Paper Citation Record · LEDGER

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO

As of 23 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 1 inbound Pith citation observation for arXiv:2501.13903.

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

pith.paper-citation-record.v1
2501.13903 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T15:43:38.291501Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:55:34.064102Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:55:34.552475Z

Reference resolution

37 of 37 outbound references displayed

verified exact0
verified fuzzy31
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1b7bc39d-0066-4cc0-b820-f73aac69ddea · outbound

This paper cites Interpreting nowhere dense graph classes as a classical notion of model theory.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Interpreting nowhere dense graph classes as a classical notion of model theory

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T15:43:38.094814Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e884a48-c3f1-489e-9efc-f84e8a985e6a · outbound

This paper cites Tree-decomposable theories.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Tree-decomposable theories

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.158813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 77203fae-c1de-4142-a1fe-eb39c073845a · outbound

This paper cites Baldwin and Saharon Shelah.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Baldwin and Saharon Shelah

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.140219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 851be43e-ce8f-4c89-bd9d-6a0a69a77fa6 · outbound

This paper cites Separator logic and star-free expressions for graphs.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Separator logic and star-free expressions for graphs

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-10T15:43:38.111187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8274364-765e-4ab9-bc9c-a692a602b6ac · outbound

This paper cites Model checking on interpretations of classes of bounded local cliquewidth.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Model checking on interpretations of classes of bounded local cliquewidth

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.122639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e6caa952-1e59-451a-a946-80efbed37ede · outbound

This paper cites Twin-width iv: Ordered graphs and matrices.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Twin-width iv: Ordered graphs and matrices

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.104109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 83220a77-d5c4-4ba8-9220-7983e0c2b0a9 · outbound

This paper cites Laskowski.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Laskowski

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T15:43:38.128279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 755e1699-e5ac-4a0e-b971-34ee306c12f3 · outbound

This paper cites Shallow vertex minors, stability, and dependence.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Shallow vertex minors, stability, and dependence

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.080652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 043c2651-eb1c-4160-b8f5-1fe5c70bb5d3 · outbound

This paper cites Graph structure and monadic second-order logic: a language-theoretic approach, volume 138.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Graph structure and monadic second-order logic: a language-theoretic approach, volume 138

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.052314Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 25719f2a-4449-4e85-8c92-843dc40d7013 · outbound

This paper cites Vertex-minors, monadic second-order logic, and a conjecture by Seese.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Vertex-minors, monadic second-order logic, and a conjecture by Seese

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.032723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3b5706a6-7f10-40dc-8074-68a955634bce · outbound

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

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO First-Order Model Checking on Monadically Stable Graph Classes

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:39.014688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bbfead51-fa72-4f84-a865-c8fb3f9cd9a0 · outbound

This paper cites First-order model checking on struc- turally sparse graph classes.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO First-order model checking on struc- turally sparse graph classes

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.997236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2ea6f052-4bcd-4584-b9be-0613f326b5bd · outbound

This paper cites Indiscernibles and flatness in monadically stable and monadically NIP classes.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Indiscernibles and flatness in monadically stable and monadically NIP classes

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.978413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 35f633f4-154a-46b4-89ac-e2fb8891581f · outbound

This paper cites Flip-breakability: A combinatorial dichotomy for monadically dependent graph classes.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Flip-breakability: A combinatorial dichotomy for monadically dependent graph classes

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.961935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4744b691-3af3-434d-9115-5494cbe3af57 · outbound

This paper cites Where first-order and monadic second-order logic coincide.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Where first-order and monadic second-order logic coincide

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.943343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7dd1efae-790d-464d-8b41-be9092a4592b · outbound

This paper cites Stockmeyer, and Moshe Y.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Stockmeyer, and Moshe Y

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.925386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 022f710c-66b0-45f2-b7d4-63e56b7ba634 · outbound

This paper cites On local and non-local properties.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO On local and non-local properties

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.905322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7f01a557-dde1-4209-9930-96026e5c7f55 · outbound

This paper cites Kernelizing mso properties of trees of fixed height, and some consequences.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Kernelizing mso properties of trees of fixed height, and some consequences

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.883371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2b5a645f-8d62-4025-9324-bcc5a391eafe · outbound

This paper cites Flipper Games for Monadically Stable Graph Classes.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Flipper Games for Monadically Stable Graph Classes

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.863978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation bb946751-2a3c-4d0e-8bc2-928b78636251 · outbound

This paper cites When trees grow low: Shrubs and fast MSO1.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO When trees grow low: Shrubs and fast MSO1

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.842458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4d1f3e6d-5868-4c22-8516-10ff2d48b988 · outbound

This paper cites Shrub-depth: Capturing height of dense graphs.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Shrub-depth: Capturing height of dense graphs

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.818781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 066a944e-ba49-45f8-af88-c5c9b6b25d30 · outbound

This paper cites Deciding first-order properties of nowhere dense graphs.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Deciding first-order properties of nowhere dense graphs

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.792448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b5332584-4c93-464f-ab07-1dce509f51a4 · outbound

This paper cites Model-theoretic methods in the study of elementary logic.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Model-theoretic methods in the study of elementary logic

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.767265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b7847a8a-ce1c-48c7-8842-e2be2801dc89 · outbound

This paper cites A Shorter Model Theory.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO A Shorter Model Theory

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-10T15:43:38.221384Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5120e03f-210e-472a-b502-44544ec13997 · outbound

This paper cites Obstructions for bounded shrub-depth and rank-depth.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Obstructions for bounded shrub-depth and rank-depth

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.730410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 470ef734-7319-47b3-ba0b-04fbfe9c1cda · outbound

This paper cites Model checking lower bounds for simple graphs.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Model checking lower bounds for simple graphs

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.710950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1396558e-240a-4263-85fc-dd5361d30c22 · outbound

This paper cites Elements of finite model theory , volume 41.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Elements of finite model theory , volume 41

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.691305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5c5abdfa-20ac-4111-9650-884178de35b6 · outbound

This paper cites PhD thesis, University of Bremen, 2024.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO PhD thesis, University of Bremen, 2024

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.669536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 21440217-f46e-46c2-9192-c14fdd62e64c · outbound

This paper cites Makowsky.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Makowsky

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.651923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e67cef85-931b-4894-ad00-6968f21afc33 · outbound

This paper cites On nowhere dense graphs.European Journal of Combinatorics , 32(4):600–617, 2011.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO On nowhere dense graphs.European Journal of Combinatorics , 32(4):600–617, 2011

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.635879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 67de5cc2-b939-460c-9865-dafb6cf3100d · outbound

This paper cites Canonical Decompositions in Monadically Stable and Bounded Shrubdepth Graph Classes.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Canonical Decompositions in Monadically Stable and Bounded Shrubdepth Graph Classes

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.618320Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 909dce24-f06b-4208-a6de-53e2e37c279e · outbound

This paper cites Transducing paths in graph classes with unbounded shrubdepth.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Transducing paths in graph classes with unbounded shrubdepth

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.600126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7939d849-ecf7-46f7-ba69-0fc292240908 · outbound

This paper cites Stable graphs.Fundamenta Mathematicae, 100(2):101– 107, 1978.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Stable graphs.Fundamenta Mathematicae, 100(2):101– 107, 1978

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.565975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 53a63fdd-c6bf-4839-b4f2-3eaf4069a7e0 · outbound

This paper cites First-order logic with connec- tivity operators.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO First-order logic with connec- tivity operators

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.544988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f1369ade-eaa6-420f-8e81-7e6122b3650a · outbound

This paper cites The structure of the models of decidable monadic theories of graphs.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO The structure of the models of decidable monadic theories of graphs

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T15:43:38.522826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a152f8c8-f8a1-48d7-b83c-497614df9caf · outbound

This paper cites A note on stability and NIP in one variable.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO A note on stability and NIP in one variable

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-10T15:43:38.291501Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ff1138b-f14c-4817-b509-15734c0207e4 · outbound

This paper cites an unresolved cited work.

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO Unresolved cited work

Reference 2025

Resolution: unresolved; raw_fallback, observed 2026-08-10T15:43:38.582444Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation cf47d74a-3ccb-4bcc-b5e3-de23b005f849 · inbound

Unavoidable pivot-minors in graphs of large rank-depth cites this paper.

Unavoidable pivot-minors in graphs of large rank-depth Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:55:34.621875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.