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Paper Citation Record · LEDGER

A Mathematical Explanation of Transformers

As of 6 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 3 inbound Pith citation observations for arXiv:2510.03989.

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

pith.paper-citation-record.v1
2510.03989 v2

Coverage vector

measured 65 of 65 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-18T10:10:32.692581Z

measured 68 of 68 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T01:25:52.665357Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-06-30T17:14:57.079865Z

Reference resolution

65 of 65 outbound references displayed

  • verified exact12
  • verified fuzzy31
  • unresolved22
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 19dc7265-4698-40ea-9a81-737e41a3b4fd · outbound

This paper cites Layer Normalization.

A Mathematical Explanation of Transformers Layer Normalization

Reference 1

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 6529469f-7410-4c19-a573-71ea38405860 · outbound

This paper cites Benning, E.

A Mathematical Explanation of Transformers Benning, E

Reference 2

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation f8d193d4-3cc8-42d9-b6ea-b62719ea0ee7 · outbound

This paper cites Bryutkin, J.

A Mathematical Explanation of Transformers Bryutkin, J

Reference 3

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 1b445e97-e6b8-49d8-9b2a-ac475c867d37 · outbound

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A Mathematical Explanation of Transformers Unresolved cited work

Reference 4

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 0b46bec2-2027-4c42-b872-7baf0b666ac3 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 5

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 0428c010-f7aa-43c7-b568-7ed72623e1f3 · outbound

This paper cites Cheng, J.

A Mathematical Explanation of Transformers Cheng, J

Reference 6

Resolution
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arxiv_id, observed 2026-05-18T10:11:13.748993Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 56103c6c-4fb5-491f-ab34-2cb2e88fbcbe · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 7

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 147ecd25-090a-4c93-b153-51b4dcf11834 · outbound

This paper cites Dosovitskiy, L.

A Mathematical Explanation of Transformers Dosovitskiy, L

Reference 8

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 8d6fd979-5bff-4465-a162-689f09954438 · outbound

This paper cites Dutta, T.

A Mathematical Explanation of Transformers Dutta, T

Reference 9

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 0835f6f9-cd6f-4519-9c93-aac76bfc3386 · outbound

This paper cites Transformers are Universal In-context Learners.

A Mathematical Explanation of Transformers Transformers are Universal In-context Learners

Reference 10

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arxiv_id, observed 2026-05-18T10:11:13.753014Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation b1b0e0c6-7824-40b4-9351-ea8bcb8cbefa · outbound

This paper cites A mathematical perspective on Transformers.

A Mathematical Explanation of Transformers A mathematical perspective on Transformers

Reference 11

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Observation f2bd92ba-cab5-4c93-b138-bbffae550542 · outbound

This paper cites Glowinski and P.

A Mathematical Explanation of Transformers Glowinski and P

Reference 12

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation a9a83cfd-758a-46ea-a0e6-303f1d46c22e · outbound

This paper cites Glowinski, S.

A Mathematical Explanation of Transformers Glowinski, S

Reference 13

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation e27613a6-1175-4d85-9e87-6fa54df062d5 · outbound

This paper cites Glowinski, T.-W.

A Mathematical Explanation of Transformers Glowinski, T.-W

Reference 14

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 01e5745c-7596-4a5e-ab44-f1b77fbd5a6c · outbound

This paper cites Graves, A.-r.

A Mathematical Explanation of Transformers Graves, A.-r

Reference 15

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 201ec9fa-ad69-45ec-b391-eb40c2915343 · outbound

This paper cites Gregor and Y.

A Mathematical Explanation of Transformers Gregor and Y

Reference 16

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 8f12e32d-2c1c-45bc-a144-e27c7709247e · outbound

This paper cites Haber, L.

A Mathematical Explanation of Transformers Haber, L

Reference 17

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 69375b66-f08a-4cad-8239-3f570c19edee · outbound

This paper cites Hagemann, J.

A Mathematical Explanation of Transformers Hagemann, J

Reference 18

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 361aa13e-1a6f-4b59-8b15-7456bf883a11 · outbound

This paper cites Havrilla and W.

A Mathematical Explanation of Transformers Havrilla and W

Reference 19

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation d88dc355-4792-460a-8b87-c35ead697298 · outbound

This paper cites Mgnet: Aunifiedframeworkofmultigridandconvolutionalneuralnetwork.

A Mathematical Explanation of Transformers Mgnet: Aunifiedframeworkofmultigridandconvolutionalneuralnetwork

Reference 20

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 0b205dd2-3ddd-4f22-8347-ca7f2408fee5 · outbound

This paper cites Jelassi, M.

A Mathematical Explanation of Transformers Jelassi, M

Reference 21

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation dbe750c2-cb13-4e4c-8b46-8ab29a059c3f · outbound

This paper cites Jiang, Y.

A Mathematical Explanation of Transformers Jiang, Y

Reference 22

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation f2fbf548-2cc2-40cc-94da-e784b7a47454 · outbound

This paper cites Krizhevsky, I.

A Mathematical Explanation of Transformers Krizhevsky, I

Reference 23

Resolution
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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation afab02ad-efe8-46ac-a57f-73e3fe6cac0c · outbound

This paper cites Attention is a smoothed cubic spline.

A Mathematical Explanation of Transformers Attention is a smoothed cubic spline

Reference 24

Resolution
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arxiv_id, observed 2026-05-18T10:11:13.766867Z

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Observation 5a114d6b-cd31-474a-8db0-077006967377 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 25

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 29a06aa3-6cfa-4bd1-b81b-785b40bf7243 · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

A Mathematical Explanation of Transformers Fourier Neural Operator for Parametric Partial Differential Equations

Reference 26

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Observation 9269da19-f018-47f4-a332-2ccad64267ea · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 27

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 638981d1-836c-4cea-a53e-7257a2b21813 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 28

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 7e78ae75-54b3-42e1-a40a-a44100f0299c · outbound

This paper cites Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation.

A Mathematical Explanation of Transformers Convex Shape Prior for Deep Neural Convolution Network based Eye Fundus Images Segmentation

Reference 29

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arxiv_id, observed 2026-05-18T10:11:13.757253Z

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Observation 30ce50c7-6ebe-4088-8031-5f6152ca22a5 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 30

Resolution
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raw_fallback, observed 2026-05-18T10:11:14.825018Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 5d708bcc-f62f-48e6-bcdd-26f20aaba230 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 31

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation a4b73140-e70b-4876-86b1-65c3af396818 · outbound

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A Mathematical Explanation of Transformers Unresolved cited work

Reference 32

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raw_fallback, observed 2026-05-18T10:11:14.840184Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 7632e106-63a6-4682-bd60-3e8c18f0778e · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 33

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 22161c44-74a8-4da2-91c1-cc863aa5192b · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 34

Resolution
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raw_fallback, observed 2026-05-18T10:11:14.718838Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 64078488-af22-4ab0-bc65-e86784f53aeb · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 35

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation 9951cae4-daf8-4abf-b3a2-ade229a88805 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 36

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raw_fallback, observed 2026-05-18T10:11:14.808494Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation ffbe0164-bf1c-4a19-8a88-212ca62efdb0 · outbound

This paper cites PnP-Flow: Plug-and-Play Image Restoration with Flow Matching.

A Mathematical Explanation of Transformers PnP-Flow: Plug-and-Play Image Restoration with Flow Matching

Reference 37

Resolution
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arxiv_id, observed 2026-05-18T10:11:13.776220Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

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Observation a99aaad1-dbf9-4ada-b61b-15dfb86d6c01 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 38

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raw_fallback, observed 2026-05-18T10:11:14.811792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:6d2b7eefd5bef7d3549efc3413a8681ba7271b6ec55202dfa0b52747c778efa8

Observation 6281ad43-350d-4f5f-8495-5fe3a6ae11a9 · outbound

This paper cites Miotto, F.

A Mathematical Explanation of Transformers Miotto, F

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.819990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:fce98bdde17e7f98e277f4b991e777f66ea73a18cec8dda819b5bd5068bd8312

Observation 67fbd88a-e234-4719-87a2-959e049078b0 · outbound

This paper cites Raissi, P.

A Mathematical Explanation of Transformers Raissi, P

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.732820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:4fc9e31a45c457be7bc794e173437bc946e45344be1b3e20dd61e1ceebe17a44

Observation fd2b367d-b837-4829-976a-b59856383bef · outbound

This paper cites Ronneberger, P.

A Mathematical Explanation of Transformers Ronneberger, P

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.799433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:4954264389976b5b33b7a507eb1e4ee32020601cbb9dc7a905345b95ba0ef1bc

Observation fa3c8eb8-38c1-4c15-9f63-4a0520e3eb63 · outbound

This paper cites Ruiz-Balet and E.

A Mathematical Explanation of Transformers Ruiz-Balet and E

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.802446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:8da22c9cf6cadcf4e9857e42182cd75af1117b8fd7cd37235c8a05ad554abf07

Observation 00257d06-32bc-4740-b0c8-07d139bbaaf0 · outbound

This paper cites Ruthotto and E.

A Mathematical Explanation of Transformers Ruthotto and E

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.793214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:7198223620731799176e1eb64f23037a6ab4e43bed7a56819905385bc8175b9d

Observation 17554625-5df4-4ec2-b118-0a6a46609f5a · outbound

This paper cites Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights.

A Mathematical Explanation of Transformers Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights

Reference 44

Resolution
verified exact
arxiv_id, observed 2026-05-20T00:02:49.976542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:5f10b297f081d699270e95e0bc2c2519d1a62eb5a927584ec9c01bba2fe853dd

Observation cbea65cf-63d8-45e7-b523-fd1ea2ba1416 · outbound

This paper cites Strudel, R.

A Mathematical Explanation of Transformers Strudel, R

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.790661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:3ecfb9d143e4883bf446bd11654c3365031e0412f76875c5837b2049a913b167

Observation 739b008c-36ff-4f36-b1a1-cd01fb627b7e · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 46

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.796526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:47d4803b3284bb42dc1df5f5e0c3cec050b0b52f61963139a6ad7a25b7baa1c1

Observation 63395770-3896-4a34-9454-31195958db89 · outbound

This paper cites Tai, H.Liu, R.

A Mathematical Explanation of Transformers Tai, H.Liu, R

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.805389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:01c4f36900ca7101a665117e1e88dd6470950945a85e9746717db3dc15d066d0

Observation 3ab210a7-3b80-4d80-9277-97758412e64e · outbound

This paper cites Takakura and T.

A Mathematical Explanation of Transformers Takakura and T

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.822362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:c9e478e99d983a79b6e6b42ac7b542d3000989fad233629acf8b77d672e95cad

Observation d0006589-0cd3-4c7e-9421-bd68476d6cbc · outbound

This paper cites , month = feb, year =.

A Mathematical Explanation of Transformers , month = feb, year =

Reference 49

Resolution
verified exact
arxiv_id, observed 2026-05-18T10:11:13.739427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:9da805971e46cd8092d58e7e8026966133bf472c4dd7baa11250c0f242b092d8

Observation 96bcada9-6c8b-4e29-8ab5-dad746472488 · outbound

This paper cites Vaswani, N.

A Mathematical Explanation of Transformers Vaswani, N

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.776311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:48a6d84f83b1dcd3d975e959c7305b0b5a36ebdc468fc1d942eb2262f236d787

Observation b9b5a133-af6e-42da-8dca-a0ce0a3bd823 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.770075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:9a2b0e86b480ad4ddd90a39111e72e87f329c3a096daae76ddcd5929b94f4ae6

Observation fcec7646-e35b-451d-9dc9-1970e79fcb8d · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.787975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:1f4f5dc3f15b2e21443b00aa51bc4c92e69fa622e5d728125cd2f47dc5a45047

Observation 83a14114-13f9-4325-b3db-891be95bf213 · outbound

This paper cites Weinan, C.

A Mathematical Explanation of Transformers Weinan, C

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.767451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:97aa3f88bd9d13f2b5d55fb791bc5827924d5d81aa957c1a3e33043b5718c840

Observation c470c3c8-99c1-4af2-9686-5631cf5c4538 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 54

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.773039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:7bcf490f5782ce0ed88afc7efeece08f85641ed9b1777065cea31cd7a31ff0fa

Observation f790415e-0566-4a8c-a45b-07895916c873 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 55

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.779330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:49f440e964d89c4c73eafa920153b9ffa80b007e9bef753284ae89fb90cf73d5

Observation fe2f5afa-781a-481e-be02-6f8f18455f91 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 56

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.760875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:e9cda7257763f09f7e21a700d70473ea1edfd7f54c8800cee6fd940e6a9afb53

Observation 98ff5674-d3b9-49b7-abc1-0e300b807f4d · outbound

This paper cites Yarotsky.

A Mathematical Explanation of Transformers Yarotsky

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.764258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:599b97b1784f508ff10b965891a1213f507202ca9b5f261e28ad5e9fad49d8a2

Observation f4b3bff0-767b-4962-842f-8a37344a156a · outbound

This paper cites PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations.

A Mathematical Explanation of Transformers PDEformer: Towards a Foundation Model for One-Dimensional Partial Differential Equations

Reference 58

Resolution
verified exact
arxiv_id, observed 2026-05-18T10:11:13.790596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:013d5823fd43f6af414ef3cf28425742f625d916a4f5e544d69d2d7f3dd8da0a

Observation 95362abf-46da-46e2-a75e-d2f5d3359422 · outbound

This paper cites Young, D.

A Mathematical Explanation of Transformers Young, D

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.743447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:9e39cbb1002ac2625dc615f96afa1fcaa424c072db3c7824486d7ef5fb65b7f1

Observation 8b74ab77-e6b2-4aae-9111-62131a2a9223 · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 60

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.754203Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:e46f8f8cec43607b501914d00afd72a0137d6ee1bfdb8f5a3aa2bb946b14a036

Observation bdc328e5-f3a2-47bf-b92f-7c2b0c7ae70d · outbound

This paper cites Zhang and R.

A Mathematical Explanation of Transformers Zhang and R

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.708096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:b211cbce9455800d4c2c4a46b86f80fd10966c7c8053ff2594989e339b0c590c

Observation cf0cbf72-975d-4aee-a594-a6ce32da1078 · outbound

This paper cites Zhang, L.

A Mathematical Explanation of Transformers Zhang, L

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.724040Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:2fd80dcad10e15e72f0c30997c993eaeec3fe11401ba936213e3849c6454afb1

Observation 4af8ddc5-5c12-4c89-9448-f94ae190db5c · outbound

This paper cites an unresolved cited work.

A Mathematical Explanation of Transformers Unresolved cited work

Reference 63

Resolution
unresolved
raw_fallback, observed 2026-05-18T10:11:14.711526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:e6ebb3bc87a44e7d52667491b45528c896bd61edb1e6fee8a7abb9bd38bde5f4

Observation bdca079b-b28c-4221-ac8d-1504cb4751ad · outbound

This paper cites Transformers without Normalization.

A Mathematical Explanation of Transformers Transformers without Normalization

Reference 64

Resolution
verified exact
arxiv_id, observed 2026-05-18T10:11:13.780648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:d46caa5cdac668642c8950dedea7b84ecae1dd5d1aba703179e6b2123bfb2825

Observation dd5f0e80-150f-4a39-bdf9-ca541dacb181 · outbound

This paper cites Ziaee and E.

A Mathematical Explanation of Transformers Ziaee and E

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-05-18T10:11:14.698572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=pdf_text observed=2026-05-18T10:10:32.692581Z digest=sha256:083254aa8404d597a632526c83f4e05063bef3cf7092a5f36c591f1b4f26597a

Pith citing papers

Observation c1a7acba-0964-4dde-ab06-34e19fd125ca · inbound

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations cites this paper.

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations A Mathematical Explanation of Transformers

Reference 173

Resolution
verified exact
local_arxiv, observed 2026-05-22T07:31:14.016780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=arxiv_source observed=2026-05-22T07:28:49.152516Z digest=sha256:868b18e9fd9b07b84e8a3f844e72db4f0563483eefd25ffe0642d9c5550b588f

Observation c7b981ee-1787-443a-8bc0-577406d00893 · inbound

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations cites this paper.

Neural Flow Operators can Approximate any Operator: Abstract Frameworks and Universal Approximations A Mathematical Explanation of Transformers

Reference 77

Resolution
verified exact
local_arxiv, observed 2026-06-30T17:14:57.081354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

source=arxiv_source observed=2026-06-30T17:08:54.066574Z digest=sha256:60f50acfdb643f734d61ee103a87fbc2f0e047d99fa5763633f1664f75cfa09c

Observation d8f3b32e-d745-40a8-a67d-b3ccc66b2aa0 · inbound

VideoSEMA: a scalable and efficient Mamba-like attention for video understanding cites this paper.

VideoSEMA: a scalable and efficient Mamba-like attention for video understanding A Mathematical Explanation of Transformers

Reference 22

Resolution
unresolved
no resolver link, observed 2026-08-02T01:25:52.665357Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T01:25:52.665357Z digest=sha256:f4d552d0fa26992e8ac223ffbc14fb80f0f9e36a64d4f777b3f8d3710dd5867b