Paper Citation Record · LEDGER

Lower bounds on transformers with infinite precision

As of 11 August 2026, this Paper Citation Record lists 7 of 7 outbound references and 2 inbound Pith citation observations for arXiv:2412.20195.

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

pith.paper-citation-record.v1
2412.20195 v1

Coverage vector

measured 7 of 7 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:36:27.138978Z

measured 9 of 9 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-09T12:23:57.818820Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-08T00:18:21.788685Z

Reference resolution

7 of 7 outbound references displayed

verified exact0
verified fuzzy4
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 06a43d3d-120e-4623-b936-d5482f1ad17c · outbound

This paper cites Separations in the Representational Capabilities of Transformers and Recurrent Architectures.

Lower bounds on transformers with infinite precision Separations in the Representational Capabilities of Transformers and Recurrent Architectures

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T23:36:27.113480Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20fcc26d-e5b9-4c05-9573-cc7ab0ef6084 · outbound

This paper cites Theoretical limitations of multi-layer Transformer.

Lower bounds on transformers with infinite precision Theoretical limitations of multi-layer Transformer

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T23:36:27.117603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35dbf6b6-ccb5-4818-aec3-ce2b828f553d · outbound

This paper cites W., and Jerrum, M.

Lower bounds on transformers with infinite precision W., and Jerrum, M

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:36:27.247403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 264bfb7b-026f-4a51-b7ae-cadb5a09595d · outbound

This paper cites Theoretical limitations of self-attention in neural sequence mod- els.

Lower bounds on transformers with infinite precision Theoretical limitations of self-attention in neural sequence mod- els

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:36:27.234895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 61d35e0b-08a5-420f-a983-eb83f8f3c1ff · outbound

This paper cites Formal language recognition by hard attention transformers: Perspectives from circuit complex ity.

Lower bounds on transformers with infinite precision Formal language recognition by hard attention transformers: Perspectives from circuit complex ity

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:36:27.222305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 60b583dd-080c-4a1c-961f-6f7264960dc7 · outbound

This paper cites On Limitations of the Transformer Architecture.

Lower bounds on transformers with infinite precision On Limitations of the Transformer Architecture

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T23:36:27.133870Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9e025174-bffb-46a6-93ae-4599eb81e8df · outbound

This paper cites J., and Telgarsky, M.

Lower bounds on transformers with infinite precision J., and Telgarsky, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:36:27.207236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation e0ae232d-ede8-4e86-b337-a761520ba6f4 · inbound

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers cites this paper.

Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformers Lower bounds on transformers with infinite precision

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T12:23:57.818820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49c33eec-0cf9-45d5-a364-6c2c18a18adb · inbound

Attention-based representations for multi-task computation cites this paper.

Attention-based representations for multi-task computation Lower bounds on transformers with infinite precision

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-08T00:18:21.793091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.