Paper Citation Record · LEDGER

Boolean combinations of graphs

As of 12 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2412.19551.

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

pith.paper-citation-record.v1
2412.19551 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:27:56.883707Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T13:40:49.816845Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact3
verified fuzzy4
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ee3784ec-54c3-43fa-83cc-b6782ca4bd50 · outbound

This paper cites On first-order transductions of classes of graphs.

Boolean combinations of graphs On first-order transductions of classes of graphs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T00:27:56.846666Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a80f946c-3fbd-440c-8c8c-26583dbd6e54 · outbound

This paper cites Randomized com munication and implicit representations for matrices and graphs of small sign-rank.

Boolean combinations of graphs Randomized com munication and implicit representations for matrices and graphs of small sign-rank

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:27:57.260700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ba90ad9d-38f4-471a-99b3-9b94a1260325 · outbound

This paper cites Induced subgraph density. VI. Bounded VC-dimension.

Boolean combinations of graphs Induced subgraph density. VI. Bounded VC-dimension

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T00:27:56.883707Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f3e778a-4115-4986-980c-bfe941f9ff3d · outbound

This paper cites Cover numbers by certain graph families.

Boolean combinations of graphs Cover numbers by certain graph families

Reference 1972

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:27:56.957373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 999b8276-67cf-46be-a3c1-4c8bc17ad33b · outbound

This paper cites Giannopoulou, Stephan Kre utzer, O-joung Kwon, Michal Pilipczuk, Roman Rabinovich, and Sebastian Siebert z.

Boolean combinations of graphs Giannopoulou, Stephan Kre utzer, O-joung Kwon, Michal Pilipczuk, Roman Rabinovich, and Sebastian Siebert z

Reference 1979

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:27:57.277465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6f09e26f-de9f-4519-95a0-8d08ad73c7c9 · outbound

This paper cites Closure properties for pri- vate classiﬁcation and online prediction.

Boolean combinations of graphs Closure properties for pri- vate classiﬁcation and online prediction

Reference 1989

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:27:57.294396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 90cb189e-d34a-410f-a186-da51b9a03c5d · outbound

This paper cites Rankwidth meets stability.

Boolean combinations of graphs Rankwidth meets stability

Reference 1993

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T00:27:57.242240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation db403fe3-4dd5-4eca-9168-60a3b1b3c7e5 · outbound

This paper cites First-Order Model Checking on Monadically Stable Graph Classes.

Boolean combinations of graphs First-Order Model Checking on Monadically Stable Graph Classes

Reference 2006

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:27:57.078945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d245431a-8aca-4dfb-ba8b-e15c9a7fbf03 · outbound

This paper cites Partitioning perfect graphs into comparability graphs.

Boolean combinations of graphs Partitioning perfect graphs into comparability graphs

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-11T00:27:56.862475Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0bb575d-676c-4dfd-ad2b-fb64b91d13d1 · outbound

This paper cites Adjacency Labeling Schemes for Small Classes.

Boolean combinations of graphs Adjacency Labeling Schemes for Small Classes

Reference 2020

Resolution: verified exact; local_arxiv, observed 2026-08-11T00:27:57.203915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation ae49bb47-dcda-4bca-b890-d5fe20bf8ede · outbound

This paper cites Laskowski.

Boolean combinations of graphs Laskowski

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-11T00:27:56.840595Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4281c986-bceb-41be-9a4f-4accbbf3636d · outbound

This paper cites Path Odd-Covers of Graphs.

Boolean combinations of graphs Path Odd-Covers of Graphs

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-11T00:27:56.829946Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation ab45cff9-3876-476d-9740-99f3b82a9eed · inbound

Set-defined graph classes: $\chi$-boundedness meets tropical algebra cites this paper.

Set-defined graph classes: $\chi$-boundedness meets tropical algebra Boolean combinations of graphs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-30T13:40:49.816845Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.