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Paper Citation Record · LEDGER

The atoms of graph product von Neumann algebras

As of 16 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 1 inbound Pith citation observation for arXiv:2506.09000.

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

pith.paper-citation-record.v1
2506.09000 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:08:37.025769Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:01:17.751149Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T17:01:20.760719Z

Reference resolution

18 of 18 outbound references displayed

  • verified exact0
  • verified fuzzy13
  • unresolved5
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2f2cc484-af13-4725-92e5-45fbd568a8dc · outbound

This paper cites Belinschi, Hari Bercovici, and Weihua Liu, The atoms of operator-valued free convolutions, Journal of Operator Theory 85 (2021), no.

The atoms of graph product von Neumann algebras Belinschi, Hari Bercovici, and Weihua Liu, The atoms of operator-valued free convolutions, Journal of Operator Theory 85 (2021), no

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:41.463045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.651045Z digest=sha256:c78028ff6a11bebed4c7ca402f17e4bb82d768a2d700ac6cd914e36fe0bdb7db

Observation 39e5328c-4068-4508-80ec-8203ac407303 · outbound

This paper cites 122, Springer-Verlag, Berlin, 2006, Theory of C^* -algebras and von N eumann algebras, Operator Algebras and Non-commutative Geometry, III.

The atoms of graph product von Neumann algebras 122, Springer-Verlag, Berlin, 2006, Theory of C^* -algebras and von N eumann algebras, Operator Algebras and Non-commutative Geometry, III

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:41.256536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.697141Z digest=sha256:3c2656f13df5f70faf5db26ededba38e3e73f3a90d9eacba131cfb91aa980c00

Observation f7efd75e-3277-467e-8272-a532267bf970 · outbound

This paper cites an unresolved cited work.

The atoms of graph product von Neumann algebras Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:08:41.003093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.824267Z digest=sha256:3da1396afb5da05ce856ad20d22fedc3f3285bcb168607ecca1f1d8c00bbba26

Observation 1676c164-6104-42c5-8064-af10546cb248 · outbound

This paper cites 37--47, Birkh \"a user Basel, Basel, 1998.

The atoms of graph product von Neumann algebras 37--47, Birkh \"a user Basel, Basel, 1998

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:40.883552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.988973Z digest=sha256:d75f0651e415799787b42ead8ecbdb21aa5a00b4e726ee66ca325b805eca1aea

Observation 0f1ac7dd-dd05-4834-b5f6-d5aade69e497 · outbound

This paper cites On the structure of graph product von Neumann algebras.

The atoms of graph product von Neumann algebras On the structure of graph product von Neumann algebras

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-07T05:08:35.195055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T05:08:35.195055Z digest=sha256:d61bde7f88537eb1b310ae3f0a93f02f6ac4b5568c616f4773a33da909012857

Observation e5500d3f-010b-4fe4-8bce-3edd49823cad · outbound

This paper cites Cartier and D.

The atoms of graph product von Neumann algebras Cartier and D

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:40.704267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.329539Z digest=sha256:fb5a348eabd5263c57b4ba2552d71b02cc6cdf70d5bc15956b45c2f02f7f9a0e

Observation a5caf5d2-2043-4b9e-acf2-c90c03cf93b2 · outbound

This paper cites Noncommut.

The atoms of graph product von Neumann algebras Noncommut

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:40.471254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.526660Z digest=sha256:31c304251b33245eb6f4513a9c1793d756ca49a0f70f1ac4bda6f09b2aeebd68

Observation 039cde58-b7d7-4a12-bd9e-fa4e2e243c02 · outbound

This paper cites 1, 97--119.

The atoms of graph product von Neumann algebras 1, 97--119

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:40.166699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.647036Z digest=sha256:599f30fd66a770f93f26b577d049f8aad49594cc7683ee729a694d3f9f543d06

Observation a4b70b4e-2883-42a7-a386-b066bb09bbe5 · outbound

This paper cites Goulden and David M.

The atoms of graph product von Neumann algebras Goulden and David M

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:39.863991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.768410Z digest=sha256:01c77c046306a88d8f8a203c66a7943b50dd5d13585bac6544abb751da21f1e1

Observation eed4ddb3-1401-488e-bb00-20dc3708ecf8 · outbound

This paper cites thesis, University of Leeds, 1990.

The atoms of graph product von Neumann algebras thesis, University of Leeds, 1990

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:39.585475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.919085Z digest=sha256:6073f80898659649b3b642bece383e5242e2fc6e46019e725f07d36c0346cbde

Observation 00c4c48b-87ea-417a-a1fc-97989a004e0f · outbound

This paper cites Hermiller and J.

The atoms of graph product von Neumann algebras Hermiller and J

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:39.308202Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.017174Z digest=sha256:33f5b04999e2a43297a084daf547af1e15a17e4268151a20ebd2ccc02b360d32

Observation be6428b6-3572-402c-b1e6-7321414fc701 · outbound

This paper cites Jones and V.

The atoms of graph product von Neumann algebras Jones and V

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:39.034105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.190640Z digest=sha256:7335be0a317e296975232ce449a49e54b3d572701378f869a093b733431c2bdd

Observation ad6b4fe6-cebf-4c5c-9552-5d813aa735ea · outbound

This paper cites Morampudi and Chris R.

The atoms of graph product von Neumann algebras Morampudi and Chris R

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:38.744512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.313592Z digest=sha256:95b851ec2b4147276a04c0876932fecb3d25184aa97b701806c6b7e695a19f7e

Observation 4b4ac597-40d4-4d70-a20f-8ea0e30c7c57 · outbound

This paper cites M otkowski, -free probability, Infinite Dimensional Analysis.

The atoms of graph product von Neumann algebras M otkowski, -free probability, Infinite Dimensional Analysis

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:38.421453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.445557Z digest=sha256:05b26b6153dfc04020f6e68c2b89109ebd1b28a522375c7d10f4b42fb406a84a

Observation 65437569-edc0-4337-8848-013e00bb3566 · outbound

This paper cites an unresolved cited work.

The atoms of graph product von Neumann algebras Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:08:38.075620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.650145Z digest=sha256:e21d7afd65315ef36e7b676be6f6210379e9e26abc6338e1e04db4fe1a1f854b

Observation ddfda70e-47e1-4149-b4a8-964c44098dca · outbound

This paper cites 60, Springer-Verlag, Berlin Heidelberg, 1971.

The atoms of graph product von Neumann algebras 60, Springer-Verlag, Berlin Heidelberg, 1971

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T05:08:37.790520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.768705Z digest=sha256:786d37b67eb7820ea961b880d818667491424aa9abe69ddd0ada6a2b20f1b382

Observation 5f207356-e687-4d93-9e22-f9f6aadec249 · outbound

This paper cites an unresolved cited work.

The atoms of graph product von Neumann algebras Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:08:37.552046Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.888191Z digest=sha256:93753cde68c9dab5e3a17e974378bb4039367463a5e3111892d2a6b6431dca0e

Observation 58440df9-fe73-4eaf-8032-b6161f6f3e93 · outbound

This paper cites an unresolved cited work.

The atoms of graph product von Neumann algebras Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T05:08:37.301070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-07T05:08:37.025769Z digest=sha256:33598774b65264dfa87e1e70329d468e3c8b1d6a2768883558f465abb6798336

Pith citing papers

Observation 37a45b05-fd4d-428b-afa9-d6f1ee1947a8 · inbound

Universal C$^{\ast}$-Algebras from Graph Products: Structure and Applications cites this paper.

Universal C$^{\ast}$-Algebras from Graph Products: Structure and Applications The atoms of graph product von Neumann algebras

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-08-06T17:01:20.819862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-06T17:01:17.751149Z digest=sha256:294df98ab5c3a23dcfc51519e9370cd27803c91e328b0d60be27422440b1720c