Paper Citation Record · LEDGER

The Wiener Wintner Theorem Along the Primes

As of 11 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2601.10459.

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

pith.paper-citation-record.v1
2601.10459 v3

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T10:23:26.500473Z

measured 31 of 31 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-11T05:48:02.247560Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

30 of 30 outbound references displayed

verified exact2
verified fuzzy0
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f6f7ccd0-2955-4dd9-a1e8-40981065f12a · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:22.641377Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 586d042b-ea50-4195-acb5-cc3c0bfe799e · outbound

This paper cites Birkhoff,Proof of the ergodic theorem, Proceedings of the National Academy of Sciences17 (December 1931), no.

The Wiener Wintner Theorem Along the Primes Birkhoff,Proof of the ergodic theorem, Proceedings of the National Academy of Sciences17 (December 1931), no

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:22.786091Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8970a4c1-04c2-425a-b89d-67965e0191b0 · outbound

This paper cites Bourgain,Double recurrence and almost sure convergence, J.

The Wiener Wintner Theorem Along the Primes Bourgain,Double recurrence and almost sure convergence, J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:22.924154Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation baca013b-b64c-4196-b4b4-1fcdc9bcccb2 · outbound

This paper cites Hautes ´Etudes Sci.

The Wiener Wintner Theorem Along the Primes Hautes ´Etudes Sci

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.014142Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecf842ec-cf2f-4a56-a5fa-94aafc07a5bd · outbound

This paper cites Math.384 (2021), Paper No.

The Wiener Wintner Theorem Along the Primes Math.384 (2021), Paper No

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.120465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2b78355-63e2-4947-8ede-45c0f6ca35c4 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.242310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47068317-f21b-4a38-a53d-1e88cca25642 · outbound

This paper cites Lacey, Terence Tao, and Christoph Thiele,Breaking the duality in the return times theorem, Duke Math.

The Wiener Wintner Theorem Along the Primes Lacey, Terence Tao, and Christoph Thiele,Breaking the duality in the return times theorem, Duke Math

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.304122Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abc18164-89e2-412e-80fa-fba5ef9c5c62 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.369288Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d24788e-ee7f-4d87-b88f-24faf3699bdb · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 9

Resolution: verified exact; doi, observed 2026-08-03T10:29:16.580944Z

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 59befc5c-4df8-4754-bf09-1831668615a4 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.513831Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 680ee76f-0a71-413d-83b6-d61f99707527 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.632306Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 927d666a-5212-49de-a760-43e141ea7213 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.806341Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47e8000f-25c6-41c2-8edb-d8d6ae2748e6 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:23.945944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 50bf8864-2c53-4894-86e6-4a236676bc95 · outbound

This paper cites 53, American Mathematical Society, Providence, RI, 2004.

The Wiener Wintner Theorem Along the Primes 53, American Mathematical Society, Providence, RI, 2004

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:24.116322Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b663f133-b69f-4d9f-9bb6-43362274c50d · outbound

This paper cites 53, American Mathematical Soc., 2021.↑34.

The Wiener Wintner Theorem Along the Primes 53, American Mathematical Soc., 2021.↑34

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:24.277181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ceebe496-dbad-4854-8a67-af4cf3e6a6a9 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:24.437202Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1226c842-5a1a-4d57-9f00-a59658145a23 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:24.584033Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b4632dd-7501-4ead-adb5-5aa0f721ebbf · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:24.732377Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e74ac74-ba76-489e-b06b-5ca0983294be · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:24.854989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0d5fc73-917b-418a-b6bc-bbb1390a0a6d · outbound

This paper cites Efficient Equidistribution of Nilsequences.

The Wiener Wintner Theorem Along the Primes Efficient Equidistribution of Nilsequences

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.047468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7be4e22-b54b-4dc4-943a-517749c5205f · outbound

This paper cites Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm.

The Wiener Wintner Theorem Along the Primes Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s+1}[N]$-norm

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.176680Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c896231-edd9-4c22-be06-60abfc30a238 · outbound

This paper cites Lesigne,Spectre quasi-discret et th´ eor` eme ergodique de Wiener-Wintner pour les polynˆ omes, Ergodic Theory Dynam.

The Wiener Wintner Theorem Along the Primes Lesigne,Spectre quasi-discret et th´ eor` eme ergodique de Wiener-Wintner pour les polynˆ omes, Ergodic Theory Dynam

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.370582Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a280db1-390d-4dcd-aac8-de4d417d0dcc · outbound

This paper cites Rudolph,A joinings proof of Bourgain ’s return time theorem, Ergodic Theory Dynam.

The Wiener Wintner Theorem Along the Primes Rudolph,A joinings proof of Bourgain ’s return time theorem, Ergodic Theory Dynam

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.491513Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2aa47ae7-7b60-4b02-b01d-36592ff401d9 · outbound

This paper cites Math.131(1998), no.

The Wiener Wintner Theorem Along the Primes Math.131(1998), no

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.624899Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f64a3939-481f-4cc8-8489-5f6ef6f8c7e6 · outbound

This paper cites PDE5(2012), no.

The Wiener Wintner Theorem Along the Primes PDE5(2012), no

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.762469Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdeb2df4-ce4f-41f8-a2b0-315ff4225a01 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:25.979271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02e5f337-8f8f-4b4b-bc56-1a2a17856ed4 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:26.031090Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a90c2c28-9e4f-4f68-8a6b-62fb427ede25 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 28

Resolution: verified exact; doi, observed 2026-08-03T10:29:16.428147Z

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 529e5396-8af8-4274-b0cf-489285746734 · outbound

This paper cites an unresolved cited work.

The Wiener Wintner Theorem Along the Primes Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:26.339581Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 93f83ad9-df98-432c-9592-510bfeb79483 · outbound

This paper cites Math.64(1988), no.

The Wiener Wintner Theorem Along the Primes Math.64(1988), no

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T10:23:26.500473Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation a80176b1-8581-46dd-986f-74f1783fff5a · inbound

A Variation Norm Carleson Theorem Along the Primes cites this paper.

A Variation Norm Carleson Theorem Along the Primes The Wiener Wintner Theorem Along the Primes

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T05:48:02.247560Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.