Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits
As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2308.03212.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-16T04:59:08.731627Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T11:37:03.257809Z
Reference resolution
0 of 0 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation 5e8362be-6f0a-4a8c-9a01-03e2a3e326b5 · 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 Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-09T12:23:57.829205Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation f125b8d1-327f-4444-a71b-e6f3b46b29a1 · inbound
BAR Conjecture: the Feasibility of Inference Budget-Constrained LLM Services with Authenticity and Reasoning cites this paper.
BAR Conjecture: the Feasibility of Inference Budget-Constrained LLM Services with Authenticity and Reasoning Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T11:04:47.223422Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b91be800-59b6-4fc9-8730-d150fc366dbe · inbound
On the Ability of Transformers to Verify Plans cites this paper.
On the Ability of Transformers to Verify Plans Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-07-13T21:49:42.006847Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1c6dacd6-29c8-4860-ad3e-ef6adafd1f0c · inbound
A First-Principles Theory of Slow Thinking and Active Perception cites this paper.
A First-Principles Theory of Slow Thinking and Active Perception Average-Hard Attention Transformers are Constant-Depth Uniform Threshold Circuits
Reference 148
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T11:37:03.259993Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 063311ae-b30d-4602-acb3-c3dea78e7710 · inbound
On the Expressive Power of Transformers cites this paper.
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.