Paper Citation Record · LEDGER

Uniformity within Parameterized Circuit Classes

As of 12 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2509.09657.

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

pith.paper-citation-record.v1
2509.09657 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T18:55:36.725704Z

measured 16 of 16 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 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

16 of 16 outbound references displayed

verified exact7
verified fuzzy0
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 984c29fa-568f-48c7-a8ef-e6f18c0ea8e8 · outbound

This paper cites Fast Parallel Fixed-Parameter Algorithms via Color Coding.

Uniformity within Parameterized Circuit Classes Fast Parallel Fixed-Parameter Algorithms via Color Coding

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.638390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e12c4aad-08e7-43fc-b7ae-0bb3b7b94b07 · outbound

This paper cites Parallel Multivariate Meta - Theorems.

Uniformity within Parameterized Circuit Classes Parallel Multivariate Meta - Theorems

Reference 2

Resolution: verified exact; doi, observed 2026-08-04T18:59:29.313344Z

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 5b53c828-d007-4eea-8067-76311a684169 · outbound

This paper cites Some lower bounds in parameterized AC0.

Uniformity within Parameterized Circuit Classes Some lower bounds in parameterized AC0

Reference 3

Resolution: verified exact; doi, observed 2026-08-04T18:59:29.131423Z

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 b02af782-e7f0-48a8-8401-ef77f074c747 · outbound

This paper cites Slicewise Definability in First - Order Logic with Bounded Quantifier Rank.

Uniformity within Parameterized Circuit Classes Slicewise Definability in First - Order Logic with Bounded Quantifier Rank

Reference 4

Resolution: verified exact; doi, observed 2026-08-04T18:59:28.985157Z

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 145c0de7-e3b2-48ad-bd62-e4fab366b412 · outbound

This paper cites On the Space and Circuit Complexity of Parameterized Problems : Classes and Completeness.

Uniformity within Parameterized Circuit Classes On the Space and Circuit Complexity of Parameterized Problems : Classes and Completeness

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.664049Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a24fd0b-5226-40c0-95f1-3b911a9eab34 · outbound

This paper cites Describing parameterized complexity classes.

Uniformity within Parameterized Circuit Classes Describing parameterized complexity classes

Reference 6

Resolution: verified exact; doi, observed 2026-08-04T18:59:28.787375Z

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 4eed83d2-9bca-44af-9f9e-a72f6824dd2a · outbound

This paper cites Parameterized complexity theory.

Uniformity within Parameterized Circuit Classes Parameterized complexity theory

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.675861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e170c14-1216-4d3f-b95e-b979a51c77b6 · outbound

This paper cites Integer multiplication in time O (n n).

Uniformity within Parameterized Circuit Classes Integer multiplication in time O (n n)

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.681219Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 920d69d5-1110-4fee-8003-c053fbc38694 · outbound

This paper cites Descriptive Complexity.

Uniformity within Parameterized Circuit Classes Descriptive Complexity

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.686596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfad03a8-e68e-468e-90f9-f6323b3180e1 · outbound

This paper cites Mix Barrington and Neil Immerman.

Uniformity within Parameterized Circuit Classes Mix Barrington and Neil Immerman

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.693230Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ff9a9b2-7fcf-41fe-9def-d3265b8abb0f · outbound

This paper cites Mix Barrington, Neil Immerman, and Howard Straubing.

Uniformity within Parameterized Circuit Classes Mix Barrington, Neil Immerman, and Howard Straubing

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.698589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ec6fbff-c83a-4b46-92bc-418f0c7b8971 · outbound

This paper cites Parameterized circuit complexity of model-checking on sparse structures.

Uniformity within Parameterized Circuit Classes Parameterized circuit complexity of model-checking on sparse structures

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.703535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a45f3414-0dc7-47de-bda9-d5c679aa6b5f · outbound

This paper cites Regan and Heribert Vollmer.

Uniformity within Parameterized Circuit Classes Regan and Heribert Vollmer

Reference 13

Resolution: verified exact; doi, observed 2026-08-04T18:59:28.620782Z

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 d309c4f1-deae-4a46-82b0-b3e02266ccff · outbound

This paper cites an unresolved cited work.

Uniformity within Parameterized Circuit Classes Unresolved cited work

Reference 14

Resolution: verified exact; doi, observed 2026-08-04T18:59:28.472453Z

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 6d77d745-b87d-484a-b886-1fd6f0a69ae7 · outbound

This paper cites On Uniformity and Circuit Lower Bounds.

Uniformity within Parameterized Circuit Classes On Uniformity and Circuit Lower Bounds

Reference 15

Resolution: verified exact; doi, observed 2026-08-04T18:59:28.116105Z

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 fcbb551d-a878-492a-862c-2ea7d329111c · outbound

This paper cites Introduction to Circuit Complexity : A Uniform Approach.

Uniformity within Parameterized Circuit Classes Introduction to Circuit Complexity : A Uniform Approach

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T18:55:36.725704Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.