Paper Citation Record · LEDGER

A Product-Neighbourhood Criterion for Fixed Price One

As of 11 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2607.20273.

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

pith.paper-citation-record.v1
2607.20273 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:35:17.171742Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-06T11:04:20.209672Z

Reference resolution

26 of 26 outbound references displayed

verified exact6
verified fuzzy0
unresolved20
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0e176f78-943c-4971-90c1-916f18fbf58b · outbound

This paper cites Abért and S.

A Product-Neighbourhood Criterion for Fixed Price One Abért and S

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:14.411097Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eaacad46-985e-4459-a92f-8c652d60915a · outbound

This paper cites Abért and N.

A Product-Neighbourhood Criterion for Fixed Price One Abért and N

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:14.497036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0db74a9-a657-4ab1-a0b1-f9b4fb8ebd2a · outbound

This paper cites Abért and L.

A Product-Neighbourhood Criterion for Fixed Price One Abért and L

Reference 3

Resolution: verified exact; doi, observed 2026-08-01T10:38:29.522123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 25a9015c-f4bc-4234-9391-0ab3514058c8 · outbound

This paper cites Abért and B.

A Product-Neighbourhood Criterion for Fixed Price One Abért and B

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:14.804689Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1afe8ed-c791-4c96-8b8e-d6fa04279705 · outbound

This paper cites Abramenko, J.

A Product-Neighbourhood Criterion for Fixed Price One Abramenko, J

Reference 5

Resolution: verified exact; doi, observed 2026-08-01T10:38:29.345967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bd6de386-e8fe-4751-9953-04d734e0e92c · outbound

This paper cites Benoist and J.-F.

A Product-Neighbourhood Criterion for Fixed Price One Benoist and J.-F

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.006459Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c88069ab-833c-4148-a992-e2c4b3354466 · outbound

This paper cites Bevilacqua and L.

A Product-Neighbourhood Criterion for Fixed Price One Bevilacqua and L

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.065988Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a97f505-9601-4fd5-a152-307ac807c9d3 · outbound

This paper cites Carderi,Asymptotic invariants of lattices in locally compact groups, C.

A Product-Neighbourhood Criterion for Fixed Price One Carderi,Asymptotic invariants of lattices in locally compact groups, C

Reference 8

Resolution: verified exact; doi, observed 2026-08-01T10:38:29.211464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation caad32b5-d110-4f6e-a21c-56171e51fe04 · outbound

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

A Product-Neighbourhood Criterion for Fixed Price One Poisson-Voronoi tessellations and fixed price in higher rank

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.261062Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d480c3c2-351c-494c-84e1-9165e0d5a3c0 · outbound

This paper cites Gaboriau,Coût des relations d’équivalence et des groupes, Invent.

A Product-Neighbourhood Criterion for Fixed Price One Gaboriau,Coût des relations d’équivalence et des groupes, Invent

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.347189Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67b2b8de-6d11-45a0-88a7-b82ac50ad850 · outbound

This paper cites Gaboriau,Invariants ℓ2 de relations d’équivalence et de groupes, Publ.

A Product-Neighbourhood Criterion for Fixed Price One Gaboriau,Invariants ℓ2 de relations d’équivalence et de groupes, Publ

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.422820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 97bc0fe5-a6e6-447d-ad91-743cc1bc074a · outbound

This paper cites Gaboriau and R.

A Product-Neighbourhood Criterion for Fixed Price One Gaboriau and R

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.490923Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fa1948c-47d6-4fa4-a11a-c2ced06cbb00 · outbound

This paper cites Poisson-Voronoi percolation in higher rank.

A Product-Neighbourhood Criterion for Fixed Price One Poisson-Voronoi percolation in higher rank

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.570609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b8c4af22-508f-4b5e-b713-5e656d829407 · outbound

This paper cites an unresolved cited work.

A Product-Neighbourhood Criterion for Fixed Price One Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.629690Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e7ac194-4ef5-401c-88d3-a331a89b5fb9 · outbound

This paper cites an unresolved cited work.

A Product-Neighbourhood Criterion for Fixed Price One Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.722622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e6e20a1a-3e0c-410c-ae76-6cf032aa589b · outbound

This paper cites Khezeli,Products of infinite countable groups have fixed price one, arXiv:2509.08325, 2025.

A Product-Neighbourhood Criterion for Fixed Price One Khezeli,Products of infinite countable groups have fixed price one, arXiv:2509.08325, 2025

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:15.772293Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1677e38a-091f-495b-b685-071c24714c53 · outbound

This paper cites an unresolved cited work.

A Product-Neighbourhood Criterion for Fixed Price One Unresolved cited work

Reference 17

Resolution: verified exact; doi, observed 2026-08-01T10:38:29.094782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3b0ebc64-83b5-4bf9-990d-71d3faeff3d1 · outbound

This paper cites Last and M.

A Product-Neighbourhood Criterion for Fixed Price One Last and M

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:16.098160Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d4f22dab-bf01-4e38-be52-f57041d854a1 · outbound

This paper cites The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings.

A Product-Neighbourhood Criterion for Fixed Price One The Normal Subgroup Theorem for lattices on two-dimensional Euclidean buildings

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:16.230171Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1eaa608f-e8f2-4011-bffb-f8e11bc40cac · outbound

This paper cites Levitt,On the cost of generating an equivalence relation, Ergodic Theory Dynam.

A Product-Neighbourhood Criterion for Fixed Price One Levitt,On the cost of generating an equivalence relation, Ergodic Theory Dynam

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:16.378959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc8a20d3-008a-4d58-9b59-03331cd4b4d6 · outbound

This paper cites an unresolved cited work.

A Product-Neighbourhood Criterion for Fixed Price One Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:16.516673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bad2b46-ed4d-4526-80af-909d4339ff71 · outbound

This paper cites Mellick,Gaboriau’s criterion and fixed price one for locally compact groups, Trans.

A Product-Neighbourhood Criterion for Fixed Price One Mellick,Gaboriau’s criterion and fixed price one for locally compact groups, Trans

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:16.650064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58b7a37a-9834-43a4-9b15-b0a5c0147d8c · outbound

This paper cites The Palm groupoid of a point process and factor graphs on amenable and Property (T) groups.

A Product-Neighbourhood Criterion for Fixed Price One The Palm groupoid of a point process and factor graphs on amenable and Property (T) groups

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:16.761782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 95bf8a94-e8b6-411c-86e0-971cdf2f1e78 · outbound

This paper cites Peterson and A.

A Product-Neighbourhood Criterion for Fixed Price One Peterson and A

Reference 24

Resolution: verified exact; doi, observed 2026-08-01T10:38:28.903806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 270da29f-463f-4079-9035-f08802dbd4b3 · outbound

This paper cites Shlyakhtenko,Free Fisher information with respect to a completely positive map and cost of equivalence relations, Comm.

A Product-Neighbourhood Criterion for Fixed Price One Shlyakhtenko,Free Fisher information with respect to a completely positive map and cost of equivalence relations, Comm

Reference 25

Resolution: verified exact; doi, observed 2026-08-01T10:38:28.718401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 25599f66-2757-4296-8eb9-b32258dd8ef8 · outbound

This paper cites Non-residually finite $\tilde{C}_2$-lattices.

A Product-Neighbourhood Criterion for Fixed Price One Non-residually finite $\tilde{C}_2$-lattices

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T10:35:17.171742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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

Sparse Random Covers and Growth of Torsion in First Homology cites this paper.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.