Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:58:50.564295Z
Paper Citation Record · LEDGER
Iteration Steps of 3x+1 Problem
As of 19 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2506.23070.
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 2026-08-19T06:32:44.657259+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
10 of 10 outbound references displayed
- verified exact2
- verified fuzzy4
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 8a10a8eb-3530-4bd4-9492-c336cc579308 · outbound
This paper cites Lagarias, The 3x+1 problem and its generalizations, Amer.
Iteration Steps of 3x+1 Problem Lagarias, The 3x+1 problem and its generalizations, Amer
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T21:58:52.880579Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d972c2c6-d947-4a5c-b178-192832b9d467 · outbound
This paper cites The 3x+1 Problem: An Annotated Bibliography, II (2000-2009).
Iteration Steps of 3x+1 Problem The 3x+1 Problem: An Annotated Bibliography, II (2000-2009)
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T21:58:51.070027Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation c43167a5-ce30-48a7-ae27-2201a9769d55 · outbound
This paper cites an unresolved cited work.
Iteration Steps of 3x+1 Problem Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T21:58:52.687488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation ae363f1d-b2e5-4b05-999f-e324d773b9e5 · outbound
This paper cites Leavens, Mike Vermeulen, 3x+1 search programs, Computers and Mathematics with Applications, 24(11):79-99, 1992.
Iteration Steps of 3x+1 Problem Leavens, Mike Vermeulen, 3x+1 search programs, Computers and Mathematics with Applications, 24(11):79-99, 1992
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T21:58:52.475671Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a3e2c54d-fd84-40e5-9716-ed76b4301b67 · outbound
This paper cites an unresolved cited work.
Iteration Steps of 3x+1 Problem Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T21:58:52.236214Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation d8f8958b-7f05-4e54-985d-8bf0f20b0d7e · outbound
This paper cites Ladue, Clusters of Integers With Equal Total Stopping Times in the 3X + 1 Problem, Fibonacci Quart, 56(2):156-162, 2018.
Iteration Steps of 3x+1 Problem Ladue, Clusters of Integers With Equal Total Stopping Times in the 3X + 1 Problem, Fibonacci Quart, 56(2):156-162, 2018
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T21:58:51.977421Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation da556b42-8de9-4b29-bbdb-faaa4ad0a3a7 · outbound
This paper cites an unresolved cited work.
Iteration Steps of 3x+1 Problem Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T21:58:51.739347Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 8e8beb22-a788-4b1a-9b43-e4e1d62a53b6 · outbound
This paper cites an unresolved cited work.
Iteration Steps of 3x+1 Problem Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T21:58:51.513684Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 7b6e8a8b-3879-42cd-80fc-e55e6e3e1955 · outbound
This paper cites Monks, 3x+1 Minus the +, Discrete Mathematics and The- oretical Computer Science, 5(1):47–54, 2002.
Iteration Steps of 3x+1 Problem Monks, 3x+1 Minus the +, Discrete Mathematics and The- oretical Computer Science, 5(1):47–54, 2002
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T21:58:51.284742Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation db049717-d085-45b4-a6d9-2ff49b5648b7 · outbound
This paper cites The relationship between stopping time and number of odd terms in Collatz sequences.
Iteration Steps of 3x+1 Problem The relationship between stopping time and number of odd terms in Collatz sequences
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T21:58:50.806494Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
No inbound Pith citation observations are available.