Paper Citation Record · LEDGER

Pair correlation of $\alpha n^{\theta}$ for random $\theta$

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2606.03781.

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

pith.paper-citation-record.v1
2606.03781 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T08:32:26.456964Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

37 of 37 outbound references displayed

verified exact5
verified fuzzy0
unresolved32
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 927a7b44-66d0-49b0-a2ad-63efee2415f5 · outbound

This paper cites Aistleitner, S.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Aistleitner, S

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74f937bc-6873-4e16-9eae-76052ed0ff27 · outbound

This paper cites Aistleitner, D.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Aistleitner, D

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f946036-6e13-4949-9a6f-efaf5c6dfc34 · outbound

This paper cites Aistleitner, T.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Aistleitner, T

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b05660d9-420d-43a9-bf6b-d2d19a610728 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 89dcc799-f18a-4e32-9483-9f3cb74b9ac3 · outbound

This paper cites Bourgain.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Bourgain

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 083291d9-2302-4017-98bb-b9810c492119 · outbound

This paper cites Browning and I.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Browning and I

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5162366-1aba-482e-b4be-5fdf9a97ad85 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee924862-d719-4dce-ad2b-f8e5d0ed7c75 · outbound

This paper cites El-Baz, J.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ El-Baz, J

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f480fa8-1218-4dc5-9ec9-aa5c2a015082 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a45dc820-e469-4c42-b8fb-cf22e9d489b0 · outbound

This paper cites Grepstad and G.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Grepstad and G

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c371275-79a2-4448-bb18-3a806d179a57 · outbound

This paper cites The bad and rough rotation is Poissonian.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ The bad and rough rotation is Poissonian

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-02T05:06:40.074703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9b2be9fe-8e36-4054-b2cc-05e733803589 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07eb9059-3c7c-48f9-8ff0-4a3e5b52290a · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38ca3895-1ecd-4db3-b030-a3c482905279 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4931ffdf-b9d2-416a-92a1-7275fccbe81f · outbound

This paper cites Iwaniec and E.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Iwaniec and E

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0583a536-c8ea-4398-a3ca-4b4264c4c5a6 · outbound

This paper cites Metric Poissonian pair correlation for real sequences and energy estimates.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Metric Poissonian pair correlation for real sequences and energy estimates

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-07-02T05:06:40.080828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4640c115-1cda-4067-98ff-5da4ea4aa6c7 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7da622d9-9718-4389-b025-3c073252b0bf · outbound

This paper cites Kuipers and H.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Kuipers and H

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e668ad5-8252-49cd-a16f-82bb0f244940 · outbound

This paper cites Larcher and W.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Larcher and W

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2ab05f22-c972-4ab8-9d3c-858c3004485b · outbound

This paper cites Poissonian correlations of $\alpha n^d$ mod $1$.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Poissonian correlations of $\alpha n^d$ mod $1$

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-07-02T05:06:40.070003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a961bde4-3015-45aa-823f-6f12fd394749 · outbound

This paper cites Lutsko, A.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Lutsko, A

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6b9fa3bd-4379-45aa-ad5a-ff633519908d · outbound

This paper cites Lutsko and N.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Lutsko and N

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 31eec1a4-1cff-4536-848f-8b2d38618093 · outbound

This paper cites Lutsko and N.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Lutsko and N

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2e27f56-6204-4332-b90d-63a46bf6fd13 · outbound

This paper cites Marklof and A.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Marklof and A

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90c9e04c-12a2-4b50-b04f-07cbd2ac7855 · outbound

This paper cites Radziwi l l and A.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Radziwi l l and A

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6690d383-e8c6-4e58-8b3c-bbff083b11ec · outbound

This paper cites Radziwi l l and N.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Radziwi l l and N

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-07-02T05:06:40.072423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e6b0209a-c896-4fdf-913f-9c025030a21a · outbound

This paper cites Robert and P.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Robert and P

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db649e6a-ad86-47fa-8ad5-c9db37bd440c · outbound

This paper cites Rudnick and P.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and P

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6effc9af-3be7-4675-b20b-efdd68563a2c · outbound

This paper cites Rudnick, P.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick, P

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59ccb2f2-66c0-47aa-ba0f-a9f85a4c20b4 · outbound

This paper cites Rudnick and N.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and N

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8947245c-d87f-4b8e-a7bc-47105d65e7c9 · outbound

This paper cites Rudnick and N.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and N

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e42c460-c5a8-4e05-b284-6f28d7c66cb6 · outbound

This paper cites Rudnick and A.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Rudnick and A

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45a6a296-8810-42c7-926b-76834712f3bc · outbound

This paper cites New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-07-02T05:06:40.077483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 21ddbe07-9b08-42f3-9328-fa08c2e0a94c · outbound

This paper cites Technau and N.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Technau and N

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7f6a176-2da5-424e-bf38-c6f661a9ec47 · outbound

This paper cites Tenenbaum.Introduction ` a la th´ eorie analytique et probabiliste des nombres.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Tenenbaum.Introduction ` a la th´ eorie analytique et probabiliste des nombres

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 97566031-c211-40fa-9482-157809eb2837 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1620732a-d62c-47ae-9402-e1ed43d6fa77 · outbound

This paper cites an unresolved cited work.

Pair correlation of $\alpha n^{\theta}$ for random $\theta$ Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-28T08:32:26.456964Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.