c2e9-4be1-966c-084ec7818b80 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.500982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f14b72ee-2bcc-4c10-a1ed-cd9d4a396a7e · outbound

This paper cites Dahmen, Z.

Expansive Natural Neural Gradient Flows for Energy Minimization Dahmen, Z

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.493719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 84b4cf3e-e4e7-4983-bb36-d5522f048521 · outbound

This paper cites Dahmen, M.

Expansive Natural Neural Gradient Flows for Energy Minimization Dahmen, M

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.485711Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 172a3aba-e6c3-4b41-ad8c-07df224a3e18 · outbound

This paper cites A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations.

Expansive Natural Neural Gradient Flows for Energy Minimization A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:30:10.281241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3a596adc-790d-4c4d-8151-2bb63852b72f · outbound

This paper cites Chen and J.

Expansive Natural Neural Gradient Flows for Energy Minimization Chen and J

Reference 19

Resolution: verified exact; doi, observed 2026-08-06T16:30:10.079745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 591fdb4c-f10b-4100-a56d-a4a00b3cf4e4 · outbound

This paper cites Goodfellow, Y.

Expansive Natural Neural Gradient Flows for Energy Minimization Goodfellow, Y

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.478781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1ded0ac6-e19d-4929-a119-33e493d2d5fd · outbound

This paper cites Goodfellow, J.

Expansive Natural Neural Gradient Flows for Energy Minimization Goodfellow, J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.471124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a4abfee3-29d2-4302-93ae-4d47455954fa · outbound

This paper cites Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics.

Expansive Natural Neural Gradient Flows for Energy Minimization Gauss-Newton Natural Gradient Descent for Physics-Informed Computational Fluid Dynamics

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:10.003701Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bff7fb17-66de-4a32-9505-5be3e22a60db · outbound

This paper cites Jordan, D.

Expansive Natural Neural Gradient Flows for Energy Minimization Jordan, D

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.463458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5b61c6b7-6573-4a59-b1d1-6a87e3989bec · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.456321Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ba081803-6dc3-458f-add1-60ce1d8ac790 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.448792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 36ec8ab8-34af-4901-a90d-0e59ce7025be · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.441813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8751f52c-9dfb-40e0-91f6-0b017f416da7 · outbound

This paper cites Li and G.

Expansive Natural Neural Gradient Flows for Energy Minimization Li and G

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.434629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a388723c-b393-45df-a542-da54d9caca0b · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.427323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 565fc009-0851-4755-ae28-6f0a8d396d71 · outbound

This paper cites Ollivier.

Expansive Natural Neural Gradient Flows for Energy Minimization Ollivier

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.420199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5503de50-fe55-4057-9c0f-05bff5e816a1 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.412150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dde54acd-cfc5-4b1e-87f4-882241f7c2ac · outbound

This paper cites Taylor and D.

Expansive Natural Neural Gradient Flows for Energy Minimization Taylor and D

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:10.026954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74da786d-712f-47fb-aeea-c7ccedbb4dcc · outbound

This paper cites Ruthotto, S.

Expansive Natural Neural Gradient Flows for Energy Minimization Ruthotto, S

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.404613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a3856f87-6d9d-4720-9941-780cf9362f97 · outbound

This paper cites Kovachki, Z.

Expansive Natural Neural Gradient Flows for Energy Minimization Kovachki, Z

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.396632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a2b5242f-78b1-4dc5-8ab7-365830e8aab2 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 34

Resolution: verified exact; doi, observed 2026-08-06T16:30:10.071471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 648ab524-2f12-4ad0-93bb-f648fce62611 · outbound

This paper cites an unresolved cited work.

Expansive Natural Neural Gradient Flows for Energy Minimization Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:30:10.388968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation ddc6307a-6446-4312-9472-ef4a7ade0be0 · outbound

This paper cites Yarotsky, Error bounds for approximations with deep ReLu networks, Neural Networks 94, (2017), 103–114.

Expansive Natural Neural Gradient Flows for Energy Minimization Yarotsky, Error bounds for approximations with deep ReLu networks, Neural Networks 94, (2017), 103–114

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:30:10.381569Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation da4f0365-732b-42f2-a89d-4dbf5529e96d · outbound

This paper cites Monge-Amp\`ere Flow for Generative Modeling.

Expansive Natural Neural Gradient Flows for Energy Minimization Monge-Amp\`ere Flow for Generative Modeling

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T16:30:10.042779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4bb4cd05-318f-4a4f-a1f8-7b6d75153883 · outbound

This paper cites Zang and G.

Expansive Natural Neural Gradient Flows for Energy Minimization Zang and G

Reference 38

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T16:30:10.184018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

Observation 7520571b-db3b-4905-a63b-20373a4874ea · inbound

A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions cites this paper.

A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions Expansive Natural Neural Gradient Flows for Energy Minimization

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:31:14.669902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 514e31f8-48d6-493a-8925-c941deaac5c9 · inbound

Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework cites this paper.

Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework Expansive Natural Neural Gradient Flows for Energy Minimization

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T15:23:32.775663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.