Paper Citation Record · LEDGER

On weighted multilinear polynomial averages in finite fields

As of 12 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 1 inbound Pith citation observation for arXiv:2507.14414.

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

pith.paper-citation-record.v1
2507.14414 v1

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:21:36.203401Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T00:46:02.796948Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

17 of 17 outbound references displayed

verified exact1
verified fuzzy7
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 168b940d-97cd-4863-9ce2-93fdd5cb818a · outbound

This paper cites Bourgain and M.-C.

On weighted multilinear polynomial averages in finite fields Bourgain and M.-C

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:34.270692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f7348f3-411f-44b5-866c-cd621a7eb079 · outbound

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

On weighted multilinear polynomial averages in finite fields Improved estimates for polynomial R oth type theorems in finite fields

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:34.361821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 842326e3-40f1-4965-847c-07fb4eeb16f9 · outbound

This paper cites Multiple ergodic theorems for arithmetic sets.

On weighted multilinear polynomial averages in finite fields Multiple ergodic theorems for arithmetic sets

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.883466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 92c5bc03-0ba7-4ab8-95fd-b28ee0bdd7fb · outbound

This paper cites Multiple recurrence and convergence for sequences related to the prime numbers.

On weighted multilinear polynomial averages in finite fields Multiple recurrence and convergence for sequences related to the prime numbers

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.870434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 07214a8d-3483-43e6-921c-a561cd0988b4 · outbound

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

On weighted multilinear polynomial averages in finite fields Polynomial averages converge to the product of integrals

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:34.686674Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 233c7903-b410-4e40-9d99-0582ee0f6725 · outbound

This paper cites Convergence of polynomial ergodic averages.

On weighted multilinear polynomial averages in finite fields Convergence of polynomial ergodic averages

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.851185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f445ee84-6dc5-4599-a15c-244b41b14299 · outbound

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

On weighted multilinear polynomial averages in finite fields Three T erm R ational F unction P rogressions in F inite F ields

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:34.905357Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3560c01f-3f64-4e54-adfc-8d5c57f06e42 · outbound

This paper cites Lacey, and Fan Yang.

On weighted multilinear polynomial averages in finite fields Lacey, and Fan Yang

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.831942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 523a3543-b304-480b-a3df-20d4485d1bc7 · outbound

This paper cites Multidimensional polynomial patterns over finite fields: bounds, counting estimates and G owers norm control.

On weighted multilinear polynomial averages in finite fields Multidimensional polynomial patterns over finite fields: bounds, counting estimates and G owers norm control

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.821239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 249486f6-7df4-4653-ba62-e59ad2599bb7 · outbound

This paper cites Multidimensional polynomial S zemer\'edi theorem in finite fields for polynomials of distinct degrees.

On weighted multilinear polynomial averages in finite fields Multidimensional polynomial S zemer\'edi theorem in finite fields for polynomials of distinct degrees

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.809024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation eb389bb2-7f35-4c04-8eab-6372d9093080 · outbound

This paper cites an unresolved cited work.

On weighted multilinear polynomial averages in finite fields Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:21:36.796524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7662242a-c75a-44cf-b0f3-91b2cd98c3b2 · outbound

This paper cites Uniform nonlinear Szemer\'{e}di theorem for corners in finite fields.

On weighted multilinear polynomial averages in finite fields Uniform nonlinear Szemer\'{e}di theorem for corners in finite fields

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:35.588146Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9fbddd6-e7a8-4837-9eda-6a407e6904e1 · outbound

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

On weighted multilinear polynomial averages in finite fields Three-term polynomial progressions in subsets of finite fields

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:35.690692Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16ebf76b-c5a9-479a-b9e9-0f78fa39dc42 · outbound

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

On weighted multilinear polynomial averages in finite fields On the polynomial S zemer\'edi theorem in finite fields

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T16:21:35.796670Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3a560228-ed58-4889-963c-8a0dfe143a95 · outbound

This paper cites Pointwise convergence of ergodic averages with M\"obius weight.

On weighted multilinear polynomial averages in finite fields Pointwise convergence of ergodic averages with M\"obius weight

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:21:36.448661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9b709408-f752-45dc-8281-19f1b4d1b7cb · outbound

This paper cites an unresolved cited work.

On weighted multilinear polynomial averages in finite fields Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T16:21:36.769857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bfd46518-63e4-4385-a614-30dba3cc6ba0 · outbound

This paper cites Wooley and Tamar D.

On weighted multilinear polynomial averages in finite fields Wooley and Tamar D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T16:21:36.661060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation af4afcb1-dd66-4377-93cf-505a1710f6e9 · inbound

Simultaneous popular polynomial differences over finite fields cites this paper.

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-14T00:46:02.796948Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.