Paper Citation Record · LEDGER

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers

As of 16 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.04365.

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

pith.paper-citation-record.v1
2607.04365 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T19:45:27.699165Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

24 of 24 outbound references displayed

verified exact0
verified fuzzy0
unresolved23
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 86ecce00-5524-4822-813e-b2f99ef6f47d · outbound

This paper cites an unresolved cited work.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Unresolved cited work

Reference 1

Resolution: parse uncertain; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bbe877a4-403d-4d77-adcd-05e9ec620bc0 · outbound

This paper cites 2022 , note =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers 2022 , note =

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e4ee833-e38e-4b4a-9ce8-6276b434cbbe · outbound

This paper cites Mathematische Zeitschrift , volume =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Mathematische Zeitschrift , volume =

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

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Observation 6dfd8e3f-b64d-4b64-87cf-22f9baf51392 · outbound

This paper cites Odd Perfect Numbers Have At Least Nine Distinct Prime Factors.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Odd Perfect Numbers Have At Least Nine Distinct Prime Factors

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

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Observation 3629f238-8734-4184-8eb2-d1e5295d7270 · outbound

This paper cites , title =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers , title =

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf56128e-d7f7-4eed-9d48-3b7014a2812c · outbound

This paper cites Odd perfect numbers are greater than \(10^.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Odd perfect numbers are greater than \(10^

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

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Unavailable: canonical work link unavailable.

Observation da3c0fc4-0316-4a31-97ff-355719eae729 · outbound

This paper cites Mathematics of Computation , volume =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Mathematics of Computation , volume =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea44411d-2842-4226-84d8-7f30f2455db7 · outbound

This paper cites , title =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers , title =

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 50e027d7-5c9e-4ff8-bd7e-93e75013db8b · outbound

This paper cites , title =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers , title =

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c360965-ba4e-462f-840e-eb4fe4f5dcf0 · outbound

This paper cites Upper bounds on the second largest prime factor of an odd perfect number.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Upper bounds on the second largest prime factor of an odd perfect number

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9b9baf9-6fc9-4ca0-b1f5-54454b40b209 · outbound

This paper cites On the number of total prime factors of an odd perfect number.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers On the number of total prime factors of an odd perfect number

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66cb0fa1-1f3a-4b9b-825f-cdd1e4b8df1a · outbound

This paper cites Integers , volume =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Integers , volume =

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1436ad2f-610c-4bc8-b982-2f78cc9f5c5f · outbound

This paper cites On the third largest prime divisor of an odd perfect number.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers On the third largest prime divisor of an odd perfect number

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61e7d869-ee9a-46ae-84e9-8d11490f5039 · outbound

This paper cites On inequalities involving counts of the prime factors of an odd perfect number.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers On inequalities involving counts of the prime factors of an odd perfect number

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

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Unavailable: canonical work link unavailable.

Observation 0497a41a-1fae-4839-9aab-12b4ed5a1e68 · outbound

This paper cites , title =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers , title =

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a8f7804-e071-4ae8-a27d-f66f83d58752 · outbound

This paper cites , title =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers , title =

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b597e34c-3d02-4590-9afb-ac0cdf6c03c8 · outbound

This paper cites Integers , volume =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Integers , volume =

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a73cfa35-0286-4f9a-8f6f-3ee2b779032c · outbound

This paper cites 2025 , eprint =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers 2025 , eprint =

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb6b8757-f1fb-4b93-b57c-5d59335db7f8 · outbound

This paper cites 2025 , eprint =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers 2025 , eprint =

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ddbdc3b-3203-4bc8-8064-3b3cbad03301 · outbound

This paper cites , title =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers , title =

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8697ab33-e6e7-4577-a9ac-0a96c828014b · outbound

This paper cites 2026 , eprint =.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers 2026 , eprint =

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a6f7d60-b6f2-44f2-ac15-7dc5afd0624d · outbound

This paper cites A note on the $q$-adic valuation of $\sigma_k(n)$.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers A note on the $q$-adic valuation of $\sigma_k(n)$

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

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Unavailable: canonical work link unavailable.

Observation 8e5b8e5f-f2f2-4778-b8b4-1b9a3cd485ae · outbound

This paper cites Monatshefte f.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers Monatshefte f

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 637e1f9e-7605-4b44-9a52-32024d8dfe57 · outbound

This paper cites and Vandiver, Harry S.

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers and Vandiver, Harry S

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T19:45:27.699165Z

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Pith citing papers

No inbound Pith citation observations are available.