Paper Citation Record · LEDGER

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients

As of 12 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2509.05235.

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

pith.paper-citation-record.v1
2509.05235 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:44:24.292842Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T06:59:13.289105Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

10 of 10 outbound references displayed

verified exact0
verified fuzzy6
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3be8a568-5d10-4308-b255-e8f97385a08e · outbound

This paper cites Bachmann,Niedere Zahlentheorie, part1, Teubner, Leipzig, 1902.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Bachmann,Niedere Zahlentheorie, part1, Teubner, Leipzig, 1902

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:44:26.117346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation dc1cf07b-204c-43e7-9f4a-713629f3434a · outbound

This paper cites an unresolved cited work.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:44:25.882542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 87a361e3-5102-4dd0-9561-11e9b5a7585f · outbound

This paper cites Comtet,Advanced Combinatorics.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Comtet,Advanced Combinatorics

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:44:25.676160Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c54873ca-c271-4140-8081-32d315610300 · outbound

This paper cites Eisenstein,Eine neue Gattung zahlentheoretischer Funktionen, welche von zwei Elementen abh¨ angen und durch gewisse lineare Funktional-Gleichungen definiert werden, Ber.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Eisenstein,Eine neue Gattung zahlentheoretischer Funktionen, welche von zwei Elementen abh¨ angen und durch gewisse lineare Funktional-Gleichungen definiert werden, Ber

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:44:25.550270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ab2f9a51-d802-4cd2-ac66-06e11daf0c2c · outbound

This paper cites an unresolved cited work.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:44:25.404405Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 5ee155d0-b6ca-4227-a918-b6a1c3c28cce · outbound

This paper cites an unresolved cited work.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:44:25.288534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cfe0bca8-bdc6-419b-80f7-d974c43392af · outbound

This paper cites Lagrange,D´ emonstration d’un th´ eor` eme nouveau concernant les nombres premiers, Nouv.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Lagrange,D´ emonstration d’un th´ eor` eme nouveau concernant les nombres premiers, Nouv

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:44:25.067557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 489a69f8-0912-42b0-84a7-e7757b3021c3 · outbound

This paper cites Lerch,Zur Theorie des Fermatschen Quotienten ap−1−1 p =q(a), Math.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Lerch,Zur Theorie des Fermatschen Quotienten ap−1−1 p =q(a), Math

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:44:24.818892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation afcde5ae-e9c5-40f0-bb34-c06033d68ca3 · outbound

This paper cites (2025),The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients (2025),The On-Line Encyclopedia of Integer Sequences, published electronically at https://oeis.org

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T05:44:24.666825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 211c6e26-84fe-4aa4-bf5c-66a07da4c06b · outbound

This paper cites an unresolved cited work.

Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-05T05:44:24.504746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 9fcbaef5-7843-4340-9d42-cf2679792256 · inbound

Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products cites this paper.

Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products Wilson's theorem modulo higher prime powers I: Fermat and Wilson quotients

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T06:59:13.289105Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.