Paper Citation Record · LEDGER

The number of primes not in a numerical semigroup

As of 8 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2506.03625.

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

pith.paper-citation-record.v1
2506.03625 v2

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:12:13.247821Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T20:35:49.910489Z

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 fuzzy7
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a44a840f-5c66-4ad0-82af-d485168825da · outbound

This paper cites Bennett, G.

The number of primes not in a numerical semigroup Bennett, G

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:14.662251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2ec29c97-7e6b-43e5-919c-17ff50cec252 · outbound

This paper cites Davenport, Multiplicative Number Theory, 2nd edn., GTM 74, Springer, New York, 1980.

The number of primes not in a numerical semigroup Davenport, Multiplicative Number Theory, 2nd edn., GTM 74, Springer, New York, 1980

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T11:12:12.539711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75ea2ae8-705b-48ca-83ef-93d3686dfe7d · outbound

This paper cites Ding, On a conjecture of Ram\'irez Alfons\' in and Ska ba, J.

The number of primes not in a numerical semigroup Ding, On a conjecture of Ram\'irez Alfons\' in and Ska ba, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:14.415098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7d427f60-b856-4348-9437-4eb6da7608c0 · outbound

This paper cites an unresolved cited work.

The number of primes not in a numerical semigroup Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:12:14.189094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4112ee3e-0b97-488d-99e2-494111954a0d · outbound

This paper cites On a conjecture of Ram\'{\i}rez Alfons\'{\i}n and Ska{\l}ba II.

The number of primes not in a numerical semigroup On a conjecture of Ram\'{\i}rez Alfons\'{\i}n and Ska{\l}ba II

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T11:12:12.815241Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2a4d740-956f-491e-8cb2-b7724484a6c7 · outbound

This paper cites Montgomery, R.C.

The number of primes not in a numerical semigroup Montgomery, R.C

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:13.999835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c7648cb9-bf4c-418c-8f93-51ec8f823949 · outbound

This paper cites Ram\'irez Alfons\'in, M.

The number of primes not in a numerical semigroup Ram\'irez Alfons\'in, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:13.803836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a712f1cd-f459-4720-8c8b-c591aee157e1 · outbound

This paper cites Rosser, L.

The number of primes not in a numerical semigroup Rosser, L

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:13.699613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d58db2ec-ee1a-404c-94c8-93d2c989db15 · outbound

This paper cites Sylvester, On subvariants, i.e.

The number of primes not in a numerical semigroup Sylvester, On subvariants, i.e

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:13.578095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5ffdb862-72c2-472c-8dcc-3ca95b5ec696 · outbound

This paper cites Sylvester, Question 7382, Mathematical Questions from Educational Times, 36 (1883).

The number of primes not in a numerical semigroup Sylvester, Question 7382, Mathematical Questions from Educational Times, 36 (1883)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:12:13.410523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 46c3bef0-a590-42c8-9a87-b2dc1d00ab91 · inbound

The Diophantine Frobenius Problem revisited cites this paper.

The Diophantine Frobenius Problem revisited The number of primes not in a numerical semigroup

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-04T20:35:49.910489Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.