Paper Citation Record · LEDGER

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers

As of 19 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 0 inbound Pith citation observations for arXiv:2608.06681.

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

pith.paper-citation-record.v1
2608.06681 v1

Coverage vector

measured 5 of 5 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:41:36.226023Z

measured 5 of 5 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

5 of 5 outbound references displayed

verified exact1
verified fuzzy1
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 29496b55-432e-4f67-a759-75b5f30bca77 · outbound

This paper cites an unresolved cited work.

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:41:36.376629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 78570348-2991-4abd-a03e-e1070e7e9e39 · outbound

This paper cites an unresolved cited work.

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T22:41:36.212772Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0120a2a-9f60-4a25-92bd-966755d45a66 · outbound

This paper cites an unresolved cited work.

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T22:41:36.359741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 68efd44d-06b9-49d8-903c-892701c5a91a · outbound

This paper cites Umans and S.

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers Umans and S

Reference 4

Resolution: verified exact; raw_fallback, observed 2026-08-10T22:41:36.337478Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c5af7c3b-cbfc-4295-a8b8-2c2cfab13eca · outbound

This paper cites Zhang, X.

Refuting a Conjecture of Umans and Wang on Arithmetic-Progression Divisor Covers Zhang, X

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:41:36.348877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.