Paper Citation Record · LEDGER

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem

As of 21 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2607.05124.

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

pith.paper-citation-record.v1
2607.05124 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T08:27:11.812739Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+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

36 of 36 outbound references displayed

verified exact0
verified fuzzy0
unresolved36
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c4e51672-ab6f-46fb-9b45-651cbd56ee78 · outbound

This paper cites BERGELSON, B.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem BERGELSON, B

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

Source-reported events for the cited work

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Observation 47c32d37-4a51-4cbe-9fc6-4d1aac75ff33 · outbound

This paper cites BERGELSON ANDA.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem BERGELSON ANDA

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 2673caf1-77a3-4238-bd8f-e6bb1b6e9079 · outbound

This paper cites BERGELSON ANDA.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem BERGELSON ANDA

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation e2f883cb-c383-4626-a392-f81e684592b9 · outbound

This paper cites Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 9982c007-8134-4726-a304-f814fd644528 · outbound

This paper cites BOURGAIN,A Szemer ´edi type theorem for sets of positive density inR k, Israel Journal of Mathematics, 54 (1986), no.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem BOURGAIN,A Szemer ´edi type theorem for sets of positive density inR k, Israel Journal of Mathematics, 54 (1986), no

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 65387e14-b1a3-41c7-baa4-e40221bfe4cf · outbound

This paper cites BOURGAIN,A nonlinear version of Roth’s theorem for sets of positive density in the real line,Journal d’Analyse Math´ematique, 50(1988), 169–181.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem BOURGAIN,A nonlinear version of Roth’s theorem for sets of positive density in the real line,Journal d’Analyse Math´ematique, 50(1988), 169–181

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 7f66d3c5-2865-4d64-aadd-442302b38d32 · outbound

This paper cites CALDER ´ON,Ergodic theory and translation invariant operators, Proceedings of the National Academy of Sciences of the United States of America, 59(1968), 349-353.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem CALDER ´ON,Ergodic theory and translation invariant operators, Proceedings of the National Academy of Sciences of the United States of America, 59(1968), 349-353

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation a479bb75-d101-4b89-a8eb-fb504f997165 · outbound

This paper cites CHEN ANDJ.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem CHEN ANDJ

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

Source-reported events for the cited work

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Observation 0d22fd09-e86e-4bd5-adaa-5e24a8d85560 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

Source-reported events for the cited work

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Observation 7bdc86b6-a057-46af-9449-8f6686d9065d · outbound

This paper cites CHEN ANDC.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem CHEN ANDC

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

Source-reported events for the cited work

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Observation 5035becb-9f75-42d6-bf95-89419ebc0e74 · outbound

This paper cites On Trilinear Oscillatory Integral Inequalities and Related Topics.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem On Trilinear Oscillatory Integral Inequalities and Related Topics

Reference 11

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Observation db3dfbec-dd84-4e34-8f03-49c418f8978c · outbound

This paper cites CHRIST, P.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem CHRIST, P

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 278abe93-ea75-4c27-b26b-588ab3b919f0 · outbound

This paper cites CHRIST, P.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem CHRIST, P

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation e6064358-e0b6-4823-8184-867918485d3a · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation a9ea87aa-3ad9-4a5c-9bec-0c76ec9e5406 · outbound

This paper cites DURCIK, S.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem DURCIK, S

Reference 15

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Observation 360b548f-b57a-4314-932e-9a6529b8c3e6 · outbound

This paper cites ERD ˝OS ANDP.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem ERD ˝OS ANDP

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation e70d9f83-1649-4034-bee3-4a4ec7de638a · outbound

This paper cites FRANTZIKINAKIS,Joint ergodicity of sequences, Advances in Mathematics, 417 (2023), p.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem FRANTZIKINAKIS,Joint ergodicity of sequences, Advances in Mathematics, 417 (2023), p

Reference 17

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Observation 83c1070f-2a25-42dd-9cf1-e1feaf215b2d · outbound

This paper cites FURSTENBERG,Ergodic behavior of diagonal measures and a theorem of sze- mer´edi on arithmetic progressions, Journal d’Analyse Math´ematique, 31 (1977), pp.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem FURSTENBERG,Ergodic behavior of diagonal measures and a theorem of sze- mer´edi on arithmetic progressions, Journal d’Analyse Math´ematique, 31 (1977), pp

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 1ea5006f-96b5-41fb-b7bd-541393539db1 · outbound

This paper cites FURSTENBERG, Y.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem FURSTENBERG, Y

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation e3cd343c-c33a-478c-b0e1-6f0515413108 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 2a28ff69-f634-48e1-9cdf-69a16cb78084 · outbound

This paper cites GRAFAKOS,Classical Fourier analysis, volume 249.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem GRAFAKOS,Classical Fourier analysis, volume 249

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 25f438ad-476c-4eb5-80ff-4bb0fb2021d1 · outbound

This paper cites GREEN ANDT.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem GREEN ANDT

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 00c7ed24-6f7d-4ebb-9fdf-46609e1f10c6 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 9eb591fe-fcdf-495e-a6de-44d0d15ba5ce · outbound

This paper cites KELLEY ANDR.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem KELLEY ANDR

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 72b52503-9df3-4f31-86c5-67ca0805a333 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 4c7684e9-5049-4b41-9f24-87c259702fa8 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 70d2cee4-030a-4b0f-a2ce-c02d20a6f79d · outbound

This paper cites KRAUSE, M.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem KRAUSE, M

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation a29a2dc4-0cbf-4bb3-b0f9-c502371f5722 · outbound

This paper cites KRAUSE, M.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem KRAUSE, M

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 0f2bf7d6-faaf-456e-a982-68682553b1ea · outbound

This paper cites LI,Bilinear Hilbert transforms along curves, I: the monomial case, Analysis & PDE, 6 (2013), no.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem LI,Bilinear Hilbert transforms along curves, I: the monomial case, Analysis & PDE, 6 (2013), no

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 4a1ea57c-afa2-479e-ae9a-41617c0d4b2c · outbound

This paper cites MIREK, T.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem MIREK, T

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation d96693a6-373e-4f04-9cfd-c0607fe8b9a5 · outbound

This paper cites PELUSE ANDS.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem PELUSE ANDS

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 739ba0ee-fab1-4684-a906-83cab05b3f60 · outbound

This paper cites PELUSE, S.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem PELUSE, S

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 9cbc7f36-bef2-4ff4-8230-2e7b07c1f0b4 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Observation 437f6a9b-207f-4d3f-ad7b-d237c9a717b6 · outbound

This paper cites SANDERS,On roth’s theorem on progressions, Annals of Mathematics, 174(2011), no.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem SANDERS,On roth’s theorem on progressions, Annals of Mathematics, 174(2011), no

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

Source-reported events for the cited work

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Observation 0a1a941f-05ae-41d4-a28b-6b8c55f1e1c5 · outbound

This paper cites SZEMER ´EDI,On sets of integers containing no k elements in arithmetic progres- sion, Acta Arith, 27 (1975), p.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem SZEMER ´EDI,On sets of integers containing no k elements in arithmetic progres- sion, Acta Arith, 27 (1975), p

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Unavailable: canonical work link unavailable.

Observation eac0f1a4-b56d-4dd8-836a-00660b8ecb36 · outbound

This paper cites an unresolved cited work.

A Roth theorem in $\mathbb R^2$ and a related ergodic theorem Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-11T08:27:11.812739Z

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Pith citing papers

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