Paper Citation Record · LEDGER

Non-uniform higher-rank lattices are character rigid

As of 10 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2507.21862.

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

pith.paper-citation-record.v1
2507.21862 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:36:11.117223Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+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

46 of 46 outbound references displayed

verified exact1
verified fuzzy20
unresolved25
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 16092bdc-ed64-45c6-b197-feec691c8292 · outbound

This paper cites 3, 465–488.

Non-uniform higher-rank lattices are character rigid 3, 465–488

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:18.287155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6614e648-de20-4e45-8931-ea83153ac927 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:18.163627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 17dac3e2-22d8-43f7-b927-5f8994988af8 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:17.950316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 619ca017-8b0d-40c3-959b-c85a0598dd74 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:17.731932Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 136f7f67-0dc1-44cc-adeb-86c7973c66be · outbound

This paper cites Spectral gap for products and a strong normal subgroup theorem.

Non-uniform higher-rank lattices are character rigid Spectral gap for products and a strong normal subgroup theorem

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T12:36:08.490850Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ac00d07-c4cc-4763-86e4-c4bf5fdca52e · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:17.557849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f557e7de-0fa4-451c-bce5-dd305f442f63 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:17.393093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d16a5223-e1d3-4e1b-b8fc-f6b6ea768026 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:17.230985Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9279f6d6-c688-4974-a8b1-922555c26e44 · outbound

This paper cites 126, Springer Science & Business Media, 2012.

Non-uniform higher-rank lattices are character rigid 126, Springer Science & Business Media, 2012

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:16.954120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b333b085-380f-4bda-b238-5314cad491d2 · outbound

This paper cites 96, Cambridge University Press, 1984, pp.

Non-uniform higher-rank lattices are character rigid 96, Cambridge University Press, 1984, pp

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:16.674893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1d36ad8e-ebcf-4cf7-8d58-c901feebeaad · outbound

This paper cites Conditional Non-Soficity of p-adic Deligne Extensions: on a Theorem of Gohla and Thom.

Non-uniform higher-rank lattices are character rigid Conditional Non-Soficity of p-adic Deligne Extensions: on a Theorem of Gohla and Thom

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T12:36:08.913704Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f4da1b9d-caf1-43fe-ab1c-05b251ab73e7 · outbound

This paper cites 26, Cambridge University Press, Cambridge, 2015.

Non-uniform higher-rank lattices are character rigid 26, Cambridge University Press, Cambridge, 2015

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:16.303798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3f268feb-4e67-441e-a903-ed8119a0cde3 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:16.004338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 77722c0c-0ac4-44d2-9c3d-945438c080a6 · outbound

This paper cites Characters of diagonal products and Hilbert-Schmidt stability.

Non-uniform higher-rank lattices are character rigid Characters of diagonal products and Hilbert-Schmidt stability

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T12:36:09.058242Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0ef615c-0c8e-4de6-b4c1-683f6d2dd807 · outbound

This paper cites Hyperlinearity, stability and asymptotic spectral gap of higher rank lattices.

Non-uniform higher-rank lattices are character rigid Hyperlinearity, stability and asymptotic spectral gap of higher rank lattices

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T12:36:09.122829Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6fae70cf-012f-449e-8c98-e95c924733cb · outbound

This paper cites W*-superrigidity for groups with infinite center.

Non-uniform higher-rank lattices are character rigid W*-superrigidity for groups with infinite center

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T12:36:09.172941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e24d24d-000a-4fa4-9e1a-7fd685fb5c7f · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:15.699418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d8fd13f1-b8a9-4ab4-b475-2435431bf015 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:15.402705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 68ef6a57-1a2c-444d-97b2-930592801c0a · outbound

This paper cites Things we can learn by considering random locally symmetric manifolds.

Non-uniform higher-rank lattices are character rigid Things we can learn by considering random locally symmetric manifolds

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T12:36:11.259451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ff0e0c91-5cee-4e22-aae2-b9aa5603cac3 · outbound

This paper cites 3, 1503–1544.

Non-uniform higher-rank lattices are character rigid 3, 1503–1544

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:15.136887Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 09272a19-b2d3-4bf3-8042-ce89e3dfc4cc · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:14.853378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 96661738-ffac-42da-9533-0b4a758599db · outbound

This paper cites High-dimensional expansion and soficity of groups.

Non-uniform higher-rank lattices are character rigid High-dimensional expansion and soficity of groups

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T12:36:09.587376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae7ede88-4932-4d2a-89a5-232bbdb1ac85 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:14.571259Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7d066dd5-f326-40aa-8c68-668cf501d4d8 · outbound

This paper cites Jones, Ten problems, Mathematics: frontiers and perspectives, 2000.

Non-uniform higher-rank lattices are character rigid Jones, Ten problems, Mathematics: frontiers and perspectives, 2000

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:14.316111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1f57553f-81d2-4847-889a-c6aa7b9b8cf8 · outbound

This paper cites 2, 349–372.

Non-uniform higher-rank lattices are character rigid 2, 349–372

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:14.124336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4258a76b-0bdc-4697-a5a1-2e646f7e647d · outbound

This paper cites 162, Russian Academy of Sciences, 1965, pp.

Non-uniform higher-rank lattices are character rigid 162, Russian Academy of Sciences, 1965, pp

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:13.904412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ca3019f7-fb1e-4c4d-a745-07c3d5381559 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:13.749507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0cf4341a-fb59-48bb-a8cf-cad599dc2687 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:13.636742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b4292163-f874-408b-aec9-02ffc04b6aee · outbound

This paper cites 3, 3181–3229.

Non-uniform higher-rank lattices are character rigid 3, 3181–3229

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:13.520081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bce24dab-cb9e-4f82-8ee1-bec69c11fee5 · outbound

This paper cites 4, 295–305.

Non-uniform higher-rank lattices are character rigid 4, 295–305

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:13.291629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 79c9ef0c-02bf-452b-ba22-bb4e8745f770 · outbound

This paper cites 3, 178–187.

Non-uniform higher-rank lattices are character rigid 3, 178–187

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:13.190879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation cb04260b-4615-4cfc-b87e-6922cac6a36b · outbound

This paper cites 17, Springer-Verlag, Berlin, 1991.

Non-uniform higher-rank lattices are character rigid 17, Springer-Verlag, Berlin, 1991

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:13.120030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e412090d-f921-4207-9295-b2a91fb28e29 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:12.948451Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1bef0c26-620b-4fd7-88cd-718fa5944c8b · outbound

This paper cites Reine Angew.

Non-uniform higher-rank lattices are character rigid Reine Angew

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:12.838142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9d03ff76-a4cf-40a7-aecf-780627004c36 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:12.703965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 227bf17e-94ae-4fa3-a5f9-a209a76bfd2e · outbound

This paper cites 3, 213–231.

Non-uniform higher-rank lattices are character rigid 3, 213–231

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:12.569471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3d2fc54b-230a-408b-a8bc-24cd1a7721f5 · outbound

This paper cites Springer, Linear algebraic groups, Modern Birkh¨ auser Classics, Birkh¨ auser Boston, 2010.

Non-uniform higher-rank lattices are character rigid Springer, Linear algebraic groups, Modern Birkh¨ auser Classics, Birkh¨ auser Boston, 2010

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:12.443865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6def32f3-a627-4584-9bdd-32107dea7a33 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:12.271207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e8bd5fa1-2b6e-4c61-9a72-520ff06c1985 · outbound

This paper cites 1, 40–61.

Non-uniform higher-rank lattices are character rigid 1, 40–61

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:12.167977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 22643403-f3bc-4216-be65-6e80af911907 · outbound

This paper cites 4, 389–402.

Non-uniform higher-rank lattices are character rigid 4, 389–402

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:12.064290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f5cbb274-6cc2-4223-a77b-9c48a45e86cb · outbound

This paper cites 2, 111–138.

Non-uniform higher-rank lattices are character rigid 2, 111–138

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:11.921576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 05f20628-8b43-4917-b561-39b13596ffa8 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:11.834104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2f5946da-3de3-44be-b026-247b6c24d91b · outbound

This paper cites 1, 193–212.

Non-uniform higher-rank lattices are character rigid 1, 193–212

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:11.729157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1e11df34-a608-4525-bfb4-128b8ef3f2c6 · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:11.642393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 85df5dc0-6829-44be-acfe-5aa30d4241e6 · outbound

This paper cites 257, Russian Academy of Sciences, 1981, pp.

Non-uniform higher-rank lattices are character rigid 257, Russian Academy of Sciences, 1981, pp

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:36:11.517876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d9ab7ee3-508d-4cf4-b3aa-f945d9f55a9a · outbound

This paper cites an unresolved cited work.

Non-uniform higher-rank lattices are character rigid Unresolved cited work

Reference 46

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:36:11.426667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

No inbound Pith citation observations are available.