Paper Citation Record · LEDGER

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices

As of 22 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2607.01655.

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

pith.paper-citation-record.v1
2607.01655 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-03T05:28:19.448298Z

measured 36 of 36 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 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 fuzzy22
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b01e33c3-82a9-4adb-bc6c-8bb9f621b86e · outbound

This paper cites Bourgain, M.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Bourgain, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.370179Z

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 e4875ee3-a469-4c51-ab47-7b2b67702654 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.342327Z

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 0143c367-47d1-4d11-b88b-4818004d1c21 · outbound

This paper cites Erd˝ os, A.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Erd˝ os, A

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.345822Z

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 0df8c842-889a-4c3b-9bbc-4df15550e24b · outbound

This paper cites Bauerschmidt, A.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Bauerschmidt, A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.338296Z

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 a1abd1e7-4a8e-47ea-a6b9-b1814040ac8d · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.387237Z

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 da545ffb-12e5-4cbe-a992-e052dcdf8aed · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.380452Z

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 b247dcc7-e42d-4d21-af4d-7f8bdedab0c5 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.410463Z

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 e58bf490-0249-4fb7-998b-91235afc8a72 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.327476Z

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 77740205-abc0-4ddf-ac42-75fe704664cc · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.331420Z

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 db86ec40-50f6-4596-826b-46e67ef400da · outbound

This paper cites Nica and R.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Nica and R

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.307214Z

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 dde9072d-6fbd-493b-963e-dd3601123d3c · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.314720Z

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 513dff90-b723-4f25-87a5-9e03d567a6ba · outbound

This paper cites Bercovici and D.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Bercovici and D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.318122Z

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 8ebc29cc-c213-427e-8e8d-c17df8edb3ed · outbound

This paper cites Hiai and D.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Hiai and D

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.335298Z

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 0b69f5cf-13e8-4dac-88aa-e704f618bc33 · outbound

This paper cites independence.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices independence

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.323629Z

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 a19365b1-c7c4-4b0f-a960-360302f1075b · outbound

This paper cites Mai and R.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Mai and R

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.295967Z

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 cec0ad73-d14c-4f6d-b2ac-c16b1ad78791 · outbound

This paper cites Lancien, P.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Lancien, P

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.383983Z

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 e6e2cea7-4121-4cda-9671-2d0a592bb204 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.394027Z

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 4865545b-cbca-4bd9-a91f-16489d22f3b4 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.367570Z

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 885930d5-2ac4-402b-9b98-3b35023480b7 · outbound

This paper cites Deift,Orthogonal Polynomials and Random Matrices: A Riemann–Hilbert Approach, Courant Lecture Notes in Mathematics, vol.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Deift,Orthogonal Polynomials and Random Matrices: A Riemann–Hilbert Approach, Courant Lecture Notes in Mathematics, vol

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.373848Z

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 f385c3d3-6fdd-4336-ba53-ff0f7c0c03a2 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.419863Z

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 84bd7605-00cf-4dd4-bca5-982716fe7915 · outbound

This paper cites Pastur and M.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Pastur and M

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.416750Z

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 80f53390-ac01-42d1-9b60-9d21c8067b71 · outbound

This paper cites Erd˝ os and H.-T.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Erd˝ os and H.-T

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.358657Z

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 3b33780b-efda-4ef0-9fc1-2975f536cf5b · outbound

This paper cites Weyl, ¨Uber die Gleichverteilung von Zahlen mod Eins, Math.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Weyl, ¨Uber die Gleichverteilung von Zahlen mod Eins, Math

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.364883Z

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 0fe5607b-e615-43df-a80a-e702b17d597d · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.355649Z

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 cc023631-3dd5-4706-aef9-344aad30f6d3 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.413453Z

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 2ea522e3-d7e4-4bf2-b081-ec30d8fda2f0 · outbound

This paper cites Rudnick, P.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Rudnick, P

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.349004Z

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 924c9270-285e-4e95-a3a5-68e19777c2c0 · outbound

This paper cites Adhikari, M.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Adhikari, M

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.352301Z

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 8efdf599-a195-480f-aabc-baeb0705c01e · outbound

This paper cites Ratner,On Raghunathan’s measure conjecture, Ann.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Ratner,On Raghunathan’s measure conjecture, Ann

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.361916Z

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 f95c80b5-8c18-4be1-861a-498da9bcbc8b · outbound

This paper cites Sarnak,Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series, Comm.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Sarnak,Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series, Comm

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.377228Z

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 8fd13081-5c7a-4c7e-9ea8-410c9e42bd65 · outbound

This paper cites Str¨ ombergsson,On the uniform equidistribution of long closed horocycles, Duke Math.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Str¨ ombergsson,On the uniform equidistribution of long closed horocycles, Duke Math

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.390816Z

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 330d7d1c-63f1-485f-980f-eca5fbcd4ae0 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.407216Z

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 8ad910d4-1e25-473f-8e0d-4654d87d1128 · outbound

This paper cites an unresolved cited work.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-07-05T13:41:13.403602Z

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 0081e5d6-6fa8-4230-899c-93a563f7f404 · outbound

This paper cites Yang,Equidistribution of expanding curves in homogeneous spaces and Diophantine approximation for square matrices, Proc.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Yang,Equidistribution of expanding curves in homogeneous spaces and Diophantine approximation for square matrices, Proc

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.299858Z

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 947c6824-c745-487e-99f5-14f8c20f3453 · outbound

This paper cites Shah and L.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Shah and L

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.397279Z

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 79b20f3e-bf39-43ec-a414-a35f580037a8 · outbound

This paper cites Chow and L.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Chow and L

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.400490Z

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 b263bf9a-ce0b-4ab3-83d5-d9c61c31fced · outbound

This paper cites Yang,Effective version of Ratner’s equidistribution theorem forSL(3,R), Ann.

Linking effective Ratner equidistribution to the semicircle law for skew-shift matrices Yang,Effective version of Ratner’s equidistribution theorem forSL(3,R), Ann

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-07-05T13:41:13.290480Z

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

No inbound Pith citation observations are available.