Paper Citation Record · LEDGER

Paradoxical behavior in Collatz sequences

As of 11 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 2 inbound Pith citation observations for arXiv:2502.00948.

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

pith.paper-citation-record.v1
2502.00948 v5

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-23T04:11:19.275615Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T04:35:55.267011Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-05-15T04:59:45.744409Z

Reference resolution

20 of 20 outbound references displayed

verified exact0
verified fuzzy12
unresolved8
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5df05c36-a971-4193-8bba-f6070a0be221 · outbound

This paper cites Albert, B.

Paradoxical behavior in Collatz sequences Albert, B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.361168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e36d39a9-9cf6-4306-aa3a-f50ce1be0017 · outbound

This paper cites Baker, Transcendental Number Theory, Cambridge University Press.

Paradoxical behavior in Collatz sequences Baker, Transcendental Number Theory, Cambridge University Press

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.430964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fffbfd95-e20b-4322-adca-4d3d304c2092 · outbound

This paper cites Barina, Convergence verification of the Collatz problem, J.

Paradoxical behavior in Collatz sequences Barina, Convergence verification of the Collatz problem, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.423308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 730a919c-6a76-4ef8-99d9-58012385f71d · outbound

This paper cites Eliahou, The 3 x + 1 problem: new lower bounds on nontrivial cycle lengths, Discrete Math.

Paradoxical behavior in Collatz sequences Eliahou, The 3 x + 1 problem: new lower bounds on nontrivial cycle lengths, Discrete Math

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.419087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 08a274f1-9015-4041-b503-2be812c3bb1d · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.389768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d5803085-7538-41e3-8c33-6f634224631f · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.372942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 15aeb4e8-987e-4730-9c31-a17a790094c6 · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.386141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f883ec30-ae2b-43c8-9656-1650b4def153 · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.414941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 92da5207-9153-47d0-b5a6-29ae7f7fde44 · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.427049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2835e781-87a3-45ea-8557-6d75186de839 · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.438815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d67675af-9761-49d7-87f1-ba853b479bb8 · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.406808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 529954b0-4c5d-4018-ada4-bcf351558eaa · outbound

This paper cites an unresolved cited work.

Paradoxical behavior in Collatz sequences Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-05-23T04:12:31.365170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7650b11f-6327-4466-ba51-884942f5368f · outbound

This paper cites Oliveira e Silva, Empirical verification of the 3 x + 1 and related conjectures, published in [9], 189–207.

Paradoxical behavior in Collatz sequences Oliveira e Silva, Empirical verification of the 3 x + 1 and related conjectures, published in [9], 189–207

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.377874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 33d2ba31-5a2d-4988-a514-6a1c4ce121df · outbound

This paper cites Rhin, Approximants de Pad´ e et mesures effectives d’irrationalit´ e, in S´ eminaire de Th´ eorie des Nombres, Paris 1985–86, Progr.

Paradoxical behavior in Collatz sequences Rhin, Approximants de Pad´ e et mesures effectives d’irrationalit´ e, in S´ eminaire de Th´ eorie des Nombres, Paris 1985–86, Progr

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.402441Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b3e5f609-0302-43fc-82f4-832c2c3584cd · outbound

This paper cites Roosendaal, On the 3x+1 problem, web site available at http://www.ericr.nl/wondrous/.

Paradoxical behavior in Collatz sequences Roosendaal, On the 3x+1 problem, web site available at http://www.ericr.nl/wondrous/

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.434733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 21bce819-29ce-4e75-bbe4-20c0624b378c · outbound

This paper cites Rozier, The 3 x + 1 problem: a lower bound hypothesis, Funct.

Paradoxical behavior in Collatz sequences Rozier, The 3 x + 1 problem: a lower bound hypothesis, Funct

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.369149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a05db886-5f7c-4e98-baff-cc26f71f1882 · outbound

This paper cites Rozier, D´ emonstration de l’absense de cycles d’une certain forme pour le probl` eme de Syracuse,Singularit´ e1 No.

Paradoxical behavior in Collatz sequences Rozier, D´ emonstration de l’absense de cycles d’une certain forme pour le probl` eme de Syracuse,Singularit´ e1 No

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.411216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3b3f3d3a-1f72-404a-ad5b-a578a5503ef8 · outbound

This paper cites Simons, B.

Paradoxical behavior in Collatz sequences Simons, B

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.381835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation af12086d-11d5-47a2-83ea-2806e0c81017 · outbound

This paper cites Tao, Almost all orbits of the Collatz map attain almost bounded values, Forum Math.

Paradoxical behavior in Collatz sequences Tao, Almost all orbits of the Collatz map attain almost bounded values, Forum Math

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.393701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3ea48fca-3d7d-47c9-87ac-a14426d317cb · outbound

This paper cites Terras, A stopping time problem on the positive integers, Acta Arith.

Paradoxical behavior in Collatz sequences Terras, A stopping time problem on the positive integers, Acta Arith

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T04:12:31.397961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation a42f90f2-c81f-4451-9c55-40d3ca42788a · inbound

Parity vectors and paradoxical sequences in the accelerated Collatz map cites this paper.

Parity vectors and paradoxical sequences in the accelerated Collatz map Paradoxical behavior in Collatz sequences

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-05-15T04:59:45.748483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d817cfcf-3339-4f6f-b410-fefbd506277d · inbound

Christoffel words as extremal structures in Collatz dynamics cites this paper.

Christoffel words as extremal structures in Collatz dynamics Paradoxical behavior in Collatz sequences

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.267011Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.