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Paper Citation Record · LEDGER

Watermarking Graph Neural Networks via Explanations for Ownership Protection

As of 6 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2501.05614.

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

pith.paper-citation-record.v1
2501.05614 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T11:50:26.030339Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+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

21 of 21 outbound references displayed

  • verified exact2
  • verified fuzzy7
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 32b022ec-c96f-49ea-871a-ef3d97269cf6 · outbound

This paper cites Semi-Supervised Classification with Graph Convolutional Networks.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Semi-Supervised Classification with Graph Convolutional Networks

Reference 1

Resolution
metadata mismatch
local_arxiv, observed 2026-05-23T05:42:36.124593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-07-11T11:50:26.030339Z digest=sha256:807e720b6cf12f5e98e94d7a54c4ba8dd77e0c94102734fcefa7fbb76fe1f66c

Observation 29490d51-eadb-431f-9a9f-ba057a85d20a · outbound

This paper cites Szyller, S., Atli, B.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Szyller, S., Atli, B

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-05-23T05:42:36.145793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:c40d161a344055df881b3ba7479782d4df74b5e1c6753f456d0f613a0b2ad8f1

Observation c2e0cded-0876-4d1a-b94a-468f7cc054d4 · outbound

This paper cites Embedding Watermarks into Deep Neural Networks.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Embedding Watermarks into Deep Neural Networks

Reference 4

Resolution
metadata mismatch
local_arxiv, observed 2026-05-23T05:42:36.350377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:8ba2302546102e905987c502f7eb6a9b64bd2c0737b61911bb98ac8997d5a770

Observation a06b2eec-8cf1-4969-ab35-47313a461723 · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-05-23T05:42:36.139223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:501c7cff0ae9835b4dbc6f5f995d9212f15996e097d9d872cfff361440281386

Observation bcc0f9f4-93e5-4eef-a0ed-3f0f9e43bd6a · outbound

This paper cites scores” corresponding to each non-existing edge. As the generator trains, this “score.

Watermarking Graph Neural Networks via Explanations for Ownership Protection scores” corresponding to each non-existing edge. As the generator trains, this “score

Reference 6

Resolution
metadata mismatch
doi, observed 2026-05-23T05:42:36.131848Z

Source-reported events for the cited work

correction dated 2024-01-09. Source: crossref record 10.1016/j.aiopen.2024.01.002->10.1016/j.aiopen.2021.01.001:correction, observed 2026-07-11T03:16:57.222018+00:00. This notice travels one citation hop only.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:5f48a6dfe71c281647b7dada3b571980d7f719eafff45ef694042dacff6ffb7a

Observation 8dd565cf-daa4-46fc-b4ad-440362fa17bc · outbound

This paper cites sufficiently large.

Watermarking Graph Neural Networks via Explanations for Ownership Protection sufficiently large

Reference 7

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verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.376050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:3e1e4700d460a158d642b4fd87afa09916649f46b0359f60511ff5ff287b8834

Observation c95adc5d-fdfc-4136-9c6e-9b3a1a224828 · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 8

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unresolved
raw_fallback, observed 2026-05-23T05:42:37.382602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:786ee33aff001da332b2c352a8f0411d57dea1a598f71e8cd73eed9058812284

Observation 3ad765b4-1917-4c7b-a2b0-535b282f62ac · outbound

This paper cites for i=1 to I simulations do Randomly select 𝑇 distinct indices 𝑖𝑑𝑥 1.

Watermarking Graph Neural Networks via Explanations for Ownership Protection for i=1 to I simulations do Randomly select 𝑇 distinct indices 𝑖𝑑𝑥 1

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.369669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:0380aec6c43e0127d3aaebde46441e7a0bf11202b9ef87fabc6b51583cc5f918

Observation 79e3db3f-17f8-4a6c-a3a7-996526aa653e · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.372853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:7ce3510b5642a38aeae196877709b8e81c2c001925fa3611d6aa1f113bef2839

Observation 88c083a1-6bdb-442c-b2ec-23b15de70e1c · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 11

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unresolved
raw_fallback, observed 2026-05-23T05:42:37.366740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:89d1b8ec9da1a9cba20c631e92cd8c6f258a92779d09a64eb0aa0e9ee7691f65

Observation ddf56d22-ef36-4c3d-89f2-c072ae95f0f7 · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.379355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:d986c1cc226c3f1586f61737279c40a4f935c2fbf3ec92f5205a87b367f4ea80

Observation 6c31cd4a-dd25-46c4-9635-3c440f39545d · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.363858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:7cfee4a618b21807273916a15ba8b5f26aeb055ce38fc42ce55532b0b1f383cf

Observation e86d0549-6bed-432f-9aa1-354db2f58b61 · outbound

This paper cites If 𝑝𝑧𝑡𝑒𝑠𝑡 < 𝛼 𝑣 , the candidate subgraphs provide enough evidence of ownership to reject 𝐻0.

Watermarking Graph Neural Networks via Explanations for Ownership Protection If 𝑝𝑧𝑡𝑒𝑠𝑡 < 𝛼 𝑣 , the candidate subgraphs provide enough evidence of ownership to reject 𝐻0

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.351373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:02f095c272bfbf9770c06fe0cd6dd3880f7f7cc73593e692a674aa17990fab93

Observation 73299d74-027e-46a2-bd67-0c6cebcae545 · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.354453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:6ad34139f9722fe02f3106d7077719de8cb58f74e04d3c008df00894bd3ab293

Observation ea44a271-dbd5-45e5-9858-1433f65a180b · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.357435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:dc586958716e1fecbe9e3681ca221ca032ed5905736c08101a7e300627b9c9d4

Observation bab13fe8-e512-47d9-a410-760d8f693c8d · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.360826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:1111aa84b4fff2b74af0dee276702a497e659ae085871c130e9785fb2c4b11d3

Observation 9f8d17dd-741b-42dd-84d9-f45e6f82a53e · outbound

This paper cites an unresolved cited work.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-05-23T05:42:37.385720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:5c43c570818db5f16fd0a460a0b90931703d96ae6fc18b5e22859eaaba2687e9

Observation 5ed8acf7-655f-49f9-917e-9ed0cfe6c256 · outbound

This paper cites For obtaining explanations of 𝑇 subgraphs during a given epoch of watermark embedding, the complexity is therefore: 𝑂 (𝑇 (𝐹2𝑁2 + 𝐹3)) Total Complexity.

Watermarking Graph Neural Networks via Explanations for Ownership Protection For obtaining explanations of 𝑇 subgraphs during a given epoch of watermark embedding, the complexity is therefore: 𝑂 (𝑇 (𝐹2𝑁2 + 𝐹3)) Total Complexity

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.389241Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:2047088a98f216cc1569d9004a3661e61f9131cfe1cd4a2ff17f8ddb4dba6a84

Observation 4a395b88-4897-4ffd-a8d9-c86a610a9981 · outbound

This paper cites Subgraphs are formed by randomly selecting 𝑛 = 𝑠 · |V 𝑡𝑟 | nodes from the training set (where |V 𝑡𝑟 | is the number of training nodes and 𝑠 is a proportion of that size).

Watermarking Graph Neural Networks via Explanations for Ownership Protection Subgraphs are formed by randomly selecting 𝑛 = 𝑠 · |V 𝑡𝑟 | nodes from the training set (where |V 𝑡𝑟 | is the number of training nodes and 𝑠 is a proportion of that size)

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.392801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:b2fe72a67883cd2e4be3ea192e2b817457d92fd702cd1b6f4c7e71e6134965fa

Observation f84e257d-7138-4670-985e-5d9d4a93933b · outbound

This paper cites Subgraphs are formed by randomly selecting 𝑛 = 𝑠 · |E𝑡𝑟 | edges.

Watermarking Graph Neural Networks via Explanations for Ownership Protection Subgraphs are formed by randomly selecting 𝑛 = 𝑠 · |E𝑡𝑟 | edges

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.396271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:79c2217bf265f0c4185122dcf7902e2273eabf584fed82de6eb239c89d8865f4

Observation e9252696-a300-4ca6-ae93-4f2f58744f21 · outbound

This paper cites teacher” model, and an untrained “student.

Watermarking Graph Neural Networks via Explanations for Ownership Protection teacher” model, and an untrained “student

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-05-23T05:42:37.399892Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

source=pdf_text observed=2026-05-23T05:39:40.731920Z digest=sha256:0b9a5440273b8949e36c21e81437868a02819b84a6363a021dff3e0818d6fcdf

Pith citing papers

No inbound Pith citation observations are available.