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Paper Citation Record · LEDGER

The atoms of graph product von Neumann algebras

As of 15 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.651045Z digest=sha256:3e06d4a2a9c98d2b7719a0c07dc8a25529b10d294492ae9a483ebcf08ccfa89e

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.697141Z digest=sha256:7d822d4c03bab1ee585c869b9fde2d91a29be511eb3219c3d0aa3924fd3f2f23

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.824267Z digest=sha256:36e5bfcf6f306f13db09e4dba9cc4f225e8113249352a927790c7806cec884e8

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:34.988973Z digest=sha256:575d03041464f94808218d308edf4e1c0cd9bdde5999b802b214dadeb7f3ea99

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=sha256:3de896d4d84753ef318bf52c87270a5f6b686789d36e4f80f452ad7219ed54e7

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.329539Z digest=sha256:6681a46e84156914aa52486e0a9efab2198084bde78dd4311da170ff2549e5be

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.526660Z digest=sha256:43c1051012ae00f0ffed4104e6cac9703f1002b5bfb95b24877c07d253c21602

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.647036Z digest=sha256:137059f833f02e6183a7ee97a67b82530f09ce8c98fc0214fb6be2fbeee79097

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.768410Z digest=sha256:35c63a2e9cd590d4c9580c321f415c1229d83ee3fb09d5d7d376c4e9261a5fdb

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:35.919085Z digest=sha256:25381f2ff5d98bd0f86826de0e813de7b32954c1e0b8890a106d3199f0e6b9a4

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.017174Z digest=sha256:69b0bdc6fd91f2e12f2dd100904773808b9fe6d9f04195f4bcd64dba86353c06

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.190640Z digest=sha256:8f2d515753dafcabe1464d62a7347552363675a891bde366478c23c4f5b7a0ab

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.313592Z digest=sha256:f53be95efbcd9b1788f74fa53421145274e09b45a03b19f735d7f481382f5bf6

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.445557Z digest=sha256:107fddc4b2989a771edd585eff1664dc7bc44b9fdd9f8c7d92414ec28904983b

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.650145Z digest=sha256:e2c4723878820b7ed8ea7bb858adde932fac6d95b810a5a8d4151b55bb759d66

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.768705Z digest=sha256:1a0564b21516d0ec948f0fdc1066c27ffc9182cfe32bad5c689f382fc80f9413

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:36.888191Z digest=sha256:946da85afa1f2ad8f9b4e541b1a3be8cee02497b4b49f5dabfe4b558447e76ce

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-07T05:08:37.025769Z digest=sha256:31647113a5f783e1fa5322cac03529ab6f7fc8beaaf6fd27264082d8eb7899cb

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-06T17:01:17.751149Z digest=sha256:1762fc74d281c9efec796660d606c139ce644c4283193cc1cfa5e222d4541191