Paper Citation Record · LEDGER

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus

As of 21 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 2 inbound Pith citation observations for arXiv:2507.14407.

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

pith.paper-citation-record.v1
2507.14407 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:15:47.880544Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-18T23:24:49.594490Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T23:26:53.987702Z

Reference resolution

30 of 30 outbound references displayed

verified exact2
verified fuzzy24
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 367a8fca-2c8c-40fe-b720-8bed05cf8425 · outbound

This paper cites Bourgain and M.-C.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Bourgain and M.-C

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.532773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9031adab-a447-426b-8d32-0d064a00d520 · outbound

This paper cites Bergelson and A.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Bergelson and A

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T16:15:43.373662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 03ebf6b5-f680-4f73-bf86-d98c806174e5 · outbound

This paper cites Bourgain.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Bourgain

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.505246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9e4786dd-7020-47a0-bdfc-67c4c972144a · outbound

This paper cites Two-point patterns determined by curves.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Two-point patterns determined by curves

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:15:48.407555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 61817643-ee5d-49d1-a426-40af73b23345 · outbound

This paper cites Pointwise convergence of certain continuous-time double ergodic averages.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Pointwise convergence of certain continuous-time double ergodic averages

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.489129Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ff529a7e-8907-4dc3-9cb3-d76be0132c0c · outbound

This paper cites Two bipolynomial R oth theorems in R.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Two bipolynomial R oth theorems in R

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.472414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 65e74e92-c98a-4636-b352-b2b6578da543 · outbound

This paper cites A polynomial R oth theorem on the real line.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus A polynomial R oth theorem on the real line

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.423987Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 544df912-a61f-4d81-8e28-7b6a84460d68 · outbound

This paper cites Improved estimates for polynomial R oth type theorems in finite fields.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Improved estimates for polynomial R oth type theorems in finite fields

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.216901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7d2d6fc0-8f4d-481d-bf07-f303eb13839b · outbound

This paper cites A new proof of an inequality of B ourgain.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus A new proof of an inequality of B ourgain

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:52.083096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8cfb0a9f-ab6d-4acf-af15-e9891320f2f7 · outbound

This paper cites Polynomial R oth theorems on sets of fractional dimensions.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Polynomial R oth theorems on sets of fractional dimensions

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:51.942602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7014da3c-f0ef-4909-b291-f6378a0c5ad5 · outbound

This paper cites Polynomial averages converge to the product of integrals.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Polynomial averages converge to the product of integrals

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:51.839780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 07570a84-e9ff-4491-a1ac-4c787d89354a · outbound

This paper cites Joint ergodicity for commuting transformations and applications to polynomial sequences.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Joint ergodicity for commuting transformations and applications to polynomial sequences

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:51.758419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a96addf5-6071-4148-9644-c70853ae1468 · outbound

This paper cites Frantzikinakis, E.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Frantzikinakis, E

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:51.648545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6d4470de-ea5a-4a56-9d68-817237a46759 · outbound

This paper cites Joint ergodicity of sequences.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Joint ergodicity of sequences

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:51.420633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 90b1c5a7-4af0-408e-b1d8-e390e97cd35f · outbound

This paper cites Three T erm R ational F unction P rogressions in F inite F ields.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Three T erm R ational F unction P rogressions in F inite F ields

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:51.244208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ee5af451-28f5-4226-a465-3a57d7c8f80d · outbound

This paper cites A 1-dimensional subset of the reals that intersects each of its translates in at most a single point.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus A 1-dimensional subset of the reals that intersects each of its translates in at most a single point

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:50.965558Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5715ba9f-9dfc-4f9c-a667-4598c6811731 · outbound

This paper cites The multilinear circle method and a question of bergelson.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus The multilinear circle method and a question of bergelson

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T16:15:46.698945Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c36de6df-4efe-46f8-ac9f-96a427a55de9 · outbound

This paper cites Polynomial progressions in topological fields.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Polynomial progressions in topological fields

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:50.683254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8ae118a8-4b2e-4683-9bb3-bfd947c1556d · outbound

This paper cites On a continuous S \'ark\"ozy-type problem.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus On a continuous S \'ark\"ozy-type problem

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:50.382786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 32aacbdc-12b0-44a7-ba2a-ee5d7e552ba4 · outbound

This paper cites A Non-Linear Roth Theorem for Fractals of Sufficiently Large Dimension.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus A Non-Linear Roth Theorem for Fractals of Sufficiently Large Dimension

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T16:15:46.992470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 522ea022-8c2f-451a-8ec8-d1ecaab4c327 · outbound

This paper cites Discrete analogues in harmonic analysis: Bourgain, Stein, and beyond , volume 224.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Discrete analogues in harmonic analysis: Bourgain, Stein, and beyond , volume 224

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:50.116627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6fe507e9-13de-4a52-bd33-e14be5b07da5 · outbound

This paper cites Arithmetic progressions in sets of fractional dimension.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Arithmetic progressions in sets of fractional dimension

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:49.778070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation bd51ed36-cabb-48a7-88fc-8e46c567c057 · outbound

This paper cites Fourier analysis and Hausdorff dimension , volume 150.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Fourier analysis and Hausdorff dimension , volume 150

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:49.484019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 89e33ca6-a391-412e-abca-d831110d8e67 · outbound

This paper cites Three-term polynomial progressions in subsets of finite fields.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Three-term polynomial progressions in subsets of finite fields

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:49.344634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7f741c63-9e47-4554-8585-20b50411534c · outbound

This paper cites On the polynomial S zemer\'edi theorem in finite fields.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus On the polynomial S zemer\'edi theorem in finite fields

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:49.173973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation e4ca9039-0275-4371-9942-837a7bab3a49 · outbound

This paper cites Quantitative bounds in the nonlinear R oth theorem.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Quantitative bounds in the nonlinear R oth theorem

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:49.002372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9955fa4a-a4a8-45cf-b2a4-c68d761b315f · outbound

This paper cites Stein and Stephen Wainger.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Stein and Stephen Wainger

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:48.782593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d25571c0-8703-4482-b0e0-84feb01f142a · outbound

This paper cites Szemerédi.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Szemerédi

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:15:48.583099Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f99ceea5-76dc-4c22-a2e3-b9fa62f24fdc · outbound

This paper cites Additive combinatorics , volume 105.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus Additive combinatorics , volume 105

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T16:15:47.776597Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c527b4a-4ae5-460e-994e-bad431edc5bc · outbound

This paper cites A quadratic Roth theorem for sets with large Hausdorff dimensions.

Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus A quadratic Roth theorem for sets with large Hausdorff dimensions

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:15:48.082548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation 2c044525-b94b-4169-b19b-295851fa6aee · inbound

On Multi-linear Maximal Operators Along Homogeneous Curves cites this paper.

On Multi-linear Maximal Operators Along Homogeneous Curves Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-18T23:26:53.991740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 12f639ed-b913-4542-962e-d54ad88e3af5 · inbound

A curved three-point pattern problem for fractal sets on the real line cites this paper.

A curved three-point pattern problem for fractal sets on the real line Polynomial Szemer\'edi for sets with large Hausdorff dimension on the Torus

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-05-12T08:41:25.908975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.