Paper Citation Record · LEDGER

Scaling of the rotation number for perturbations of rational rotations

As of 22 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2506.19508.

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

pith.paper-citation-record.v1
2506.19508 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:42:30.271718Z

measured 29 of 29 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 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

29 of 29 outbound references displayed

verified exact2
verified fuzzy26
unresolved0
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0166be78-b72e-4386-b5df-f1b0f57fa86f · outbound

This paper cites Avrutin, L.

Scaling of the rotation number for perturbations of rational rotations Avrutin, L

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.619798Z

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 f36f6a78-2be9-4e24-82c7-6314ef8dab71 · outbound

This paper cites Baesens, J.

Scaling of the rotation number for perturbations of rational rotations Baesens, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.609617Z

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 0d30da59-55d3-4f89-a673-cd577c3cab84 · outbound

This paper cites Boyland (1986) Bifurcations of circle maps: Arnol’d tongues, bistability and rota- tion intervals, Commun.

Scaling of the rotation number for perturbations of rational rotations Boyland (1986) Bifurcations of circle maps: Arnol’d tongues, bistability and rota- tion intervals, Commun

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.599889Z

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 2ca5e2c1-d325-43b2-bedc-f96e0957b351 · outbound

This paper cites Pinched Arnol'd tongues for Families of circle maps.

Scaling of the rotation number for perturbations of rational rotations Pinched Arnol'd tongues for Families of circle maps

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:42:30.324962Z

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 a9ed2e4d-643f-430e-b820-95975aee712c · outbound

This paper cites Braun, Diﬀerential Equations and Their Applications: An Introduc tion to Applied Mathematics, Texts in Applied Mathematics 11, Springer, New York, 1993.

Scaling of the rotation number for perturbations of rational rotations Braun, Diﬀerential Equations and Their Applications: An Introduc tion to Applied Mathematics, Texts in Applied Mathematics 11, Springer, New York, 1993

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.590128Z

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 b1e70514-88d3-47f2-94e2-c74c18b95101 · outbound

This paper cites Brunovsky (1974) Generic properties of the rotation numbe r of one-parameter diﬀeo- morphisms of the circle, Czech.

Scaling of the rotation number for perturbations of rational rotations Brunovsky (1974) Generic properties of the rotation numbe r of one-parameter diﬀeo- morphisms of the circle, Czech

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.579978Z

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 047769ea-f992-4c8e-ab15-450a72baba83 · outbound

This paper cites Campbell, R.

Scaling of the rotation number for perturbations of rational rotations Campbell, R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.569651Z

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 1b58394b-6d06-4917-823c-6823ac0304eb · outbound

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

Scaling of the rotation number for perturbations of rational rotations Carretero-Gonz´ alez, D.K

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.559405Z

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 29c3d93a-c75c-4180-b8e2-7af172cc0895 · outbound

This paper cites Derks, P.A.

Scaling of the rotation number for perturbations of rational rotations Derks, P.A

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.548999Z

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 5142f371-dc37-4562-bf10-4dbf704173c5 · outbound

This paper cites Devaney An Introduction to Chaotic Dynamical Systems.

Scaling of the rotation number for perturbations of rational rotations Devaney An Introduction to Chaotic Dynamical Systems

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.539008Z

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 304d9cd2-f4d2-4ea0-a319-648d08b0f722 · outbound

This paper cites Dzhalilov, D.

Scaling of the rotation number for perturbations of rational rotations Dzhalilov, D

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.528672Z

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 e66eae08-59c9-4ed7-9ec0-2dcd9f41f39e · outbound

This paper cites Gaiv˜ ao, M.

Scaling of the rotation number for perturbations of rational rotations Gaiv˜ ao, M

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.517963Z

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 162a4a3f-728c-4829-9724-f5cff5d11ed0 · outbound

This paper cites Glass (1991) Cardiac arrhythmias and circle maps - A classical problem, Chaos, 1, 13-19.

Scaling of the rotation number for perturbations of rational rotations Glass (1991) Cardiac arrhythmias and circle maps - A classical problem, Chaos, 1, 13-19

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.507160Z

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 99a307cb-06af-4477-9749-8f5efd168b93 · outbound

This paper cites Piecewise linear circle maps and conjugation to rigid rational rotations.

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.

Observation b5103ad0-037c-49b1-90d9-493257f4a99d · outbound

This paper cites Herman, M´ esure de Lebesgue et Nombre de Rotation, in Geometry and Topology, eds.

Scaling of the rotation number for perturbations of rational rotations Herman, M´ esure de Lebesgue et Nombre de Rotation, in Geometry and Topology, eds

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.496746Z

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 6c6cf51a-1c06-40e8-84a6-6e917d834a62 · outbound

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

Scaling of the rotation number for perturbations of rational rotations Herman (1979) Sur la conjugaison diﬀ´ erentiable des diﬀ´ eomorphismes du cercle ` a des rotations, IHES Publ

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.486068Z

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 ab423c19-d286-4419-ac0b-761ce4eef030 · outbound

This paper cites Jeﬀrey, G.

Scaling of the rotation number for perturbations of rational rotations Jeﬀrey, G

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.475165Z

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 892460e5-2263-47ab-89e2-100a0ea7d83d · outbound

This paper cites Katznelson, An introduction to harmonic analysis , 3 rd edition, CUP, Cambridge, 2004.

Scaling of the rotation number for perturbations of rational rotations Katznelson, An introduction to harmonic analysis , 3 rd edition, CUP, Cambridge, 2004

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.463960Z

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 cf80809b-041b-4d1f-88c2-eaedcf463224 · outbound

This paper cites Khanin and D.

Scaling of the rotation number for perturbations of rational rotations Khanin and D

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.452789Z

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 a8072868-2417-4b8c-9b32-d42a5c77ad40 · outbound

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

Scaling of the rotation number for perturbations of rational rotations Liousse (2005) Nombre de rotation, mesures invariantes et ratio set des hom´ eomorphismes aﬃnes par morceaux du cercle, Ann

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.440573Z

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 9b5498b1-305a-4495-a184-23d3b1bcb946 · outbound

This paper cites Mackay and C.

Scaling of the rotation number for perturbations of rational rotations Mackay and C

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.429187Z

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 76fd021b-6a50-45c8-9dab-ed90b04a5661 · outbound

This paper cites Marangio, J.

Scaling of the rotation number for perturbations of rational rotations Marangio, J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.418456Z

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 20f2e2e6-f7e7-4a91-a80e-82e74af55c28 · outbound

This paper cites de Melo and S.

Scaling of the rotation number for perturbations of rational rotations de Melo and S

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.407823Z

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 67c6ae6c-f935-4dc8-85dd-fbdab2ab730c · outbound

This paper cites Parkhe (2013) One-parameter families of circle diﬀeomorphis ms with strictly mono- tone rotation number, Proc.

Scaling of the rotation number for perturbations of rational rotations Parkhe (2013) One-parameter families of circle diﬀeomorphis ms with strictly mono- tone rotation number, Proc

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.397089Z

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 f19bf6be-24d9-4336-8b00-4f57b31e02a0 · outbound

This paper cites Pomeau and P.

Scaling of the rotation number for perturbations of rational rotations Pomeau and P

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.385199Z

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 72ae66f9-269a-4f4f-be5f-4d4a179d8ec8 · outbound

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

Scaling of the rotation number for perturbations of rational rotations Quas (1992) Invariant measures for families of circle maps, Math

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.372442Z

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 08ff9b75-4012-4b14-b058-a188d717aedf · outbound

This paper cites Rhodes and C.L.

Scaling of the rotation number for perturbations of rational rotations Rhodes and C.L

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.361036Z

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 326eb605-a435-4741-b39e-df3fe2e8d114 · outbound

This paper cites an unresolved cited work.

Scaling of the rotation number for perturbations of rational rotations Unresolved cited work

Reference 28

Resolution: parse uncertain; raw_fallback, observed 2026-08-15T18:42:30.349627Z

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 3c8b0eba-aa03-4fe8-8ee0-828d67abb014 · outbound

This paper cites Simpson (2018) The structure of mode-locking regions of piecewise-linear con- tinuous maps: II.

Scaling of the rotation number for perturbations of rational rotations Simpson (2018) The structure of mode-locking regions of piecewise-linear con- tinuous maps: II

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:42:30.337004Z

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

No inbound Pith citation observations are available.