Paper Citation Record · LEDGER

Volume Entropy Rigidity for Random Groups at Low Densities

As of 24 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2505.23364.

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

pith.paper-citation-record.v1
2505.23364 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:16:48.859880Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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 exact2
verified fuzzy24
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7da0368c-af67-492f-9102-607f4819833e · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:55.382759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1dcd5cbb-8cfc-4aa9-a050-cc6fd3e30005 · outbound

This paper cites 06, 2429–2434.

Volume Entropy Rigidity for Random Groups at Low Densities 06, 2429–2434

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:55.191893Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation fad99a93-65c0-42ed-b625-2b5c3bf323e2 · outbound

This paper cites 5, 731–799.

Volume Entropy Rigidity for Random Groups at Low Densities 5, 731–799

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:54.989571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 88d0b228-0e89-4df2-932a-c1c8026451e1 · outbound

This paper cites 2, 123–148.

Volume Entropy Rigidity for Random Groups at Low Densities 2, 123–148

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:54.826311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 80c86c8f-337d-4c7c-a9c2-1bcabe082691 · outbound

This paper cites Marked length spectrum rigidity from rigidity on subsets.

Volume Entropy Rigidity for Random Groups at Low Densities Marked length spectrum rigidity from rigidity on subsets

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:16:49.423883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6f68949d-a224-42e0-853a-93ddd01d5115 · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:54.602705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ac551d63-e33d-43aa-b27a-fe0a68cee5d9 · outbound

This paper cites 4, 1615–1681.

Volume Entropy Rigidity for Random Groups at Low Densities 4, 1615–1681

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:54.431085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b5a47d92-1642-4626-8bdb-bf3213976002 · outbound

This paper cites Volume entropy and rigidity for RCD-spaces.

Volume Entropy Rigidity for Random Groups at Low Densities Volume entropy and rigidity for RCD-spaces

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T13:16:46.126162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 082b1eba-d114-40eb-b547-b4c7dba092e4 · outbound

This paper cites de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, 2000.

Volume Entropy Rigidity for Random Groups at Low Densities de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, 2000

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T13:16:46.313172Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 951b9575-135a-4588-a397-a05d879d20fc · outbound

This paper cites Drut ¸u and M.

Volume Entropy Rigidity for Random Groups at Low Densities Drut ¸u and M

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:54.244799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 942da2d5-9b4a-4b7e-a585-dba81992da87 · outbound

This paper cites Flajolet and R.

Volume Entropy Rigidity for Random Groups at Low Densities Flajolet and R

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T13:16:46.611891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b44b51c-d158-4105-acb9-1c9fb4a0c0c1 · outbound

This paper cites 3, 1427–1470.

Volume Entropy Rigidity for Random Groups at Low Densities 3, 1427–1470

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:54.020539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 37dea278-86e9-4455-b1f8-5ba2f5b2ac08 · outbound

This paper cites 149–166, Springer Berlin Heidelberg, Berlin, Heidelbe rg, 2002.

Volume Entropy Rigidity for Random Groups at Low Densities 149–166, Springer Berlin Heidelberg, Berlin, Heidelbe rg, 2002

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:53.792850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ba2e245a-4313-4135-a308-4ec16369c2bc · outbound

This paper cites 1, 67–83.

Volume Entropy Rigidity for Random Groups at Low Densities 1, 67–83

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:53.604789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5cc5df78-6a75-4282-999d-cfb61965dca9 · outbound

This paper cites Grigorchuk and Pierre de la Harpe, On problems related to growth, entropy, and spectrum in group theory , Journal of Dynamical and Control Systems 3 (1997), 51–89.

Volume Entropy Rigidity for Random Groups at Low Densities Grigorchuk and Pierre de la Harpe, On problems related to growth, entropy, and spectrum in group theory , Journal of Dynamical and Control Systems 3 (1997), 51–89

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:53.387199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 824d211d-b478-4220-a0bf-006bb00d8db8 · outbound

This paper cites Gromov, Hyperbolic groups, Springer New York, New York, NY, 1987.

Volume Entropy Rigidity for Random Groups at Low Densities Gromov, Hyperbolic groups, Springer New York, New York, NY, 1987

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:53.185481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a0337041-98f6-4d86-b8a7-12aa1c2cb2cf · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:53.018845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 59dbd0b6-6c64-40ba-8be0-3a609512680a · outbound

This paper cites Hille and R.S.

Volume Entropy Rigidity for Random Groups at Low Densities Hille and R.S

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:52.798528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b7c52804-9886-476e-ab62-fae8ed325475 · outbound

This paper cites 1, 139–165.

Volume Entropy Rigidity for Random Groups at Low Densities 1, 139–165

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:52.611279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 05029f9a-f1dc-42d3-9468-6d9ff49ec3b0 · outbound

This paper cites 3, 849 – 867.

Volume Entropy Rigidity for Random Groups at Low Densities 3, 849 – 867

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:52.372804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f51e7c50-66df-4ab5-8f3e-9c125f361200 · outbound

This paper cites 10, 5089–5100.

Volume Entropy Rigidity for Random Groups at Low Densities 10, 5089–5100

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:52.230289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 442f9ece-51f4-4610-8d5f-91f58c41b499 · outbound

This paper cites Lyndon and Paul E.

Volume Entropy Rigidity for Random Groups at Low Densities Lyndon and Paul E

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:52.023667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a1edd3aa-71a3-4387-81a0-c7c01597c65b · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:51.837645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b8cff676-5f5c-42b6-b81b-30a10321e035 · outbound

This paper cites 3, 567–573.

Volume Entropy Rigidity for Random Groups at Low Densities 3, 567–573

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:51.670122Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 26940641-4bb4-4d4c-960f-52404c82eaa5 · outbound

This paper cites McMullen, Entropy and the clique polynomial , Journal of Topology 8 (2014), no.

Volume Entropy Rigidity for Random Groups at Low Densities McMullen, Entropy and the clique polynomial , Journal of Topology 8 (2014), no

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:51.488967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 537abd5c-aea7-4091-ace0-23223afb4224 · outbound

This paper cites Milnor, A note on curvature and fundamental group , Journal of Diﬀerential Geom- etry 2 (1968), 1–7.

Volume Entropy Rigidity for Random Groups at Low Densities Milnor, A note on curvature and fundamental group , Journal of Diﬀerential Geom- etry 2 (1968), 1–7

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:51.316248Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4b62aa20-706e-4a2d-a510-d2f72e4429b9 · outbound

This paper cites Myers, Forbidden substrings on weighted alphabets , Australas.

Volume Entropy Rigidity for Random Groups at Low Densities Myers, Forbidden substrings on weighted alphabets , Australas

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:51.117476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c5308a61-ff4a-4383-b0c7-028caadd643f · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:50.882745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation cb00d6c9-9131-4eb5-9f56-619b604472a4 · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:50.659529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 86a1f82d-376e-41af-8d87-be445ea10244 · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:16:50.457087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation ebb852de-19b9-4b73-b155-499bbcd17879 · outbound

This paper cites 3, 914–942.

Volume Entropy Rigidity for Random Groups at Low Densities 3, 914–942

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:50.286105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0524a627-0a80-4a89-bfc4-08e7673f29c4 · outbound

This paper cites 4, 345–363.

Volume Entropy Rigidity for Random Groups at Low Densities 4, 345–363

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:50.086361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation dac97367-205a-45a8-8e13-346e9bfab7f7 · outbound

This paper cites an unresolved cited work.

Volume Entropy Rigidity for Random Groups at Low Densities Unresolved cited work

Reference 34

Resolution: verified exact; raw_fallback, observed 2026-08-07T13:16:49.255723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b2050f62-c2ea-4d13-8aa2-7509c4da5394 · outbound

This paper cites 4, 510–515.

Volume Entropy Rigidity for Random Groups at Low Densities 4, 510–515

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:49.887549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6bf31bf6-03a4-4048-8457-ee879281533d · outbound

This paper cites 1, 93–133.

Volume Entropy Rigidity for Random Groups at Low Densities 1, 93–133

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:49.700508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a1e180ae-cb5f-4aec-9887-9ca6c1c97601 · outbound

This paper cites Entropy and stability of hyperbolic manifolds.

Volume Entropy Rigidity for Random Groups at Low Densities Entropy and stability of hyperbolic manifolds

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T13:16:48.766007Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f29abf7-20b5-4c76-bf26-cd6e89d9f8ee · outbound

This paper cites Wilson, On exponential growth and uniformly exponential growth for groups, Inven- tiones mathematicae 155 (2004), 287–303.

Volume Entropy Rigidity for Random Groups at Low Densities Wilson, On exponential growth and uniformly exponential growth for groups, Inven- tiones mathematicae 155 (2004), 287–303

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:16:49.570351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.