Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-09T22:35:17.657430Z
Paper Citation Record · LEDGER
Towards Understanding the Expressive Power of GNNs with Global Readout
As of 18 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2604.22870.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
15 of 15 outbound references displayed
- verified exact1
- verified fuzzy9
- unresolved5
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 9182ea3a-750f-4aed-92c1-11a42eb31fab · outbound
This paper cites Preservation Theorems for Unravelling-Invariant Classes: A Uniform Approach for Modal Logics and Graph Neural Networks.
Towards Understanding the Expressive Power of GNNs with Global Readout Preservation Theorems for Unravelling-Invariant Classes: A Uniform Approach for Modal Logics and Graph Neural Networks
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-09T22:39:14.494187Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 065e1a1b-c348-447a-a129-22b1c2d7a783 · outbound
This paper cites u(k) 1 ∈V 1 withk≤c there is some distinctu (1) 2.
Towards Understanding the Expressive Power of GNNs with Global Readout u(k) 1 ∈V 1 withk≤c there is some distinctu (1) 2
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.399759Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation da8a721b-3ee0-4cf2-bad6-613e86933c28 · outbound
This paper cites in the middle.
Towards Understanding the Expressive Power of GNNs with Global Readout in the middle
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.441359Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 2aa7215f-69b0-4711-8dfb-44d94927e345 · outbound
This paper cites Then,φmust be invari- ant under∼ L,c,∗ ∃ , whereLis the number of layers inN (Lemma 16).
Towards Understanding the Expressive Power of GNNs with Global Readout Then,φmust be invari- ant under∼ L,c,∗ ∃ , whereLis the number of layers inN (Lemma 16)
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.429094Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation dea3a9c1-7129-471c-823f-aa485d0e4794 · outbound
This paper cites predictably.
Towards Understanding the Expressive Power of GNNs with Global Readout predictably
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.435555Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 99c0342b-ccd1-40ed-9628-9c87275515a4 · outbound
This paper cites canonical.
Towards Understanding the Expressive Power of GNNs with Global Readout canonical
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.391827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 4179bb7c-d4b9-4e8c-96a9-ad6e396f4016 · outbound
This paper cites an unresolved cited work.
Towards Understanding the Expressive Power of GNNs with Global Readout Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-05-23T14:25:43.409579Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation a6183eb5-fa10-473d-8a7c-398e4a056659 · outbound
This paper cites Proof.Let us fix anyv∈Vhavingn G(v) = 1and let G′ be the graphGbut withE ′ :=E\ {(v, u)|u∈ V}.
Towards Understanding the Expressive Power of GNNs with Global Readout Proof.Let us fix anyv∈Vhavingn G(v) = 1and let G′ be the graphGbut withE ′ :=E\ {(v, u)|u∈ V}
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.405371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 55c0be21-227e-4d07-93be-09b4e7d0fcd4 · outbound
This paper cites an unresolved cited work.
Towards Understanding the Expressive Power of GNNs with Global Readout Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-05-23T14:25:43.424767Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 418715ad-3098-4ed6-a25d-8f9a86a7bffc · outbound
This paper cites an unresolved cited work.
Towards Understanding the Expressive Power of GNNs with Global Readout Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-05-23T14:25:43.395153Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation f73607f8-17a4-4fb2-9740-5c0a5faa49c7 · outbound
This paper cites Proof.LetG ⋆ be the graph obtained fromGby applying Lemma 32.
Towards Understanding the Expressive Power of GNNs with Global Readout Proof.LetG ⋆ be the graph obtained fromGby applying Lemma 32
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.384539Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation e5732c2d-1cb5-4cb8-8c73-a9acbd6b2cfc · outbound
This paper cites an unresolved cited work.
Towards Understanding the Expressive Power of GNNs with Global Readout Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-05-23T14:25:43.420505Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation bf6af2ef-3108-4386-abc5-c6c004eb5762 · outbound
This paper cites an unresolved cited work.
Towards Understanding the Expressive Power of GNNs with Global Readout Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-05-23T14:25:43.388068Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 9c709830-06ff-4afe-ae96-cda9ef6f73ea · outbound
This paper cites Proof.We begin by providing an analogue of Lemma 32 for G2.
Towards Understanding the Expressive Power of GNNs with Global Readout Proof.We begin by providing an analogue of Lemma 32 for G2
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.413088Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 368f25ce-0963-4ed4-81ef-d70ba2d2c6b1 · outbound
This paper cites By 1 and (†) we haveG 1, v1 ∼L,c G2, v2.
Towards Understanding the Expressive Power of GNNs with Global Readout By 1 and (†) we haveG 1, v1 ∼L,c G2, v2
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-23T14:25:43.417131Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
No inbound Pith citation observations are available.