Paper Citation Record · LEDGER

Iteration Steps of 3x+1 Problem

As of 12 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.

pith.paper-citation-record.v1
2506.23070 v3

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:58:50.564295Z

measured 10 of 10 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

No inbound Pith citation observations are available.