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Paper Citation Record · LEDGER

Separation profiles of free products

As of 13 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 1 inbound Pith citation observation for arXiv:2604.24462.

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

pith.paper-citation-record.v1
2604.24462 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-08T02:34:26.090561Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-10T17:38:19.230508Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-10T17:47:25.477498Z

Reference resolution

13 of 13 outbound references displayed

  • verified exact3
  • verified fuzzy9
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 674ad033-a204-4a33-9445-9e0c58ad20ef · outbound

This paper cites Bodlaender.

Separation profiles of free products Bodlaender

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.265916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:1e27ec2357500ad85b9bf53fbadfe58826a1c52a51fe86f24487d43d6e62a1d6

Observation 46ea28fb-b63f-4557-a63c-a260c48134df · outbound

This paper cites On the separation profile of infinite graphs.

Separation profiles of free products On the separation profile of infinite graphs

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.262949Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:b7a503a2ea208ca145fcae1637b278afa8d866318541c8109b7e6e40ce00b078

Observation bb99d0a4-faf8-425e-8b55-39d7d45acb44 · outbound

This paper cites Poincar\'e profiles of lamplighter diagonal products.

Separation profiles of free products Poincar\'e profiles of lamplighter diagonal products

Reference 3

Resolution
verified exact
arxiv_id, observed 2026-05-11T22:41:41.086151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:d53a22d5f653c0156d91124145aacee0e094dbd530dfc85f076b4aff901514e3

Observation c9d9cd2f-ca35-48b4-8e27-36a824eacbb6 · outbound

This paper cites Tree-graded spaces and asymptotic cones of groups.

Separation profiles of free products Tree-graded spaces and asymptotic cones of groups

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.259517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:796ed69e7f49d8531995f035795e2fd8c9504c7af882393832f58ba55a4400e7

Observation 3fd6e3b0-fa08-4998-954b-a4f7760ba468 · outbound

This paper cites Treewidth of graphs with balanced separations.

Separation profiles of free products Treewidth of graphs with balanced separations

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.238290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:2143c29b416d9655c911f550f1db5149f91dd3f5b020e6a9fa0ecf8a81ab017b

Observation 6bb23d13-b2b0-4e36-9112-933e6fb2c75a · outbound

This paper cites Separation profile, isoperimetry, growth and compression.

Separation profiles of free products Separation profile, isoperimetry, growth and compression

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.243345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:1f98739fe485d730ce6f77ccb59f31413a8d9c18b3e49b0cd6d7b0a7c1bf57cb

Observation 04d29856-562f-40f3-9383-a9842fdbf112 · outbound

This paper cites Separation profiles of graphs of fractals.

Separation profiles of free products Separation profiles of graphs of fractals

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.252378Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:68922c467df7456552f1de5d8c81da59d221272e3b46acaa6eebe7c0af1f2243

Observation a7c6b8bf-0dd6-470b-bd1e-5a0e49f1a117 · outbound

This paper cites QED corrections to the thermal neutrino interaction rate.

Separation profiles of free products QED corrections to the thermal neutrino interaction rate

Reference 8

Resolution
verified exact
arxiv_id, observed 2026-05-11T22:41:41.171339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:2594739cd6593b13d7acb2d229d544ff526998505f977bc84b545166a0c3bb9a

Observation c7e6a089-d214-4bc6-81da-d7dcf6203363 · outbound

This paper cites an unresolved cited work.

Separation profiles of free products Unresolved cited work

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-05-11T22:41:41.185030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:c58d1f6289c674e6c812f989da2a0c1b9a097796f6b4321a93d2c7f3d094d7f4

Observation f8e7c2a6-7bba-441a-bd9e-8eaedef068f9 · outbound

This paper cites Mackay, and Romain Tessera.

Separation profiles of free products Mackay, and Romain Tessera

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.234352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:5a1a9bb9e74e011cbcdeaad05f9322d05d89f262046de71328167692b3fe89e7

Observation ec19cb1a-277b-432c-878a-8a207e265e53 · outbound

This paper cites Mackay, and Romain Tessera.

Separation profiles of free products Mackay, and Romain Tessera

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.230110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:78c70a341a01ca5d40c9b8d24a3a3ca6c370452275ee997ac0f66ff70025553b

Observation d33b16fc-780a-479e-bce5-907ebec24278 · outbound

This paper cites Quasi-isometries between groups with infinitely many ends.

Separation profiles of free products Quasi-isometries between groups with infinitely many ends

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-26T22:58:12.248545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:ba4fca16759a1acaa5cfe1cf91d6f4bd0472cb9bc39d9ad4ab27e146dbe52661

Observation 426b6956-edd3-4988-8879-4a92838bb2c9 · outbound

This paper cites an unresolved cited work.

Separation profiles of free products Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-05-26T22:58:12.255803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=arxiv_source observed=2026-05-08T02:34:26.090561Z digest=sha256:0d0b0e8911df1db675c06ad9520d09ef7dd8170ceb21b7c4766327c19a6cd365

Pith citing papers

Observation 73c4c3cf-e60b-4b70-b96e-3aace65ac1e4 · inbound

Separation profiles of hyperbolic planar and apex-minor-free graphs cites this paper.

Separation profiles of hyperbolic planar and apex-minor-free graphs Separation profiles of free products

Reference 17

Resolution
verified exact
local_arxiv, observed 2026-07-10T17:47:25.479168Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-07-10T17:38:19.230508Z digest=sha256:5ea1d29f1caa1ede11a1b79061d7c618e25e789542443224ba8042294e49dd10