Paper Citation Record · LEDGER

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing

As of 4 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2605.19702.

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

pith.paper-citation-record.v1
2605.19702 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-20T01:47:41.536825Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-03T06:30:56.289259+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

41 of 41 outbound references displayed

verified exact0
verified fuzzy37
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 300b7c2d-b9fe-4203-aab8-504d39cb94e0 · outbound

This paper cites Combinatorica , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Combinatorica , volume=

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.536707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 054d3f70-1619-4c7a-8945-5707bc8a8438 · outbound

This paper cites Computational Complexity , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Computational Complexity , volume=

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.592014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 40f47f99-191c-446e-a244-72fa535255de · outbound

This paper cites Acta Mathematica Sinica , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Acta Mathematica Sinica , pages=

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.544885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 04a5f3ba-830d-4446-9736-b625e2dc8814 · outbound

This paper cites Canadian Journal of Mathematics , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Canadian Journal of Mathematics , volume=

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.579182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 6861486d-754e-4d73-8e90-18f2d1cf0568 · outbound

This paper cites 2017 , institution=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing 2017 , institution=

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.482274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 9d4d38be-63c8-4746-bdee-0b17c65d9ae1 · outbound

This paper cites 2016 , institution=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing 2016 , institution=

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.501187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 3599caf5-0814-4844-a642-e5c00bd9886a · outbound

This paper cites ACM Transactions on Computational Logic (TOCL) , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing ACM Transactions on Computational Logic (TOCL) , volume=

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.514310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 4a0804b9-43aa-4c41-8637-9a2093396174 · outbound

This paper cites ACM Transactions on Computation Theory (TOCT) , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing ACM Transactions on Computation Theory (TOCT) , volume=

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.505667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 75faad8d-5592-4f59-8323-8bdc3e0b1d29 · outbound

This paper cites Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the 48th Annual ACM Symposium on Theory of Computing (STOC) , pages=

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.540664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 13198ced-6bf4-4eb9-a7fd-162c8d0d23ec · outbound

This paper cites Proceedings of the tenth annual ACM symposium on Theory of computing , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the tenth annual ACM symposium on Theory of computing , pages=

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.532581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 5fd402ad-eb56-488a-b24b-a3154d407b9b · outbound

This paper cites an unresolved cited work.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-05-20T01:47:57.665626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 855e8533-2eec-4484-a30b-885f289190ab · outbound

This paper cites Journal of computer and system sciences , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Journal of computer and system sciences , volume=

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.638592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation a3d0bf51-2654-427d-9c33-d89dfb8f0626 · outbound

This paper cites Proceedings of the ninth annual ACM symposium on Theory of computing , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the ninth annual ACM symposium on Theory of computing , pages=

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.617595Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 97dcbfa7-39b7-4538-8045-f9b901f404db · outbound

This paper cites Pacific Journal of Mathematics , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Pacific Journal of Mathematics , volume=

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.609006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation a7b27d79-23a8-4932-ad5d-07e565ab1568 · outbound

This paper cites The $k$-Dimensional Weisfeiler-Leman Algorithm.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing The $k$-Dimensional Weisfeiler-Leman Algorithm

Reference 15

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T01:47:57.286343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation f7ea216f-3af9-4a8a-807b-1ecae2fbeac8 · outbound

This paper cites Nauchno-Technicheskaya Informatsia (NTI) Series , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Nauchno-Technicheskaya Informatsia (NTI) Series , volume=

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.491344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 4506e908-cdbc-47b8-b67d-7989b1dc64bc · outbound

This paper cites Proceedings of the 22th Annual European Symposium on Algorithms (ESA) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the 22th Annual European Symposium on Algorithms (ESA) , pages=

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.634597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 7ea85919-166c-4a23-b15d-02a63610e227 · outbound

This paper cites Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI) , pages=

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.630712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation afab978f-d703-4831-b984-4fb8cc725472 · outbound

This paper cites Proceedings of the 14th Annual ACM Symposium on Theory of Computing (STOC) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the 14th Annual ACM Symposium on Theory of Computing (STOC) , pages=

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.487043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 5d5329e6-d98e-4dd0-a964-42bedb20b579 · outbound

This paper cites Proceedings of the 6th Annual ACM Symposium on Theory of Computing (STOC) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Proceedings of the 6th Annual ACM Symposium on Theory of Computing (STOC) , pages=

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.669620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation f084de18-3fad-46fc-9f1d-18c869bc75f1 · outbound

This paper cites Journal of Algorithms , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Journal of Algorithms , volume=

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.605716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 06b30a11-4a9c-44a6-93ca-81db1f21a456 · outbound

This paper cites North-Holland Mathematics Studies , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing North-Holland Mathematics Studies , volume=

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.622942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 985393d5-f1fc-44b9-8284-a7b71f85f9f7 · outbound

This paper cites Discrete Applied Mathematics , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Discrete Applied Mathematics , volume=

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.626806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation d666e292-7300-425b-b07e-1ab576bfaaae · outbound

This paper cites The monotone and planar circuit value problems are log space complete for.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing The monotone and planar circuit value problems are log space complete for

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.570165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation a60e9e57-7a23-454c-8d30-43f038507354 · outbound

This paper cites 2020 , school=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing 2020 , school=

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.598836Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation f48f4d2d-def9-45bf-a1b4-332aa0d92f2d · outbound

This paper cites The Power of the.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing The Power of the

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.565001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 34ef41f9-62a7-45e5-8728-3265785feee9 · outbound

This paper cites An Introduction to Lifted Probabilistic Inference , year=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing An Introduction to Lifted Probabilistic Inference , year=

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.585027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 6dcecd33-7d9f-44db-ad41-b4bbb78deb3e · outbound

This paper cites 1990 , publisher=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing 1990 , publisher=

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.654028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 948b27c2-e44f-43c0-a8cf-178d0bde5c0a · outbound

This paper cites International Colloquium on Automata, Languages, and Programming (ICALP) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing International Colloquium on Automata, Languages, and Programming (ICALP) , pages=

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.549413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 272a4734-9803-42ed-83ec-c91719639802 · outbound

This paper cites an unresolved cited work.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-05-20T01:47:57.518682Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation cea93961-d453-477b-8cf6-f1dc2168b43a · outbound

This paper cites Journal of Graph Theory , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Journal of Graph Theory , volume=

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.495915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation ab260b8c-b84c-49c6-a04a-1e9a8c8b8601 · outbound

This paper cites 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) , pages=

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.509983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 10721004-0369-48ab-abdb-190acacb6763 · outbound

This paper cites Congressus Numerantium , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Congressus Numerantium , volume=

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.523044Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation bbf2f887-0ab3-4866-8fc3-5ea030f45ed5 · outbound

This paper cites International Symposium on Mathematical Foundations of Computer Science , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing International Symposium on Mathematical Foundations of Computer Science , pages=

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.553921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 89d2a4c1-c402-4956-b2dc-920c8dffe4ef · outbound

This paper cites Weisfeiler and.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Weisfeiler and

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.657871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation ba003b80-e360-4d44-9afd-7f6a3b5d6b70 · outbound

This paper cites 32nd International Symposium on Algorithms and Computation (ISAAC) , pages=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing 32nd International Symposium on Algorithms and Computation (ISAAC) , pages=

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.527850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 81da250d-115e-4e95-9fc1-f6c7b562ca9f · outbound

This paper cites Weisfeiler and.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Weisfeiler and

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.661771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 5c53a8e7-d8f3-4362-b930-358c2f30b63b · outbound

This paper cites ACM Transactions on Computation Theory (TOCT) , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing ACM Transactions on Computation Theory (TOCT) , volume=

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.646606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 67691653-3cd3-4190-a307-98811f0550c2 · outbound

This paper cites Bounding the.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Bounding the

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.642645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 07a0c6e0-7d3b-4b8e-b790-8418b89bb71d · outbound

This paper cites Graph isomorphisms in quasi-polynomial time.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Graph isomorphisms in quasi-polynomial time

Reference 40

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T01:47:57.293643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Observation 5ef2adae-bb19-44c4-a62b-630bf6394a86 · outbound

This paper cites Fundamenta Informaticae , volume=.

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing Fundamenta Informaticae , volume=

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T01:47:57.650257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-03T06:30:56.289259+00:00.

Pith citing papers

No inbound Pith citation observations are available.