Paper Citation Record · LEDGER

Sparse Random Covers and Growth of Torsion in First Homology

As of 19 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2608.05037.

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

pith.paper-citation-record.v1
2608.05037 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T11:04:20.092537Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

32 of 32 outbound references displayed

verified exact1
verified fuzzy24
unresolved7
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External citation measurements

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Outbound references

Observation adaf31ac-c0dd-4ec9-b102-bf81325338b5 · outbound

This paper cites On the growth ofL2-invariants for sequences of lattices in Lie groups.Ann.

Sparse Random Covers and Growth of Torsion in First Homology On the growth ofL2-invariants for sequences of lattices in Lie groups.Ann

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.482813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 91c44826-87c6-49c3-bd1a-0c0178b25101 · outbound

This paper cites On homology torsion growth.J.

Sparse Random Covers and Growth of Torsion in First Homology On homology torsion growth.J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.463535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ce0dcb55-ba41-40da-b5e0-1ccd7431c0b8 · outbound

This paper cites Rank, combinatorial cost, and homology torsion growth in higher rank lattices.Duke Math.

Sparse Random Covers and Growth of Torsion in First Homology Rank, combinatorial cost, and homology torsion growth in higher rank lattices.Duke Math

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T11:04:18.581595Z

Source-reported events for the cited work

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Observation ddb61109-3691-4c4f-b9a7-8380d21f945e · outbound

This paper cites Point processes, cost, and the growth of rank in locally compact groups.

Sparse Random Covers and Growth of Torsion in First Homology Point processes, cost, and the growth of rank in locally compact groups

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.431506Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 468d4bdc-5fd0-4487-909a-23b83e57eec0 · outbound

This paper cites Homology and homotopy complexity in negative curvature.

Sparse Random Covers and Growth of Torsion in First Homology Homology and homotopy complexity in negative curvature

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.408148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7cb24c27-f5e9-480c-8b04-aa661ca8437f · outbound

This paper cites Higher property T and below-rank phenomena of lattices, 2025.

Sparse Random Covers and Growth of Torsion in First Homology Higher property T and below-rank phenomena of lattices, 2025

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.385663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c251e5e2-77b1-4d5e-b570-9a745d14be5b · outbound

This paper cites Ballmann, M.

Sparse Random Covers and Growth of Torsion in First Homology Ballmann, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.365123Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cd632e4e-7215-4ccd-b890-b244e29a4064 · outbound

This paper cites Torsion homology growth in arithmetic groups.

Sparse Random Covers and Growth of Torsion in First Homology Torsion homology growth in arithmetic groups

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.343791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5b13b2e3-ec92-48c8-81a4-35b118561837 · outbound

This paper cites The asymptotic growth of torsion homology for arithmetic groups.

Sparse Random Covers and Growth of Torsion in First Homology The asymptotic growth of torsion homology for arithmetic groups

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.322031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6244011f-df12-4e46-ab18-49a04fcdd20e · outbound

This paper cites an unresolved cited work.

Sparse Random Covers and Growth of Torsion in First Homology Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:04:21.303460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 58b00ddf-bed2-49e7-8652-1c8c0a64a4a8 · outbound

This paper cites Torsion homology of arithmetic lattices andK2 of imaginary fields.Math.

Sparse Random Covers and Growth of Torsion in First Homology Torsion homology of arithmetic lattices andK2 of imaginary fields.Math

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.285548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4b9cbd51-1936-4376-8d2a-c6c895e2cf25 · outbound

This paper cites Growth of mod-2homology in higher-rank locally symmetric spaces.Duke Math.

Sparse Random Covers and Growth of Torsion in First Homology Growth of mod-2homology in higher-rank locally symmetric spaces.Duke Math

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.266552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1b3026e4-b4a0-4471-83c6-0fee08a31655 · outbound

This paper cites Growth of mod-2 homology in higher-rank locally symmetric spaces.Duke Mathematical Journal, 171(2):247–271, 2022.

Sparse Random Covers and Growth of Torsion in First Homology Growth of mod-2 homology in higher-rank locally symmetric spaces.Duke Mathematical Journal, 171(2):247–271, 2022

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.243155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 69080b33-9ec7-4a8f-87ee-741569a36f9a · outbound

This paper cites Topological complexity of arithmetic locally symmetric spaces.Invent.

Sparse Random Covers and Growth of Torsion in First Homology Topological complexity of arithmetic locally symmetric spaces.Invent

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.215013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 13737d14-9d0d-4387-93e3-195450aa0223 · outbound

This paper cites Poisson-Voronoi tessellations and fixed price in higher rank.

Sparse Random Covers and Growth of Torsion in First Homology Poisson-Voronoi tessellations and fixed price in higher rank

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T11:04:19.289919Z

Source-reported events for the cited work

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Observation ec9f034e-b4b1-46fe-92a7-39361e497cbe · outbound

This paper cites Homotopy type and volume of locally symmetric manifolds.Duke Math.

Sparse Random Covers and Growth of Torsion in First Homology Homotopy type and volume of locally symmetric manifolds.Duke Math

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.185482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6b4e4df2-bdb7-4de6-9611-6a0012e0d119 · outbound

This paper cites Volume versus rank of lattices.J.

Sparse Random Covers and Growth of Torsion in First Homology Volume versus rank of lattices.J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.165737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 006520ba-6b57-4bc6-a95b-3c4e80b9ceb4 · outbound

This paper cites Invariant random subgroups over non-Archimedean local fields.Math.

Sparse Random Covers and Growth of Torsion in First Homology Invariant random subgroups over non-Archimedean local fields.Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.143110Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 46603421-19ad-4599-bc6b-4be8c3a3c7d7 · outbound

This paper cites On the minimal size of a generating set of lattices in Lie groups.J.

Sparse Random Covers and Growth of Torsion in First Homology On the minimal size of a generating set of lattices in Lie groups.J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.119892Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6fb280e5-cffe-4f87-b786-52d4f0f6a41b · outbound

This paper cites A quantitative Selberg’s lemma.Groups Geom.

Sparse Random Covers and Growth of Torsion in First Homology A quantitative Selberg’s lemma.Groups Geom

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.091380Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a70e140b-4c3d-4222-a19a-61ca2a0e21bd · outbound

This paper cites Cambridge University Press, Cambridge, 2002.

Sparse Random Covers and Growth of Torsion in First Homology Cambridge University Press, Cambridge, 2002

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T11:04:19.567210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f805ceb4-c31f-40ba-8d31-13cd9a987426 · outbound

This paper cites Betti numbers of negatively curved orbifolds with coefficients in arbitrary fields, 2026.

Sparse Random Covers and Growth of Torsion in First Homology Betti numbers of negatively curved orbifolds with coefficients in arbitrary fields, 2026

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.057190Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c85f2111-19a0-45f1-b432-2010912af4b7 · outbound

This paper cites an unresolved cited work.

Sparse Random Covers and Growth of Torsion in First Homology Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T11:04:21.030990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a26ba4fa-d608-40c9-ae4a-585c3403a183 · outbound

This paper cites Cambridge University Press, Cambridge, 2018.

Sparse Random Covers and Growth of Torsion in First Homology Cambridge University Press, Cambridge, 2018

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:21.010690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation eeb532c2-f849-4213-b128-25dd4f48c8c6 · outbound

This paper cites Kazhdan’s property (T),L2-spectrum and isoperimetric inequalities for locally symmetric spaces.Comment.

Sparse Random Covers and Growth of Torsion in First Homology Kazhdan’s property (T),L2-spectrum and isoperimetric inequalities for locally symmetric spaces.Comment

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:20.983075Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8c91ca61-37bb-410f-8ae7-9c526bd1b43f · outbound

This paper cites The cheap embedding principle: Dynamical upper bounds for homology growth, 2025.

Sparse Random Covers and Growth of Torsion in First Homology The cheap embedding principle: Dynamical upper bounds for homology growth, 2025

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:20.746154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2a3e563e-5f99-4f97-acd7-d8e2f08d9a91 · outbound

This paper cites On the asymptotic number of generators of high rank arithmetic lattices.Michigan Math.

Sparse Random Covers and Growth of Torsion in First Homology On the asymptotic number of generators of high rank arithmetic lattices.Michigan Math

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T11:04:19.815076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ef302d7-f6c8-4f75-864e-ba21808ea996 · outbound

This paper cites ApproximatingL2-invariants by their finite-dimensional analogues.Geom.

Sparse Random Covers and Growth of Torsion in First Homology ApproximatingL2-invariants by their finite-dimensional analogues.Geom

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:20.604555Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3a56aee4-ef2d-4b94-85a4-ff70d0db1984 · outbound

This paper cites Survey on approximatingL2-invariants by their classical counterparts: Betti numbers, torsion invariants and homology growth.EMS Surv.

Sparse Random Covers and Growth of Torsion in First Homology Survey on approximatingL2-invariants by their classical counterparts: Betti numbers, torsion invariants and homology growth.EMS Surv

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:20.518664Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 293eca59-424c-4683-aa07-716a604d79c4 · outbound

This paper cites Buildings and hecke algebras.J.

Sparse Random Covers and Growth of Torsion in First Homology Buildings and hecke algebras.J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T11:04:20.373068Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8fa1be93-1c51-473c-99c3-b4b92da40427 · outbound

This paper cites On torsion in the cohomology of locally symmetric varieties.Ann.

Sparse Random Covers and Growth of Torsion in First Homology On torsion in the cohomology of locally symmetric varieties.Ann

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T11:04:20.035043Z

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Unavailable: canonical work link unavailable.

Observation 1d1d70ef-566d-4571-81fc-04c02a6e9430 · outbound

This paper cites A Product-Neighbourhood Criterion for Fixed Price One.

Sparse Random Covers and Growth of Torsion in First Homology A Product-Neighbourhood Criterion for Fixed Price One

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-08-06T11:04:20.254844Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

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