Paper Citation Record · LEDGER

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic

As of 21 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 1 inbound Pith citation observation for arXiv:2601.12772.

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

pith.paper-citation-record.v1
2601.12772 v2

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T09:48:36.150887Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T05:51:11.131049Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

11 of 11 outbound references displayed

verified exact0
verified fuzzy0
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7c287b3d-101a-4ada-9e1d-f5583ee63f64 · outbound

This paper cites Cambridge University Press, Cam- bridge, 1975.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Cambridge University Press, Cam- bridge, 1975

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.125628Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c96b815-0478-4ada-9109-99d52652fa21 · outbound

This paper cites Bernstein.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Bernstein

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.185794Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 316dcae4-8b29-4a8d-b39d-469938ebd1ee · outbound

This paper cites an unresolved cited work.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.289273Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b4e3a64-ff51-47e4-bf0e-be6f2c23b7e0 · outbound

This paper cites Semigroups, Presburger formulas, and lan- guages.Pacific Journal of Mathematics, 16(2):285–296, 1966.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Semigroups, Presburger formulas, and lan- guages.Pacific Journal of Mathematics, 16(2):285–296, 1966

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.434534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 80ecd1a0-5cc8-44a6-a811-1ffe52fc78c5 · outbound

This paper cites Lagarias.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Lagarias

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.536533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c64982e1-cbb2-4fea-b976-4515f86b9b36 · outbound

This paper cites Lagarias.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Lagarias

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.648802Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68dcf404-605f-4adb-a780-6ab9eda19591 · outbound

This paper cites Cambridge University Press, 1981.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Cambridge University Press, 1981

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.774757Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ba65ed03-509f-454b-b1cf-7f7f23fc9444 · outbound

This paper cites ¨ uber die vollst¨ andigkeit eines gewissen systems der arithmetik ganzer zahlen.Comptes Rendus du I congr` es de Math´ ematiciens des Pays Slaves, pages 92–101, 1929.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic ¨ uber die vollst¨ andigkeit eines gewissen systems der arithmetik ganzer zahlen.Comptes Rendus du I congr` es de Math´ ematiciens des Pays Slaves, pages 92–101, 1929

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.898323Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4b11e835-3541-4704-a2ec-03e16a0c803d · outbound

This paper cites Theoretical and computational bounds form- cycles of the 3n+ 1 problem.Acta Arithmetica, 117:51–70, 2005.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Theoretical and computational bounds form- cycles of the 3n+ 1 problem.Acta Arithmetica, 117:51–70, 2005

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:35.961123Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac26ac0a-d019-4bce-bab4-ba43923f8d1e · outbound

This paper cites Almost all Collatz orbits attain almost bounded values.Forum of Mathematics, Pi, 10:e12, 2022.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Almost all Collatz orbits attain almost bounded values.Forum of Mathematics, Pi, 10:e12, 2022

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:36.029939Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b30b564c-1eae-40cf-879e-1cf22200ac20 · outbound

This paper cites Wirsching.The Dynamical System Generated by the3n+ 1Function, volume 1681 ofLecture Notes in Mathematics.

Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic Wirsching.The Dynamical System Generated by the3n+ 1Function, volume 1681 ofLecture Notes in Mathematics

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T09:48:36.150887Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation fb62e150-2787-44bf-b119-3882d826da9b · inbound

Non-Definability of Reachability in B\"uchi Arithmetic for a Family of Generalized Collatz Maps cites this paper.

Non-Definability of Reachability in B\"uchi Arithmetic for a Family of Generalized Collatz Maps Logical Undefinability of the Generalized Collatz Transition Relation in B\"uchi Arithmetic

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T05:51:11.131049Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.