Paper Citation Record · LEDGER

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers

As of 14 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2412.08076.

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

pith.paper-citation-record.v1
2412.08076 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:20:25.130696Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

45 of 45 outbound references displayed

verified exact2
verified fuzzy20
unresolved23
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 56bd2c88-b3b3-4920-b68a-ab3d61e0b5c0 · outbound

This paper cites Quarteroni, A.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Quarteroni, A

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.918890Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd68bf2c-9baa-49e0-bb93-135af92eb3ed · outbound

This paper cites Saad, Iterative methods for sparse linear systems, SIAM, 2003.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Saad, Iterative methods for sparse linear systems, SIAM, 2003

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.924049Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed584d38-c777-495e-a600-5f2053b8fded · outbound

This paper cites Nesterov, Introductory lectures on convex optimization: A basic course, Vol.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Nesterov, Introductory lectures on convex optimization: A basic course, Vol

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.837819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 06d09bd6-5ea7-45f4-af82-3f37d904b8b6 · outbound

This paper cites Nesterov, A method for unconstrained convex minimization problem with the rate of convergence, Doklady AN SSSR 269 (1983) 543–547.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Nesterov, A method for unconstrained convex minimization problem with the rate of convergence, Doklady AN SSSR 269 (1983) 543–547

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.822145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 2c56436e-7571-4cdd-8a88-fb3e03dbfffc · outbound

This paper cites Trottenberg, C.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Trottenberg, C

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.806844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 9771e437-ac43-4076-9c52-23e50574d8b9 · outbound

This paper cites The Barron Space and the Flow-induced Function Spaces for Neural Network Models.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers The Barron Space and the Flow-induced Function Spaces for Neural Network Models

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.942673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7dcfe088-c788-44b0-8edf-4412f0785099 · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.792030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a96150e7-2095-404d-bc32-7bc5199b2add · outbound

This paper cites Raissi, P.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Raissi, P

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.775745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation e008caff-6b07-4267-a5dd-58e54466e59c · outbound

This paper cites Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Yu, et al., The deep ritz method: a deep learning-based numerical algorithm for solving variational problems, Communications in Mathematics and Statistics 6 (1) (2018) 1–12

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.957658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8476f4d-c6b2-4214-a381-d5961c9101c8 · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.962660Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32e72fb3-5806-4341-b2a1-4c2f72da2d64 · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.740534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4183a4e6-54cc-428c-b30d-05d1137482e2 · outbound

This paper cites A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers A Neural Multigrid Solver for Helmholtz Equations with High Wavenumber and Heterogeneous Media

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.972606Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1cc67686-76fe-4bb5-b245-779ac5906b72 · outbound

This paper cites A Deep Conjugate Direction Method for Iteratively Solving Linear Systems.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers A Deep Conjugate Direction Method for Iteratively Solving Linear Systems

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:20:25.334510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c8170476-e30b-4853-80e1-045cdbb0962c · outbound

This paper cites Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:24.983021Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39b08f67-c930-4c8d-9c33-7b1c5ee1bd10 · outbound

This paper cites Katrutsa, T.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Katrutsa, T

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.726525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation c3ee7654-5e5d-4114-8525-7e6ff9fc151d · outbound

This paper cites Huang, R.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Huang, R

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.711799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 5b5d4f53-fe89-4cde-a85b-f64e7e172251 · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.695028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1130522b-380e-4c87-9cb3-d2bdb19b4af0 · outbound

This paper cites Greenfeld, M.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Greenfeld, M

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.678873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation a9ae13e5-db02-43d7-bfd7-e60e2e4ae738 · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.663127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3e66ef50-0d1b-48f7-8472-f54e1f389e3f · outbound

This paper cites DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.015164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c18060ca-bed0-4408-ad7d-29658bf731de · outbound

This paper cites Learning a generalized multiscale prolongation operator.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Learning a generalized multiscale prolongation operator

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.019629Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dca750b6-3a69-4172-84a3-213de826c790 · outbound

This paper cites Taghibakhshi, S.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Taghibakhshi, S

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.646318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ed6689c1-f0d5-49a1-8632-09869b5c92f3 · outbound

This paper cites Caldana, P.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Caldana, P

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.630951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bccb969b-a044-476e-969b-53893a3e622c · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.617195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7ae17515-0afc-4bdb-a783-63385486b817 · outbound

This paper cites Klawonn, M.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Klawonn, M

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.602296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 06039ce3-2872-4202-b606-3ae39a89c561 · outbound

This paper cites Taghibakhshi, N.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Taghibakhshi, N

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.587110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation bb42e930-fe18-4c59-b436-7bcfc2829e6e · outbound

This paper cites Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell's equations with different wave numbers.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell's equations with different wave numbers

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.046871Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2c65f072-2d30-4701-b1f7-fe6cd2ffbd54 · outbound

This paper cites Taghibakhshi, N.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Taghibakhshi, N

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.572675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation eab83064-01b3-454a-9495-badf640ea463 · outbound

This paper cites Zhang, A.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Zhang, A

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.557093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 3ff68967-6eee-4703-bfc3-aa2649d64e1d · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.541788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d4b93827-5b55-4593-a92f-1dc1367f8ec2 · outbound

This paper cites A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers A Hybrid Iterative Neural Solver Based on Spectral Analysis for Parametric PDEs

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-11T18:20:25.244956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation f11f93f5-5df8-466f-8a62-0ce9c0c71dd6 · outbound

This paper cites A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.070567Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69b07d50-74b8-45dd-8990-8cc6f0daa5b5 · outbound

This paper cites MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.075162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42fd9f60-a3dc-44a8-8da3-a01516baa039 · outbound

This paper cites Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Neural operators meet conjugate gradients: The FCG-NO method for efficient PDE solving

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.079898Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cd5c5d3-b198-4d53-9629-55c417c0e5a4 · outbound

This paper cites Rahaman, A.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Rahaman, A

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.527719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 4e9103fb-01e5-48f2-8652-ad1dcb1a5e6d · outbound

This paper cites On the Activation Function Dependence of the Spectral Bias of Neural Networks.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers On the Activation Function Dependence of the Spectral Bias of Neural Networks

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-11T18:20:25.088971Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 691109e5-7c2d-4db2-acce-6d14f01b904a · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.512833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 11cbcc2f-8367-446d-867d-36a1362d64fb · outbound

This paper cites Grimmer, Provably faster gradient descent via long steps, SIAM Journal on Optimization 34 (3) (2024) 2588–2608.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Grimmer, Provably faster gradient descent via long steps, SIAM Journal on Optimization 34 (3) (2024) 2588–2608

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.495838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 744996b5-fb13-40ba-ac41-28a81d8a82ae · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.478558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 0d0c1b89-6cc8-46b7-918b-27b787c145e3 · outbound

This paper cites Axelsson, P.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Axelsson, P

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.459665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 417bac4a-d35d-4bf9-bfa4-1ff5d43c1fa4 · outbound

This paper cites an unresolved cited work.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:20:25.441818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 02828d86-0579-432c-b984-1a545ed9d278 · outbound

This paper cites Adams, M.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Adams, M

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.427667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation aac3f33f-85e4-4ddf-ad9f-febae07538a6 · outbound

This paper cites Qian, On the momentum term in gradient descent learning algorithms, Neural networks 12 (1) (1999) 145–151.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Qian, On the momentum term in gradient descent learning algorithms, Neural networks 12 (1) (1999) 145–151

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.413323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 79e33b61-e8b0-4415-bd42-10fa07264d2c · outbound

This paper cites Botev, G.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Botev, G

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.398713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 1c010169-dd99-42ea-8ef8-8b6293d9f8ae · outbound

This paper cites Treister, E.

Momentum-Accelerated Richardson(m) and Their Multilevel Neural Solvers Treister, E

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:20:25.383125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.