Paper Citation Record · LEDGER

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions

As of 7 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2512.01558.

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

pith.paper-citation-record.v1
2512.01558 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T19:15:42.926692Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:28:15.612179Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

verified exact0
verified fuzzy0
unresolved33
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f98d4312-53b9-433a-82d2-ba2f6c9a6cc0 · outbound

This paper cites This provides a controlled comparison: identical architecture, identical training protocol, but learning the full signal rather than the correction.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions This provides a controlled comparison: identical architecture, identical training protocol, but learning the full signal rather than the correction

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:39.882499Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7e9e840e-38c0-4464-9141-8bf2d8be81ef · outbound

This paper cites The total parameter count for sequential 2×2×32 corrections (2,372 parameters) is compared against single-stage 3×64 networks (8,578 parameters).

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions The total parameter count for sequential 2×2×32 corrections (2,372 parameters) is compared against single-stage 3×64 networks (8,578 parameters)

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.021504Z

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Observation a9a68e85-860b-46ed-8982-b9bbd21b45ac · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 3

Resolution: malformed identifier; no resolver link, observed 2026-08-03T19:15:40.133460Z

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Observation 599c208c-135d-4b4e-8f70-7ba1cc462716 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.319808Z

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Observation dabb6af4-338c-4a5f-b78b-92c627a02727 · outbound

This paper cites Greydanus, M.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Greydanus, M

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.460540Z

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Observation b9272f4c-8599-4444-9c6c-2b4ba6bc076b · outbound

This paper cites Cranmer, S.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Cranmer, S

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.627560Z

Source-reported events for the cited work

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Observation 7c5c4d65-d90d-4994-8ada-b1c2f99eaf12 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.753304Z

Source-reported events for the cited work

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Observation 07a09352-dc00-4e60-9c3d-4930ce58dc13 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.891087Z

Source-reported events for the cited work

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Observation 9d75043d-48ca-4f5c-acff-c1e1da001875 · outbound

This paper cites Illarionov, S.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Illarionov, S

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:40.963039Z

Source-reported events for the cited work

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Observation 5cafde04-0189-4f18-a0a5-17d0e27a6e92 · outbound

This paper cites Poincar´ e, Acta Mathematica13, 1 (1890).

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Poincar´ e, Acta Mathematica13, 1 (1890)

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.055670Z

Source-reported events for the cited work

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Observation 1867b71b-12ec-415d-94ec-d341313b5192 · outbound

This paper cites Laskar, Nature338, 237 (1989).

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Laskar, Nature338, 237 (1989)

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.126645Z

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Observation bd5d687b-bfea-40b6-8d5c-97d4a4ffc732 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.262505Z

Source-reported events for the cited work

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Observation 985a6400-f33c-4e44-9641-8da012482414 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.333077Z

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Observation c6f89b98-425d-4712-abcb-e6e1c20df5a7 · outbound

This paper cites Sanchez-Gonzalez, J.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Sanchez-Gonzalez, J

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.391799Z

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Observation 3792d0ea-93dc-4571-a676-c524bc7fb397 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.454865Z

Source-reported events for the cited work

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Observation 8b2dca90-ea00-481a-86c6-3f921cbff639 · outbound

This paper cites Batzner, A.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Batzner, A

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.521960Z

Source-reported events for the cited work

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Observation 6003d59b-ed51-4f94-877a-dc838c4d7a68 · outbound

This paper cites Kondor, Proceedings of the National Academy of Sci- ences122(2025), in press.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Kondor, Proceedings of the National Academy of Sci- ences122(2025), in press

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.601502Z

Source-reported events for the cited work

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Observation d2a57f05-1716-4006-972f-ed618f536afe · outbound

This paper cites Raissi, P.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Raissi, P

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.654833Z

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Observation e152406d-4727-4b3c-b888-a94ca96cc873 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.708960Z

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Observation fa96da00-8993-4765-b1e8-2b4c0d8ff9b8 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.772331Z

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Observation d988ddc2-2522-413b-a6f1-91302857affa · outbound

This paper cites Hairer, C.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Hairer, C

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.816498Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 474f4b3c-d4d4-4b9b-ba22-d65e8cd0efd1 · outbound

This paper cites Elfwing, E.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Elfwing, E

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.901549Z

Source-reported events for the cited work

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Observation 1c52dbdf-4783-45e7-b985-8feaa0cf44db · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Adam: A Method for Stochastic Optimization

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:41.984665Z

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Observation 1df14e4b-e7d6-457f-9e45-ab66df873e87 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.055142Z

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Observation dbbcd02f-0c68-484d-aa2a-5cbe4a91e330 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.084453Z

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Observation 015b9e9c-bfc0-416a-8b4d-f07d6643a8ed · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.162015Z

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Observation 121df10b-3951-4df9-9364-37d3cc344adf · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.289745Z

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Observation 0e8fd4ec-67fb-4127-ae8f-83cdf7e74a70 · outbound

This paper cites Reichstein, G.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Reichstein, G

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.366451Z

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Observation 14bf2961-cde0-4269-86fc-a367eeea6c41 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.401070Z

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Observation 81a75bb1-7c18-4a22-bb4b-b82d2c2153f6 · outbound

This paper cites Lecar, F.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Lecar, F

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.517049Z

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Observation def6de19-3f32-4701-9efe-aca79b7f60af · outbound

This paper cites Kevorkian and J.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Kevorkian and J

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.616504Z

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Observation c002deff-1a3e-4421-b252-dfa46dac0e62 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.692953Z

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Observation 056d13de-8971-4aff-b5d0-5a1f14e606a6 · outbound

This paper cites an unresolved cited work.

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.766957Z

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Observation ea21e919-1085-43da-9456-fcc62df29f22 · outbound

This paper cites Talagrand,What Is a Quantum Field Theory?(Cam- bridge University Press, 2022).

Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions Talagrand,What Is a Quantum Field Theory?(Cam- bridge University Press, 2022)

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T19:15:42.926692Z

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Pith citing papers

Observation 41f4a61a-1124-4123-9b29-871bb7e5c91b · inbound

Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics cites this paper.

Dynamical and Optimization Trade-offs of Levi--Civita Coordinates for Learned Close-Encounter Dynamics Neural Network Perturbation Theory (NNPT): Learning Residual Corrections from Exact Solutions

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T10:28:15.612179Z

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