Paper Citation Record · LEDGER

On the Expressive Power of Transformers

As of 19 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2608.12671.

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

pith.paper-citation-record.v1
2608.12671 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T04:59:08.755912Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

31 of 31 outbound references displayed

verified exact1
verified fuzzy10
unresolved19
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b4467b81-443f-48c4-9438-1248161ab257 · outbound

This paper cites A Survey of Neural Networks and Formal Languages.

On the Expressive Power of Transformers A Survey of Neural Networks and Formal Languages

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.602715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4303779e-d1b0-427f-a7ee-302052ae6b9d · outbound

This paper cites Barceló, A.

On the Expressive Power of Transformers Barceló, A

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.258140Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 84686f62-b342-498b-8094-3dbf5f870edd · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:09.226622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9344c54f-290e-4850-ae52-1a13cd88b17d · outbound

This paper cites Onthecomputationalpoweroftransformersanditsimplications in sequence modeling.

On the Expressive Power of Transformers Onthecomputationalpoweroftransformersanditsimplications in sequence modeling

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.627086Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e93bdbc9-39ad-40e1-8348-ad3a6093752d · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:09.210531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f33b03ce-e121-43d9-a6f1-21483cdecb18 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:09.195454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6c1c3398-ab91-4863-84d6-56b9de942c59 · outbound

This paper cites Chiang, P.

On the Expressive Power of Transformers Chiang, P

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.176810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f8d40d2c-7972-49e2-9457-64aa55a410a9 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.645346Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation deabfeef-6055-42f6-8b34-fe7796a3652d · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.650146Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9216f393-35b6-4396-89d6-4006e0612b55 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.655500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22a37721-c967-4190-af24-0a576a4f3a52 · outbound

This paper cites Holtzman, J.

On the Expressive Power of Transformers Holtzman, J

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.162162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4492951f-a9b9-4276-8897-968e2dfc592c · outbound

This paper cites Immerman.Descriptive complexity.

On the Expressive Power of Transformers Immerman.Descriptive complexity

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.664108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5326e42-5b66-48d2-9ae6-39257abd1413 · outbound

This paper cites Jiang, M.

On the Expressive Power of Transformers Jiang, M

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.144261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 918449d8-ced4-4177-bd3d-3ea915e10893 · outbound

This paper cites Chainofthoughtempowerstransformerstosolveinherentlyserialprob- lems.

On the Expressive Power of Transformers Chainofthoughtempowerstransformerstosolveinherentlyserialprob- lems

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.121750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cdb51c1c-7bb0-4efe-a718-62e455717386 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:09.099213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 56bf0fee-25dd-48a4-8321-2c4c5a2743de · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.684918Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c93abc8-2933-4385-ae94-dd5e0acc3873 · outbound

This paper cites Merrill and A.

On the Expressive Power of Transformers Merrill and A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.080020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1e4d479d-ed4b-4b19-a79a-6e1fcfe43f0c · outbound

This paper cites Merrill and A.

On the Expressive Power of Transformers Merrill and A

Reference 18

Resolution: malformed identifier; no resolver link, observed 2026-08-16T04:59:08.693531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e07c08a5-a0f4-4b23-9279-a058556360f2 · outbound

This paper cites Merrill and A.

On the Expressive Power of Transformers Merrill and A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.058814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f3ad4d9e-0ceb-4651-92d9-601addfcfb59 · outbound

This paper cites Merrill, V.

On the Expressive Power of Transformers Merrill, V

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.042620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation aaa45d9f-718e-4e9e-8c28-77108bfe0a18 · outbound

This paper cites Merrill, A.

On the Expressive Power of Transformers Merrill, A

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.716661Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5b985dc-fc97-42b8-82ff-c2e37c8e619e · outbound

This paper cites Pérez, P.

On the Expressive Power of Transformers Pérez, P

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.029782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8501953e-93e9-4601-9291-50304863def7 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:09.015925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 063311ae-b30d-4602-acb3-c3dea78e7710 · outbound

This paper cites Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits.

On the Expressive Power of Transformers Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.731627Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02ac472a-e882-44e4-90e7-2530d6cedb42 · outbound

This paper cites Strobl, W.

On the Expressive Power of Transformers Strobl, W

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.735575Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b495c01-7bbb-49e9-a958-2007578eeb47 · outbound

This paper cites Vaswani, N.

On the Expressive Power of Transformers Vaswani, N

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:59:09.001111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation deeef5e7-d5c6-495b-a227-e82b72d14d05 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:08.988023Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c222fe58-3dbf-48e4-8758-da8a8f34af55 · outbound

This paper cites Simulating Hard Attention Using Soft Attention.

On the Expressive Power of Transformers Simulating Hard Attention Using Soft Attention

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-16T04:59:08.932893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 89c82a57-569a-4016-99ca-262395f971a5 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:08.974810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e070a6d7-e517-402b-b944-b263f05a97de · outbound

This paper cites doi: 10.18653/v1/2021.emnlp-main.133.

On the Expressive Power of Transformers doi: 10.18653/v1/2021.emnlp-main.133

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-16T04:59:08.712135Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 718a4ccb-6f76-4aea-831f-4cc2d7a4c054 · outbound

This paper cites an unresolved cited work.

On the Expressive Power of Transformers Unresolved cited work

Reference 2024

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:59:09.243094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.