Paper Citation Record · LEDGER

A strong height gap theorem for $PGL_2$

As of 21 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:2507.22266.

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

pith.paper-citation-record.v1
2507.22266 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:04:31.172758Z

measured 20 of 20 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

20 of 20 outbound references displayed

verified exact0
verified fuzzy15
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 72458244-2f9d-407e-85c2-b27d214e8b07 · outbound

This paper cites Abert, N.

A strong height gap theorem for $PGL_2$ Abert, N

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.428549Z

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 27e2d46c-3544-4d0d-b4bb-7cf7443bfc59 · outbound

This paper cites an unresolved cited work.

A strong height gap theorem for $PGL_2$ Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:04:31.415212Z

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 dfc20bc2-20c9-4bc5-a508-07871c55565d · outbound

This paper cites Belolipetsky , Arithmetic hyperbolic reflection groups , Bull.

A strong height gap theorem for $PGL_2$ Belolipetsky , Arithmetic hyperbolic reflection groups , Bull

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.403157Z

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 74c5ccef-911f-4474-8467-84ff351a3d3f · outbound

This paper cites Belolipetsky, N.

A strong height gap theorem for $PGL_2$ Belolipetsky, N

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.390795Z

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 7e5108d6-3235-4607-978f-93988f6f2790 · outbound

This paper cites Belolipetsky, G.

A strong height gap theorem for $PGL_2$ Belolipetsky, G

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.378025Z

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 013013bb-7f47-4799-8681-b622aa5b03f4 · outbound

This paper cites Borel , Commensurability classes and volumes of hyperbolic 3-manifolds, Ann.

A strong height gap theorem for $PGL_2$ Borel , Commensurability classes and volumes of hyperbolic 3-manifolds, Ann

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.366054Z

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 ec712e0c-1ce3-45b6-88a1-aaf56bb30da5 · outbound

This paper cites Breuillard , A height gap theorem for finite subsets of GLd(Q) and nonamenable sub- groups, Ann.

A strong height gap theorem for $PGL_2$ Breuillard , A height gap theorem for finite subsets of GLd(Q) and nonamenable sub- groups, Ann

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.346242Z

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 8f78e89e-3f4b-4b65-99c2-458fbf918ddf · outbound

This paper cites an unresolved cited work.

A strong height gap theorem for $PGL_2$ Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:04:31.336372Z

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 6af019c7-5a34-4b19-8dab-018ee575371e · outbound

This paper cites Elstrodt, F.

A strong height gap theorem for $PGL_2$ Elstrodt, F

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.326569Z

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 025092d5-eb95-4784-8f8e-f189e21654ee · outbound

This paper cites Eskin, S.

A strong height gap theorem for $PGL_2$ Eskin, S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.317045Z

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 3b757f8f-166a-4648-a1e0-8f690d57cc93 · outbound

This paper cites Fisher and S.

A strong height gap theorem for $PGL_2$ Fisher and S

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.306600Z

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 19db5f79-9289-4c0b-b2a4-ba2a9bba7102 · outbound

This paper cites Fraczyk , Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds , Invent.

A strong height gap theorem for $PGL_2$ Fraczyk , Strong limit multiplicity for arithmetic hyperbolic surfaces and 3-manifolds , Invent

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.296813Z

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 7817c5de-08f2-4245-8d54-71c4d0fcc17f · outbound

This paper cites Fraczyk, S.

A strong height gap theorem for $PGL_2$ Fraczyk, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.285912Z

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 68170edc-5a76-452d-b235-956b331e16f1 · outbound

This paper cites Fraczyk and J.

A strong height gap theorem for $PGL_2$ Fraczyk and J

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.275778Z

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 3db277c9-b736-4b14-8d93-ce804abf531d · outbound

This paper cites Maclachlan and A.

A strong height gap theorem for $PGL_2$ Maclachlan and A

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.265410Z

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 e24c0df1-ac89-4382-818a-3eab9debb792 · outbound

This paper cites an unresolved cited work.

A strong height gap theorem for $PGL_2$ Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:04:31.253998Z

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 c64743fe-88f2-440a-8979-daaa16642282 · outbound

This paper cites an unresolved cited work.

A strong height gap theorem for $PGL_2$ Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:04:31.242186Z

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 ede8624f-0740-4ba3-8e44-8fdd74cf67b0 · outbound

This paper cites an unresolved cited work.

A strong height gap theorem for $PGL_2$ Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T12:04:31.230135Z

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 d219405c-78e6-499c-9a2d-2ce6dc1e6209 · outbound

This paper cites Prasad and A.

A strong height gap theorem for $PGL_2$ Prasad and A

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.217640Z

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 bc855c86-c000-4934-be38-25a0ee705c65 · outbound

This paper cites Thom, Convergent sequences in discrete groups , Canad.

A strong height gap theorem for $PGL_2$ Thom, Convergent sequences in discrete groups , Canad

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:04:31.205203Z

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.