Paper Citation Record · LEDGER

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity

As of 9 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 1 inbound Pith citation observation for arXiv:2507.22570.

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

pith.paper-citation-record.v1
2507.22570 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T11:43:56.925203Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T15:57:59.386340Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

22 of 22 outbound references displayed

verified exact0
verified fuzzy12
unresolved10
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 121a9c44-6b87-45d5-9f95-21841417fe17 · outbound

This paper cites Bouchon , Monotonicity of some perturbations of irreducibly diagonally dominant m- matrices, Numer.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Bouchon , Monotonicity of some perturbations of irreducibly diagonally dominant m- matrices, Numer

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:59.420839Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 678dda18-6362-471c-98b1-87539af49c8a · outbound

This paper cites an unresolved cited work.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:43:59.259309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 7bde67b1-9b05-4cf5-ab78-970ef130d598 · outbound

This paper cites Brandts, S.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Brandts, S

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:59.105722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 75b86a12-bd29-4eeb-a54a-a2836e5f056c · outbound

This paper cites Breiman, J.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Breiman, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:58.993759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b9601665-4178-49c3-86fb-3ea0b670846d · outbound

This paper cites Buzzard, Mathematical reasoning and the computer, Bulletin of the American Mathemat- ical Society, 61 (2024), pp.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Buzzard, Mathematical reasoning and the computer, Bulletin of the American Mathemat- ical Society, 61 (2024), pp

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:58.892645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0a7173a7-3b03-479a-8175-94826998f17d · outbound

This paper cites Linear algebra with transformers.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Linear algebra with transformers

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T11:43:55.637806Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8637ce37-e09f-4a50-9c22-e4f43cd967f7 · outbound

This paper cites an unresolved cited work.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:43:58.779848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e66298d1-b602-4a3e-9c32-63ed98549eb5 · outbound

This paper cites an unresolved cited work.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:43:58.613316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f8e6f8fb-1543-4222-8ad3-8b7e52c62ee0 · outbound

This paper cites Coles, An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statis- tics, Springer, London, 2001, https://doi.org/10.1007/978-1-4471-3675-0.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Coles, An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statis- tics, Springer, London, 2001, https://doi.org/10.1007/978-1-4471-3675-0

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T11:43:55.876316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 055b6a9d-a724-4c31-b62d-097539f95281 · outbound

This paper cites Collatz, Aufgaben monotone art , Arch.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Collatz, Aufgaben monotone art , Arch

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:58.493503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ae7ff13a-6e0b-4c31-85bc-7b22c6f371b4 · outbound

This paper cites Cortes and V.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Cortes and V

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:58.342912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1070be31-b5b4-4683-ad6b-cc9f9c1e10d9 · outbound

This paper cites Cranmer, A.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Cranmer, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:58.206784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 38f203b6-2943-47ae-9222-69453a59fb7c · outbound

This paper cites Davies, P.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Davies, P

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T11:43:56.208111Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ae01385-1d4f-4064-9e36-0514d6a88fd2 · outbound

This paper cites Dwivedi, D.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Dwivedi, D

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T11:43:56.269855Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5054a19c-287d-4c30-9b8c-dc78280910a4 · outbound

This paper cites Lattice-Valued Bottleneck Duality.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Lattice-Valued Bottleneck Duality

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T11:43:56.360665Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38f0f5c4-39c4-42a4-96cd-347a655356cb · outbound

This paper cites Kar´atson and S.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Kar´atson and S

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:58.074262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 53b1befd-ed0b-4598-bb60-3b6a768950e9 · outbound

This paper cites Lorenz, Zur inversmonotonie diskreter probleme , Numer.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Lorenz, Zur inversmonotonie diskreter probleme , Numer

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:57.896449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 082c6c26-7ba0-4688-afea-76395954322d · outbound

This paper cites an unresolved cited work.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:43:57.726124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 350e09f5-9fb7-4825-aac9-2daa52e459f0 · outbound

This paper cites Novikov, N.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Novikov, N

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:57.531534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 04828cc6-9e4e-4008-b9e3-e00ff5ebbfab · outbound

This paper cites Sundararajan, A.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Sundararajan, A

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:57.393442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5bebe065-f47d-4837-84db-5278f7321fff · outbound

This paper cites V arga, Matrix Iterative Analysis , Prentice-Hall, New Jersey, 1962.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity V arga, Matrix Iterative Analysis , Prentice-Hall, New Jersey, 1962

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:43:57.178892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 999db711-e158-4b4c-8313-a2921d0c7d2c · outbound

This paper cites Is deep learning a useful tool for the pure mathematician?.

Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity Is deep learning a useful tool for the pure mathematician?

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T11:43:56.925203Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation a9e17120-be8e-453a-b961-6768c28830a5 · inbound

Totally Positive Matrices and the Highest-Order Coefficients of the Characteristic Polynomial cites this paper.

Totally Positive Matrices and the Highest-Order Coefficients of the Characteristic Polynomial Explaining Deep Network Classification of Matrices: A Case Study on Monotonicity

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T15:57:59.386340Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.