Paper Citation Record · LEDGER

Piecewise linear circle maps and conjugation to rigid rational rotations

As of 22 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2505.13689.

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

pith.paper-citation-record.v1
2505.13689 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:21:18.344810Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:42:30.218715Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-15T18:42:30.301113Z

Reference resolution

23 of 23 outbound references displayed

verified exact1
verified fuzzy16
unresolved5
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 14e329ee-5c7b-4377-8427-dbf203791811 · outbound

This paper cites Adouani (2016) Conjugation between circle maps with severa l break points, Ergod.

Piecewise linear circle maps and conjugation to rigid rational rotations Adouani (2016) Conjugation between circle maps with severa l break points, Ergod

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.683123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dfccb167-15ef-42a0-809f-86b3e2dc99c9 · outbound

This paper cites Adouani and H.

Piecewise linear circle maps and conjugation to rigid rational rotations Adouani and H

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.668908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation af27fd36-5033-4187-970e-ca9ae5d7b5e9 · outbound

This paper cites an unresolved cited work.

Piecewise linear circle maps and conjugation to rigid rational rotations Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T20:21:18.654975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 64fca914-1967-4ef5-8549-587b1e3ede75 · outbound

This paper cites Carretero-Gonz´ alez, D.K.

Piecewise linear circle maps and conjugation to rigid rational rotations Carretero-Gonz´ alez, D.K

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T20:21:18.260909Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17556b32-ac4a-48c6-8083-367f33773428 · outbound

This paper cites Coelho, A.

Piecewise linear circle maps and conjugation to rigid rational rotations Coelho, A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.631464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ab05cbfa-75ca-4fb4-b7bf-328efcf0c478 · outbound

This paper cites Devaney An Introduction to Chaotic Dynamical Systems.

Piecewise linear circle maps and conjugation to rigid rational rotations Devaney An Introduction to Chaotic Dynamical Systems

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.616574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c6027307-6d2c-4662-8d88-4e77c7773682 · outbound

This paper cites Dzhalilov and I.

Piecewise linear circle maps and conjugation to rigid rational rotations Dzhalilov and I

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.602504Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9af6cd5a-1341-42d3-bade-28817a3a36d9 · outbound

This paper cites Dzhalilov, D.

Piecewise linear circle maps and conjugation to rigid rational rotations Dzhalilov, D

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.587297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4f38e365-b55c-4c97-8e58-f6c4788c7fc5 · outbound

This paper cites Dzhalilov, D.

Piecewise linear circle maps and conjugation to rigid rational rotations Dzhalilov, D

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.571777Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ce59a476-94cf-4383-8a04-1274528e73e6 · outbound

This paper cites Glendinning, S.

Piecewise linear circle maps and conjugation to rigid rational rotations Glendinning, S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.557858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e2b44378-9c1d-41d2-b1d1-355cec7105f7 · outbound

This paper cites Herman (1979) Sur la conjugaison diﬀ´ erentiable des diﬀ´ eom orphismes du cercle ` a des rotations, IHES Publ.

Piecewise linear circle maps and conjugation to rigid rational rotations Herman (1979) Sur la conjugaison diﬀ´ erentiable des diﬀ´ eom orphismes du cercle ` a des rotations, IHES Publ

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.542844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 92e3b22d-f543-4747-8593-06b47bb6de9c · outbound

This paper cites Khanin and D.

Piecewise linear circle maps and conjugation to rigid rational rotations Khanin and D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.528327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 28987056-340d-4c4d-8358-e1a2ade64749 · outbound

This paper cites Khmelev (2005) Rational rotation numbers for homeomorp hisms with several break-type singularities, Ergod.

Piecewise linear circle maps and conjugation to rigid rational rotations Khmelev (2005) Rational rotation numbers for homeomorp hisms with several break-type singularities, Ergod

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.513278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0998b73f-4998-4b07-b185-955b39bf508c · outbound

This paper cites Liousse (2005) Nombre de rotation, mesures invariantes et ratio set des hom´ eomorphismes aﬃnes par morceaux du cercle, Ann.

Piecewise linear circle maps and conjugation to rigid rational rotations Liousse (2005) Nombre de rotation, mesures invariantes et ratio set des hom´ eomorphismes aﬃnes par morceaux du cercle, Ann

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T20:21:18.306157Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1831fdb-862b-4191-812c-cf5643e579de · outbound

This paper cites Ma (2025) Dynamics of chessboard-style ﬂows and piecewise linear cir cle homeomor- phisms, PhD Dissertation, University of Manchester, submitted.

Piecewise linear circle maps and conjugation to rigid rational rotations Ma (2025) Dynamics of chessboard-style ﬂows and piecewise linear cir cle homeomor- phisms, PhD Dissertation, University of Manchester, submitted

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.490239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0ceb76e5-9fa8-4286-9673-b37990ce9d67 · outbound

This paper cites Mackay and C.

Piecewise linear circle maps and conjugation to rigid rational rotations Mackay and C

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.475589Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 31e139e6-50c8-4a45-a1a6-ae9339d5addf · outbound

This paper cites de Melo and S.

Piecewise linear circle maps and conjugation to rigid rational rotations de Melo and S

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.461380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2d5b5c02-b193-4e42-aeb3-4524c3db743f · outbound

This paper cites Quas (1992) Invariant measures for families of circle maps, Math.

Piecewise linear circle maps and conjugation to rigid rational rotations Quas (1992) Invariant measures for families of circle maps, Math

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T20:21:18.323078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4b0f704-2ae4-4d79-9a19-2e84bfb14726 · outbound

This paper cites Rhodes and C.L.

Piecewise linear circle maps and conjugation to rigid rational rotations Rhodes and C.L

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T20:21:18.327170Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 731361e9-d749-4a90-8a5b-e60ff56f63ba · outbound

This paper cites an unresolved cited work.

Piecewise linear circle maps and conjugation to rigid rational rotations Unresolved cited work

Reference 20

Resolution: parse uncertain; no resolver link, observed 2026-08-15T20:21:18.331473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51a12385-6145-484b-9d33-ef37fb1ea951 · outbound

This paper cites The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps.

Piecewise linear circle maps and conjugation to rigid rational rotations The necessity of the sausage-string structure for mode-locking regions of piecewise-linear maps

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-15T20:21:18.385521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 257ce82f-8c01-4915-a8b2-61ae36e406a4 · outbound

This paper cites Simpson and J.D.

Piecewise linear circle maps and conjugation to rigid rational rotations Simpson and J.D

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.417703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 459e03b4-106d-491a-8762-a4375a4faa3d · outbound

This paper cites Yoccoz (1983) C 1-conjugaison des diﬀ´ eomorphismes du cercle, in Geometric Dy- namics, ed.

Piecewise linear circle maps and conjugation to rigid rational rotations Yoccoz (1983) C 1-conjugaison des diﬀ´ eomorphismes du cercle, in Geometric Dy- namics, ed

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T20:21:18.401955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation 99a307cb-06af-4477-9749-8f5efd168b93 · inbound

Scaling of the rotation number for perturbations of rational rotations cites this paper.

Scaling of the rotation number for perturbations of rational rotations Piecewise linear circle maps and conjugation to rigid rational rotations

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:42:30.307543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.