Paper Citation Record · LEDGER

First-order transducibility among classes of sparse graphs

As of 8 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2505.15655.

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

pith.paper-citation-record.v1
2505.15655 v1

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:22:48.661739Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:24:42.655973Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T06:16:28.064256Z

Reference resolution

16 of 16 outbound references displayed

verified exact2
verified fuzzy10
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f0dc35fd-11c3-47e6-8b5a-048e53da58cf · outbound

This paper cites Twin-width I: Tractable FO model checking.

First-order transducibility among classes of sparse graphs Twin-width I: Tractable FO model checking

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:50.959279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a7c22829-3380-4e30-adea-02ffd8165b9e · outbound

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

First-order transducibility among classes of sparse graphs On first-order transductions of classes of graphs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T15:22:47.444099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4863c138-fc33-43e6-ae78-37c422438049 · outbound

This paper cites Lacon-, shrub- and parity-decompositions: Characterizing transductions of bounded ex- pansion classes.

First-order transducibility among classes of sparse graphs Lacon-, shrub- and parity-decompositions: Characterizing transductions of bounded ex- pansion classes

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:50.797326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ff1406ea-7def-4d5e-8516-5fff5677a6d2 · outbound

This paper cites an unresolved cited work.

First-order transducibility among classes of sparse graphs Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:22:50.596030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 29bc4032-4e1b-4ec2-895e-a4fe6067db0b · outbound

This paper cites First-order interpretations of bounded expansion classes.

First-order transducibility among classes of sparse graphs First-order interpretations of bounded expansion classes

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:50.460923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d5af29f3-d32c-4d55-917d-1604550bcd74 · outbound

This paper cites 3D-grids are not transducible from planar graphs.

First-order transducibility among classes of sparse graphs 3D-grids are not transducible from planar graphs

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-07T15:22:49.010156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dec2a590-eea5-44bc-82cf-a6e9e870fc0e · outbound

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

First-order transducibility among classes of sparse graphs Shrub- depth: Capturing height of dense graphs

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:50.281586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bc9f4fcc-440f-4a20-9507-e95a542cf955 · outbound

This paper cites Stavropoulos.

First-order transducibility among classes of sparse graphs Stavropoulos

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:50.030316Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3d768e71-7b3c-42cc-b4fc-727c1952a4c0 · outbound

This paper cites Transductions of Graph Classes Admitting Product Structure.

First-order transducibility among classes of sparse graphs Transductions of Graph Classes Admitting Product Structure

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T15:22:47.919103Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 124ff1a0-9556-4cae-9f4f-c618b2c9f12c · outbound

This paper cites Sparsity — Graphs, Structures, and Algorithms , vol- ume 28 of Algorithms and combinatorics.

First-order transducibility among classes of sparse graphs Sparsity — Graphs, Structures, and Algorithms , vol- ume 28 of Algorithms and combinatorics

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:49.889105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c6bf9153-b305-421b-ad4c-0364f9c1165f · outbound

This paper cites Sparsity.

First-order transducibility among classes of sparse graphs Sparsity

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:49.655770Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5a846041-7052-4f33-9eb6-78ffb634455d · outbound

This paper cites On the number of types in sparse graphs.

First-order transducibility among classes of sparse graphs On the number of types in sparse graphs

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:49.431735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0e2e4f6a-8260-4722-bec0-c6e80c144fe6 · outbound

This paper cites Graph classes through the lens of logic.

First-order transducibility among classes of sparse graphs Graph classes through the lens of logic

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T15:22:48.350737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 89a95101-6ac9-4a48-9d12-fd0d7b6ad640 · outbound

This paper cites On the generalized coloring numbers.

First-order transducibility among classes of sparse graphs On the generalized coloring numbers

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-08-07T15:22:48.837482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 837131a0-c469-4e10-ace5-a6b746f40898 · outbound

This paper cites On the generalised colouring numbers of graphs that exclude a fixed minor.

First-order transducibility among classes of sparse graphs On the generalised colouring numbers of graphs that exclude a fixed minor

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:49.233296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 83de6608-3162-4e75-975f-26427713e371 · outbound

This paper cites Colouring graphs with bounded generalized colouring number.

First-order transducibility among classes of sparse graphs Colouring graphs with bounded generalized colouring number

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:22:49.122105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 551569f1-1878-42d2-bf3b-9c549d617d57 · inbound

k-Planar and Fan-Crossing Drawings and Transductions of Embeddable Graphs cites this paper.

k-Planar and Fan-Crossing Drawings and Transductions of Embeddable Graphs First-order transducibility among classes of sparse graphs

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:24:42.855928Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.