Paper Citation Record · LEDGER

Christoffel words as extremal structures in Collatz dynamics

As of 20 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2607.24844.

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

pith.paper-citation-record.v1
2607.24844 v1

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T04:35:55.429512Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

15 of 15 outbound references displayed

verified exact0
verified fuzzy0
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8a1e28ab-6f11-4fa6-add0-914973c8dfba · outbound

This paper cites Terras,A stopping time problem on the positive integers, Acta Arithmetica, 30 (1976), 241–252.

Christoffel words as extremal structures in Collatz dynamics Terras,A stopping time problem on the positive integers, Acta Arithmetica, 30 (1976), 241–252

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.565081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4ec3a151-c55f-4a48-9f45-a93348278df2 · outbound

This paper cites an unresolved cited work.

Christoffel words as extremal structures in Collatz dynamics Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.632076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 260198ca-a03d-4bc0-8ac1-4aafbd2ff71b · outbound

This paper cites an unresolved cited work.

Christoffel words as extremal structures in Collatz dynamics Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.695335Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8ed11ec-3a6c-4bb1-8eca-896ff837c3fe · outbound

This paper cites an unresolved cited work.

Christoffel words as extremal structures in Collatz dynamics Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.757426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71e9f669-e441-4196-8b51-00b2cad8b8ef · outbound

This paper cites Allouche, J.

Christoffel words as extremal structures in Collatz dynamics Allouche, J

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.817907Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9530c45-a0d2-4953-a0c2-fff0713e950d · outbound

This paper cites Wirsching,The Dynamical System Generated by the3n+ 1Function, Springer, 1998.

Christoffel words as extremal structures in Collatz dynamics Wirsching,The Dynamical System Generated by the3n+ 1Function, Springer, 1998

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.877495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dde2b291-d379-4b67-8436-0e573e1c547d · outbound

This paper cites Applegate, J.

Christoffel words as extremal structures in Collatz dynamics Applegate, J

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:54.931421Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b1cbd6e-bfb8-47f9-b6e7-d4837b042624 · outbound

This paper cites Krasikov, J.

Christoffel words as extremal structures in Collatz dynamics Krasikov, J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.019214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1efdfee-7099-4f6e-94e9-2136b6cebe16 · outbound

This paper cites Almost all orbits of the Collatz map attain almost bounded values.

Christoffel words as extremal structures in Collatz dynamics Almost all orbits of the Collatz map attain almost bounded values

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.103536Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e40fa81-ee2d-4542-9520-dabd623dafd6 · outbound

This paper cites Kontorovich, J.

Christoffel words as extremal structures in Collatz dynamics Kontorovich, J

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.158583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4c50998f-1b6d-406a-8888-c05593717e77 · outbound

This paper cites Characteristic numbers and characteristic equations of parity vectors of Collatz sequences.

Christoffel words as extremal structures in Collatz dynamics Characteristic numbers and characteristic equations of parity vectors of Collatz sequences

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.194609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

This paper cites Paradoxical behavior in Collatz sequences.

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.

Observation 31babc33-c5a8-4eb7-8f92-672114c17a93 · outbound

This paper cites Lothaire,Algebraic Combinatorics on Words, Cambridge University Press, 2002.

Christoffel words as extremal structures in Collatz dynamics Lothaire,Algebraic Combinatorics on Words, Cambridge University Press, 2002

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.322782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 703063b0-f621-45e0-99ac-b3fbac235266 · outbound

This paper cites Berstel, A.

Christoffel words as extremal structures in Collatz dynamics Berstel, A

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.381859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8640268b-d9b5-45e0-9f6f-e407c2eabb05 · outbound

This paper cites Knight,Collatz high dycles do not exist, Disrrete Mathematics, 349 (2026) 114812.

Christoffel words as extremal structures in Collatz dynamics Knight,Collatz high dycles do not exist, Disrrete Mathematics, 349 (2026) 114812

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T04:35:55.429512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.