Paper Citation Record · LEDGER

Neural Preconditioning via Krylov Subspace Geometry

As of 9 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2507.15452.

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

pith.paper-citation-record.v1
2507.15452 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:40:06.587257Z

measured 25 of 25 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

25 of 25 outbound references displayed

verified exact0
verified fuzzy19
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8319e4e3-e9cf-48ac-9943-67647c753fd1 · outbound

This paper cites application to tissue perfusion problems.

Neural Preconditioning via Krylov Subspace Geometry application to tissue perfusion problems

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.808551Z

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 68d9daab-bfde-499a-99c7-8a98fb341110 · outbound

This paper cites an unresolved cited work.

Neural Preconditioning via Krylov Subspace Geometry Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:40:06.801156Z

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 c03a3379-f99a-4e9e-9386-72456e010ab0 · outbound

This paper cites SIAM Journal on Numerical Analysis 59(1), 558–582 (2021).

Neural Preconditioning via Krylov Subspace Geometry SIAM Journal on Numerical Analysis 59(1), 558–582 (2021)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.793851Z

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 3df6f3ed-795e-427c-9fb4-f708103db6d7 · outbound

This paper cites Mathematical Models and Methods in Applied Sciences 33(12), 2425–2462 (2023).

Neural Preconditioning via Krylov Subspace Geometry Mathematical Models and Methods in Applied Sciences 33(12), 2425–2462 (2023)

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.786413Z

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 58c97b85-952d-4b35-835c-08de217193cb · outbound

This paper cites Applied Mathematics.

Neural Preconditioning via Krylov Subspace Geometry Applied Mathematics

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.778709Z

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 6e413fd5-d5fd-422f-9efc-094d593904a7 · outbound

This paper cites Numerical Linear Algebra with Applications 18(1), 1–40 (2011).

Neural Preconditioning via Krylov Subspace Geometry Numerical Linear Algebra with Applications 18(1), 1–40 (2011)

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.771257Z

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 34582ead-111b-41f8-9eeb-8ce0ca1e47c8 · outbound

This paper cites an unresolved cited work.

Neural Preconditioning via Krylov Subspace Geometry Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:40:06.763912Z

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 68c88171-4b22-47e4-8282-dcbe5152cc5e · outbound

This paper cites Elsevier, Amsterdam, The Netherlands (2000).

Neural Preconditioning via Krylov Subspace Geometry Elsevier, Amsterdam, The Netherlands (2000)

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.755781Z

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 8924bae7-9ad9-40dd-bce5-9496c65496b6 · outbound

This paper cites Oxford University Press, Oxford, UK (1999).

Neural Preconditioning via Krylov Subspace Geometry Oxford University Press, Oxford, UK (1999)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.747410Z

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 5e8784da-b8c8-4bfb-bde0-20528d1505f8 · outbound

This paper cites SIAM Journal on Scientific Computing 38(6), 962–987 (2016).

Neural Preconditioning via Krylov Subspace Geometry SIAM Journal on Scientific Computing 38(6), 962–987 (2016)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.738757Z

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 3ebd3db7-caf0-4903-97a2-8c4d93f6073b · outbound

This paper cites SIAM Journal on Scientific Computing 46(3), 1461–1486 (2024) 22.

Neural Preconditioning via Krylov Subspace Geometry SIAM Journal on Scientific Computing 46(3), 1461–1486 (2024) 22

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.730280Z

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 bc3e3c95-3ea2-45c2-9ce4-70da82eb6e60 · outbound

This paper cites Computer Methods in Applied Mechanics and Engineering 431, 117256 (2024).

Neural Preconditioning via Krylov Subspace Geometry Computer Methods in Applied Mechanics and Engineering 431, 117256 (2024)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.722023Z

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 5ece6ea9-1987-4745-ac30-dfe9df28e3e5 · outbound

This paper cites SIAM Journal on Scientific Computing 45(3), 127–151 (2023).

Neural Preconditioning via Krylov Subspace Geometry SIAM Journal on Scientific Computing 45(3), 127–151 (2023)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.712675Z

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 05da9e44-e045-4e6e-90ce-28a16e6954ca · outbound

This paper cites SIAM Journal on Scientific Computing 47(1), 151–181 (2025).

Neural Preconditioning via Krylov Subspace Geometry SIAM Journal on Scientific Computing 47(1), 151–181 (2025)

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T15:40:06.558491Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67d29e4c-4ecb-4c11-b75e-6dd6de57e739 · outbound

This paper cites Nature Machine Intelligence 3, 218–229 (2021).

Neural Preconditioning via Krylov Subspace Geometry Nature Machine Intelligence 3, 218–229 (2021)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.700219Z

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 b255d5c0-0dec-4875-bcbd-fa6f754f825a · outbound

This paper cites Communications on Applied Mathematics and Computation, 1–38 (2024).

Neural Preconditioning via Krylov Subspace Geometry Communications on Applied Mathematics and Computation, 1–38 (2024)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.692763Z

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 4c4dae05-fea4-4874-af7f-491fdba2d29a · outbound

This paper cites Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner.

Neural Preconditioning via Krylov Subspace Geometry Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T15:40:06.566254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 888804d2-fd0e-4bb4-9d57-34e726d2c3a3 · outbound

This paper cites A Unified Framework for U-Net Design and Analysis.

Neural Preconditioning via Krylov Subspace Geometry A Unified Framework for U-Net Design and Analysis

Reference 18

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T15:40:06.628091Z

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 fa49b704-fd2c-4aaa-b2dc-c0ff98175c46 · outbound

This paper cites arXiv e-prints, 1502 (2015).

Neural Preconditioning via Krylov Subspace Geometry arXiv e-prints, 1502 (2015)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.684002Z

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 256460b1-4d4c-4757-ba04-39c48bb87cb1 · outbound

This paper cites SIAM Journal on Scientific Computing 14(2), 461–469 (1993).

Neural Preconditioning via Krylov Subspace Geometry SIAM Journal on Scientific Computing 14(2), 461–469 (1993)

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.675697Z

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 343d9082-ffbc-4f77-ad3a-49d38b838950 · outbound

This paper cites ESAIM: Mathematical Modelling and Numerical Analysis 53(6), 2047–2080 (2019).

Neural Preconditioning via Krylov Subspace Geometry ESAIM: Mathematical Modelling and Numerical Analysis 53(6), 2047–2080 (2019)

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.667771Z

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 ed04aa51-2417-4c49-aa0a-16a9b08c552d · outbound

This paper cites Acta Numerica 10, 251–312 (2001).

Neural Preconditioning via Krylov Subspace Geometry Acta Numerica 10, 251–312 (2001)

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.660295Z

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 2d921174-a838-4f3e-bb8c-b93cc5f8a23e · outbound

This paper cites PyTorch: An Imperative Style, High-Performance Deep Learning Library.

Neural Preconditioning via Krylov Subspace Geometry PyTorch: An Imperative Style, High-Performance Deep Learning Library

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T15:40:06.582330Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35833f9c-1d93-4d26-9666-e1f90d1ac4e5 · outbound

This paper cites Journal of Scientific Computing 97(35) (2023) 23.

Neural Preconditioning via Krylov Subspace Geometry Journal of Scientific Computing 97(35) (2023) 23

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.652655Z

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 5d6a3f3a-b684-4796-9d3a-ff3c04630351 · outbound

This paper cites arXiv (2018) 24.

Neural Preconditioning via Krylov Subspace Geometry arXiv (2018) 24

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:40:06.645240Z

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

No inbound Pith citation observations are available.