Paper Citation Record · LEDGER

Virtual First Betti Number of GGS Groups

As of 8 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2505.23269.

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

pith.paper-citation-record.v1
2505.23269 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:03:19.574547Z

measured 21 of 21 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

21 of 21 outbound references displayed

verified exact0
verified fuzzy10
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f55baea5-550a-4d77-a575-66d2442460ec · outbound

This paper cites Bartholdi, B.

Virtual First Betti Number of GGS Groups Bartholdi, B

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:23.975020Z

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 165b063f-b671-4650-9a2e-000548c32db6 · outbound

This paper cites Bartholdi and R.

Virtual First Betti Number of GGS Groups Bartholdi and R

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:23.786277Z

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 23447e34-797d-44e3-aee9-6910366197c0 · outbound

This paper cites Bartholdi, R.

Virtual First Betti Number of GGS Groups Bartholdi, R

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:23.535158Z

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 d9a0439f-2f98-427a-9269-264127d41ccd · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:23.279469Z

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 ecb7cd80-e100-4917-aa40-9767e3bb54e9 · outbound

This paper cites Bartholdi, V.

Virtual First Betti Number of GGS Groups Bartholdi, V

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:23.076113Z

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 bec0eebb-347e-46e1-95ea-b372e0a0168e · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:22.860021Z

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 e00b94ff-e597-419e-94ad-38279167f21b · outbound

This paper cites Delzant, `Sur l'anneau d'un groupe hyperbolique', C.

Virtual First Betti Number of GGS Groups Delzant, `Sur l'anneau d'un groupe hyperbolique', C

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:22.675686Z

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 81b568cd-2a58-4400-aa18-eda8646b9aa0 · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:22.496674Z

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 2fea9923-b5d2-4f46-b7aa-a7a53f4cf3f9 · outbound

This paper cites Fabrykowski and N.

Virtual First Betti Number of GGS Groups Fabrykowski and N

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:22.312953Z

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 43fce03b-ff5d-4dde-bf22-dd06af579922 · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:22.126239Z

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 2571eb15-cb96-494b-bc31-882952f68af9 · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:21.882358Z

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 25d0730c-c2ad-43b8-9396-96e31e12be06 · outbound

This paper cites Gardam, A counterexample to the unit conjecture for group rings, Ann.

Virtual First Betti Number of GGS Groups Gardam, A counterexample to the unit conjecture for group rings, Ann

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:21.598906Z

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 7a806c04-b9a4-40e4-a8d2-d74c3db5fc48 · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:21.327005Z

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 d3c10562-d1c1-468e-8ee6-3c2fa0e3285e · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:21.094959Z

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 c5aa4e96-cafb-4526-bf5a-32043defbc2e · outbound

This paper cites Kionke and J.

Virtual First Betti Number of GGS Groups Kionke and J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:20.852307Z

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 aa68392c-2d6d-40f7-a60c-a1c8faec1ced · outbound

This paper cites Hereditarily just-infinite torsion groups with positive first $\ell^2$-Betti number.

Virtual First Betti Number of GGS Groups Hereditarily just-infinite torsion groups with positive first $\ell^2$-Betti number

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T13:03:19.116023Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12d04dd1-83a3-47d4-af37-2d8c76663930 · outbound

This paper cites Linnell and D.

Virtual First Betti Number of GGS Groups Linnell and D

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:20.630180Z

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 363dc648-40c6-494d-af1b-4910b96603af · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:20.438103Z

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 f486943e-278a-41e3-9c91-842b4921e0d6 · outbound

This paper cites A note on up groups.

Virtual First Betti Number of GGS Groups A note on up groups

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:03:20.194528Z

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 7300e909-1568-4948-b39b-a4cc6935244a · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:19.964398Z

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 4297f27c-b386-4c85-8581-1e7d20fe7e3c · outbound

This paper cites an unresolved cited work.

Virtual First Betti Number of GGS Groups Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:03:19.814977Z

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.

Pith citing papers

No inbound Pith citation observations are available.