Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-07T18:40:42.392040Z
Paper Citation Record · LEDGER
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis
As of 12 August 2026, this Paper Citation Record lists 6 of 6 outbound references and 0 inbound Pith citation observations for arXiv:2607.05301.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
6 of 6 outbound references displayed
- verified exact1
- verified fuzzy2
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1c0dc053-1679-440e-aed6-32cd71ed21db · outbound
This paper cites an unresolved cited work.
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-07-07T18:44:06.166453Z
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 e5c5a179-f4f1-4564-9087-c7122d77b93e · outbound
This paper cites Infinite matrix of odd natural numbers. A bit about Sophie Germain prime numbers.
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis Infinite matrix of odd natural numbers. A bit about Sophie Germain prime numbers
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-07-07T18:44:06.130030Z
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 13f96df3-e1e4-4d8b-bce4-46880ca9c1f1 · outbound
This paper cites Robinson.
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis Robinson
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-07T18:44:06.158361Z
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 90f61716-cfc9-4d5a-a69c-ed2621a751da · outbound
This paper cites an unresolved cited work.
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-07-07T18:44:06.160961Z
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 b08d6aed-59e9-47fe-9b87-b79ea3f918e9 · outbound
This paper cites Natural density, 2026.
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis Natural density, 2026
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-07T18:44:06.169590Z
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 cbd11c52-0eea-4265-8c2e-34d3abdc8b33 · outbound
This paper cites an unresolved cited work.
Calculating the natural density of Mersenne numbers using nonstandard mathematical analysis Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-07-07T18:44:06.163917Z
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
No inbound Pith citation observations are available.