Paper Citation Record · LEDGER

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections

As of 19 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2607.09358.

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

pith.paper-citation-record.v1
2607.09358 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-13T03:37:26.796410Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

34 of 34 outbound references displayed

verified exact15
verified fuzzy0
unresolved12
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malformed identifier7
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External citation measurements

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Outbound references

Observation c3e77202-eaca-4ff6-bcfb-4b8d30f4475d · outbound

This paper cites Multiple recurrence and popular differences for poly- nomial patterns in rings of integers.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Multiple recurrence and popular differences for poly- nomial patterns in rings of integers

Reference 1

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.680897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f270e666-a9aa-4fa7-9e35-f92b2df124bb · outbound

This paper cites Multiple recurrence and large intersec- tions for abelian group actions.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Multiple recurrence and large intersec- tions for abelian group actions

Reference 2

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.696039Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c2051bfd-aa08-4218-8f96-8c72763e5c24 · outbound

This paper cites Khintchine-type recurrence for 3-point configurations.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Khintchine-type recurrence for 3-point configurations

Reference 3

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.686189Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cd6be720-aa2b-48e6-92c2-2d4ee6fab923 · outbound

This paper cites On the maximal spectral type of nil- systems.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections On the maximal spectral type of nil- systems

Reference 4

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.676214Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation db7dcace-a20d-4c36-8619-2f93f7121ca6 · outbound

This paper cites Minimal idempotents and ergodic Ramsey theory.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Minimal idempotents and ergodic Ramsey theory

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 302664a1-5749-42f3-810e-d6fbc5596c99 · outbound

This paper cites Weakly mixing PET.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Weakly mixing PET

Reference 6

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.668745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d04813c-f31a-4b06-bdbe-dacb09e080f6 · outbound

This paper cites Cubic averages and large intersections.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Cubic averages and large intersections

Reference 7

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.648110Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 91ddc0c9-d87e-4808-aad8-3b8ace5df08c · outbound

This paper cites Rigidity and non- recurrence along sequences.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Rigidity and non- recurrence along sequences

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation 7f10cfc1-16c3-40c8-bf39-1f179f5f5f54 · outbound

This paper cites Ergodic Ramsey theory—an update.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Ergodic Ramsey theory—an update

Reference 9

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.656717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a2826273-8134-43f4-8a01-dd845858fad0 · outbound

This paper cites Ultrafilters, IP sets, dynamics, and combinatorial number theory.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Ultrafilters, IP sets, dynamics, and combinatorial number theory

Reference 10

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.730657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c6dc3d7e-6c9a-4f8e-a2f2-d8e0d843ea29 · outbound

This paper cites IP-sets and polynomial recur- rence.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections IP-sets and polynomial recur- rence

Reference 11

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.633774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b986adeb-1905-4f87-94c6-ab088104c549 · outbound

This paper cites IP-systems, generalized polynomials and recurrence.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections IP-systems, generalized polynomials and recurrence

Reference 12

Resolution: malformed identifier; doi_truncated, observed 2026-07-13T03:39:17.700769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1d4a6f54-bd81-421a-8d08-479ca4f71301 · outbound

This paper cites Multiple recurrence and nilsequences.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Multiple recurrence and nilsequences

Reference 13

Resolution: malformed identifier; doi_truncated, observed 2026-07-13T03:39:17.718805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation caf7a122-9b52-493e-97e8-7610d61d1c7c · outbound

This paper cites Aspects of unifor- mity in recurrence.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Aspects of unifor- mity in recurrence

Reference 14

Resolution: malformed identifier; doi_truncated, observed 2026-07-13T03:39:17.706756Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3fab1d99-0046-42a8-8685-08f701e8d1d3 · outbound

This paper cites An ergodic IP polynomial Szemer ´edi theorem.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections An ergodic IP polynomial Szemer ´edi theorem

Reference 15

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.711124Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 99247b38-bebd-4e30-a295-41a50720adf9 · outbound

This paper cites Multiple ergodic averages along func- tions from a Hardy field: convergence, recurrence and combinatorial applications.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Multiple ergodic averages along func- tions from a Hardy field: convergence, recurrence and combinatorial applications

Reference 16

Resolution: malformed identifier; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation 1c23913b-15e2-4fc0-a88c-da1b56d28add · outbound

This paper cites an unresolved cited work.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation d05536c2-71e7-4e18-8e87-8b7cdc7e8b5c · outbound

This paper cites Under-recurrence in the Khint- chine recurrence theorem.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Under-recurrence in the Khint- chine recurrence theorem

Reference 18

Resolution: malformed identifier; doi_truncated, observed 2026-07-13T03:39:17.638237Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b68d57f3-6cf1-412c-b364-0e55530cfd9c · outbound

This paper cites Resolving the joint ergodicity problem for Hardy sequences.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Resolving the joint ergodicity problem for Hardy sequences

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation b42becb2-26d5-4c18-afbd-f428be544b0c · outbound

This paper cites Optimal lower bounds for multiple recurrence.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Optimal lower bounds for multiple recurrence

Reference 20

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.723506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f2b49466-cf08-4286-bd33-f245d2a29021 · outbound

This paper cites Ergodic averages for independent polynomials and appli- cations.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Ergodic averages for independent polynomials and appli- cations

Reference 21

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.664735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 970814bb-6682-49c3-a76b-cf57e6241004 · outbound

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

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Polynomial averages converge to the product of integrals

Reference 22

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.660617Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a40839d9-a022-4ba2-af1b-f4a67284dc71 · outbound

This paper cites Joint ergodicity for commuting transformations and ap- plications to polynomial sequences.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Joint ergodicity for commuting transformations and ap- plications to polynomial sequences

Reference 23

Resolution: malformed identifier; doi_truncated, observed 2026-07-13T03:39:17.652647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ba20fe4f-3cbe-4bb9-9302-aa03e38c9412 · outbound

This paper cites An ergodic Szemer ´edi theorem for IP-systems and combi- natorial theory.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections An ergodic Szemer ´edi theorem for IP-systems and combi- natorial theory

Reference 24

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.642870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6e478307-27fd-4090-b7ae-ec0553878070 · outbound

This paper cites A mean ergodic theorem for (1/N)PN n=1 f(T nx)g(T n2 x).

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections A mean ergodic theorem for (1/N)PN n=1 f(T nx)g(T n2 x)

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation 91c80a49-ba12-440c-a467-e67bbd5a3c80 · outbound

This paper cites Ergodic behaviour of diagonal measures and a theorem of Szemer ´edi on arith- metic progressions.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Ergodic behaviour of diagonal measures and a theorem of Szemer ´edi on arith- metic progressions

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation 2302ce19-c9c3-4723-98ac-1689a2f9b990 · outbound

This paper cites Nonconventional ergodic averages and nilmanifolds.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Nonconventional ergodic averages and nilmanifolds

Reference 27

Resolution: malformed identifier; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation 184e7409-24d7-4dad-b339-353755214dc7 · outbound

This paper cites an unresolved cited work.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation 2ad4eb00-c3bd-4743-b163-f7a78dd95f98 · outbound

This paper cites Ergodic averages and the large intersection property along IP sets.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Ergodic averages and the large intersection property along IP sets

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 624cf5a9-cde4-4193-8dd8-e798a62fd7b5 · outbound

This paper cites Convergence of multiple ergodic averages along polynomials of several vari- ables.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Convergence of multiple ergodic averages along polynomials of several vari- ables

Reference 30

Resolution: verified exact; doi, observed 2026-07-13T03:39:17.691748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 39061f80-d24b-430b-9e30-fa9a46da034b · outbound

This paper cites Pointwise convergence of ergodic averages for polynomial sequences of transla- tions on a nilmanifold.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Pointwise convergence of ergodic averages for polynomial sequences of transla- tions on a nilmanifold

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e3302e3f-10c6-4cc8-b231-504852614895 · outbound

This paper cites Multiple ergodic averages in abelian groups and Khintchine type recurrence.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Multiple ergodic averages in abelian groups and Khintchine type recurrence

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation d0a646a0-f9c6-4cfd-b1a0-d3f4518f1e76 · outbound

This paper cites On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections On the Furstenberg-Katznelson constant for the IP Szemeredi theorem over finite fields

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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Unavailable: canonical work link unavailable.

Observation fad660da-fb1a-4d20-bbed-d0c0c133a765 · outbound

This paper cites Universal characteristic factors and Furstenberg averages.

$\mathrm{IP}_{\mathrm{rat}}$-polynomial recurrence and large intersections Universal characteristic factors and Furstenberg averages

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-13T03:37:26.796410Z

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