Paper Citation Record · LEDGER

Groupoid Cardinality and Random Permutations

As of 15 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2412.16386.

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

pith.paper-citation-record.v1
2412.16386 v2

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T10:41:16.899901Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

11 of 11 outbound references displayed

verified exact0
verified fuzzy0
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 83de5812-5b5f-4dbd-afa3-2ad0575a53ed · outbound

This paper cites Available at https://doi.org/10.1214/aop/1176989707 https://doi.org/10.1214/aop/1176989707.

Groupoid Cardinality and Random Permutations Available at https://doi.org/10.1214/aop/1176989707 https://doi.org/10.1214/aop/1176989707

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T10:41:16.838768Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07bdc0e6-b930-4ee1-91c9-dfe65f1b6238 · outbound

This paper cites an unresolved cited work.

Groupoid Cardinality and Random Permutations Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T10:41:16.845176Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5fcb8086-536e-450d-8ca9-99670f5f5359 · outbound

This paper cites Higher-Dimensional Algebra VII: Groupoidification.

Groupoid Cardinality and Random Permutations Higher-Dimensional Algebra VII: Groupoidification

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T10:41:16.850727Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 408b06e8-154f-4d41-9676-3d1de1a30b52 · outbound

This paper cites an unresolved cited work.

Groupoid Cardinality and Random Permutations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:41:17.396966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a4ef2847-0946-4cf6-b9f7-e2b2454d60c3 · outbound

This paper cites an unresolved cited work.

Groupoid Cardinality and Random Permutations Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:41:17.374933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 528878fa-b2db-423e-a704-8459d8708305 · outbound

This paper cites Cycle type of random permutations: A toolkit.

Groupoid Cardinality and Random Permutations Cycle type of random permutations: A toolkit

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T10:41:16.869262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9413e9b5-a9cb-400f-9095-4bf131ad1e93 · outbound

This paper cites Random matrix theory over finite fields: a survey.

Groupoid Cardinality and Random Permutations Random matrix theory over finite fields: a survey

Reference 7

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T10:41:17.010059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9231feac-69e9-4154-9f19-ea7cf0fe03f3 · outbound

This paper cites an unresolved cited work.

Groupoid Cardinality and Random Permutations Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:41:17.349103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 285a7c71-8dfa-498a-847b-a03c7d2dcf73 · outbound

This paper cites The probability that an operator is nilpotent.

Groupoid Cardinality and Random Permutations The probability that an operator is nilpotent

Reference 9

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T10:41:16.985431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 231a07d3-a428-4649-b3b3-fd334f5a3538 · outbound

This paper cites Algebraic groups over the field with one element.

Groupoid Cardinality and Random Permutations Algebraic groups over the field with one element

Reference 10

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T10:41:16.959735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ec365278-01fc-478c-9efa-9daa7b902867 · outbound

This paper cites an unresolved cited work.

Groupoid Cardinality and Random Permutations Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-11T10:41:17.326509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

No inbound Pith citation observations are available.