Paper Citation Record · LEDGER

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity

As of 22 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2607.21950.

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

pith.paper-citation-record.v1
2607.21950 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:43:03.695066Z

measured 44 of 44 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 2026-08-04T12:52:58.771204Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-04T18:16:12.699793Z

Reference resolution

43 of 43 outbound references displayed

verified exact13
verified fuzzy4
unresolved25
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e8d38c70-90c1-477d-8762-67ab37ac42ca · outbound

This paper cites Bellow, R.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Bellow, R

Reference 1

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.355352Z

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 435df6d7-c4de-4bc3-9b09-c7b91550065e · outbound

This paper cites Bellow, V.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Bellow, V

Reference 2

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.338377Z

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 ee8e7065-e493-46a9-9b2e-dc2bc353a5e4 · outbound

This paper cites Bourgain, On invariant tori of full dimension for 1D periodic NLS.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Bourgain, On invariant tori of full dimension for 1D periodic NLS

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.478815Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f710ea7f-ad18-4aa4-ad36-f1251cf874c9 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:43:04.550592Z

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 60242157-6fb1-4402-b4dc-6be721b6c883 · outbound

This paper cites Cheng, L.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Cheng, L

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.490766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 688f0b21-d390-4a0b-9b83-c23c42060ce0 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.496262Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75fdd5ac-f920-415f-85f4-6903d1e3d438 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.502582Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation efe2c3ef-1128-4721-b34a-75ba23da2271 · outbound

This paper cites del Junco, J.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity del Junco, J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.508156Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb177517-1f97-417a-8025-edf8a64af81b · outbound

This paper cites Duignan, J.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Duignan, J

Reference 9

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T15:43:04.445897Z

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 81c3b7c2-097a-4a7f-b3dd-f7f5f0a2a98f · outbound

This paper cites Durand, D.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Durand, D

Reference 10

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.252423Z

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 03a48033-7436-4e5c-810c-215919d31288 · outbound

This paper cites Fan, Weighted Birkhoff ergodic theorem with oscillating weights.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Fan, Weighted Birkhoff ergodic theorem with oscillating weights

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.524053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9239adcb-3d92-4186-adb1-0cdd751b4d00 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 12

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.216220Z

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 75db0e3c-89d6-4826-8a44-484f08e44eca · outbound

This paper cites Grafakos, Classical Fourier analysis.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Grafakos, Classical Fourier analysis

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.534821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 453a86d4-54d5-4c4f-9f3b-337850a9ccb3 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.540254Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef7076fa-c66c-4533-8927-46acb46b01c5 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.545479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b4d7648-a535-44cd-99ed-0c849be872ef · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 16

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.166158Z

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 99bedfda-ba5c-4731-81a2-01782f9f0c1b · outbound

This paper cites Kakutani, K.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Kakutani, K

Reference 17

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.148975Z

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 1f715e5e-44be-4ab1-a9f5-c98dc877ca24 · outbound

This paper cites Katznelson, The action of diffeomorphism of the circle on the Lebesgue measure.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Katznelson, The action of diffeomorphism of the circle on the Lebesgue measure

Reference 18

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.131959Z

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 8d5d26c3-40d2-41eb-812e-bef8f2620ef8 · outbound

This paper cites Katznelson, An introduction to harmonic analysis.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Katznelson, An introduction to harmonic analysis

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.566389Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d04db9b9-fd9e-4321-80f9-302010709876 · outbound

This paper cites Khanin, A.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Khanin, A

Reference 20

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.102656Z

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 516782ab-3866-4bde-9965-5e0d04aff187 · outbound

This paper cites Krengel, On the speed of convergence in the ergodic theorem.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Krengel, On the speed of convergence in the ergodic theorem

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.577279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f6b9a41-df7b-4ff8-bc7c-27e09dcb143d · outbound

This paper cites Laskar, Frequency analysis for multi-dimensional systems.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Laskar, Frequency analysis for multi-dimensional systems

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.582507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f0bb77d-5c71-4f1e-af3e-b7828abcf66c · outbound

This paper cites Laskar, Frequency analysis of a dynamical system.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Laskar, Frequency analysis of a dynamical system

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.587742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2370c5af-1858-4dac-bc2d-99c585022907 · outbound

This paper cites Laskar, Introduction to frequency map analysis.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Laskar, Introduction to frequency map analysis

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.592969Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb51e495-3d90-407a-84b8-fe540b3a0115 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 25

Resolution: verified exact; doi, observed 2026-08-15T15:43:04.041391Z

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 f9b063c1-1afc-4d46-a8b5-b116ac91e363 · outbound

This paper cites Montalto, M.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Montalto, M

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.603522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b401b084-cf48-40d4-ae6c-4534511fb2c2 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.609261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fac0b709-a054-4723-b3e6-d5fd1c236014 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.614935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d77a7cd6-fe92-4fa2-8864-3eeec7413154 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 29

Resolution: verified exact; doi, observed 2026-08-15T15:43:03.991539Z

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 b5db9592-80c3-410b-9449-909020bd1aec · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 30

Resolution: verified exact; doi, observed 2026-08-15T15:43:03.974278Z

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 9e8432af-8164-47bd-aa4b-924606e1a561 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.630579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51e74d44-0690-4c82-a41e-90c78a61e86d · outbound

This paper cites Slow convergence of Birkhoff ergodic averages.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Slow convergence of Birkhoff ergodic averages

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:43:03.945458Z

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 cff8df1d-2bbe-4112-97fe-c6527855c7c1 · outbound

This paper cites Slow convergence almost everywhere of ergodic averages.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Slow convergence almost everywhere of ergodic averages

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:43:03.920575Z

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 b6ea31f6-b349-4a01-acb6-7ee743cc31c5 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:43:04.533560Z

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 cfdf8e31-f7a8-4608-bc8e-40c3ee116f55 · outbound

This paper cites Stein, R.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Stein, R

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:43:04.516716Z

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 dfc2d326-f689-44f4-a0bd-8b9651666cd6 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.658973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fed3b1f8-fd85-40af-961e-f316e426f55a · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.663847Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd1325ed-1050-4223-82bf-ac7f759fe4b1 · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.668905Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86d3dcac-f110-43ff-a7aa-fe86a51c63fa · outbound

This paper cites an unresolved cited work.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.674096Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e55e2677-1016-4961-b264-7305ea3536c5 · outbound

This paper cites Optimal rates of uniform convergence for weighted Birkhoff averages via almost all rotations.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Optimal rates of uniform convergence for weighted Birkhoff averages via almost all rotations

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T15:43:03.679186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16c1b10b-fdfe-46b1-9e85-f2bd971330a0 · outbound

This paper cites Yoccoz, Sur la disparition de propri\' e t\' e s de type D enjoy- K oksma en dimension 2 , C.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Yoccoz, Sur la disparition de propri\' e t\' e s de type D enjoy- K oksma en dimension 2 , C

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:43:04.500009Z

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 cdfa9806-e8da-4a6a-9026-9aeda6294bd8 · outbound

This paper cites Yoccoz, Lin\' e arisation des germes de diff\' e omorphismes holomorphes de ( C , 0).

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Yoccoz, Lin\' e arisation des germes de diff\' e omorphismes holomorphes de ( C , 0)

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:43:04.481705Z

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 88a1055d-ef5b-4483-b9bd-fff8f9eef471 · outbound

This paper cites Yoccoz, Centralisateurs et conjugaison diff\' e rentiable des diff\' e omorphismes du cercle, Petits diviseurs en dimension 1 , Ast\' e risque No.

Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Yoccoz, Centralisateurs et conjugaison diff\' e rentiable des diff\' e omorphismes du cercle, Petits diviseurs en dimension 1 , Ast\' e risque No

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:43:04.465015Z

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 d9dc7f2c-60ac-4378-8cef-a91946de2f9c · inbound

Laskar's frequency map analysis revisited cites this paper.

Laskar's frequency map analysis revisited Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity

Reference 64

Resolution: verified exact; local_arxiv, observed 2026-08-04T12:53:20.934242Z

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.