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Paper Citation Record · LEDGER

Learning Laplacian Positional Encodings for Heterophilous Graphs

As of 22 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:2504.20430.

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

pith.paper-citation-record.v1
2504.20430 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T05:36:25.632802Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

14 of 14 outbound references displayed

  • verified exact0
  • verified fuzzy5
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cf989eda-774b-4075-9341-242e2cf35b9c · outbound

This paper cites Yes (b) An analysis of the properties and complexity (time, space, sample size) of any algorithm.

Learning Laplacian Positional Encodings for Heterophilous Graphs Yes (b) An analysis of the properties and complexity (time, space, sample size) of any algorithm

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:36:25.913169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.557067Z digest=sha256:94174d43cedf74176a3292924d5624ac3a1f7970a38b75e8d5a5c5ecd9c51ca3

Observation c11840a1-4e1b-4b9d-9e2f-2dacf26d145b · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.893939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.563852Z digest=sha256:3622c42c332654bf8ba6491ddb3fb0af6ab219676d6980178f9260caed63a8e6

Observation 67b8efa2-699f-42c7-a222-fa78a10e2394 · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.877214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.569174Z digest=sha256:52e2950e91c02895eacb8121ed67b3773d5086041a2b4f87546402970a76eac3

Observation 6cdfbeb5-4d5c-4a3d-ad2d-99e6333db723 · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.859219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.574457Z digest=sha256:ef168f4cc3c9556b4d2e37c8e28e5393dfed40b930fd95d64a18b45fd7ad826a

Observation 34af8cb4-3f12-4228-b1c8-b9323db8c5ce · outbound

This paper cites 2 2.2 Homophily, GNNs and Graph PEs.

Learning Laplacian Positional Encodings for Heterophilous Graphs 2 2.2 Homophily, GNNs and Graph PEs

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:36:25.841753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.579886Z digest=sha256:b9eebf40f25e36da02d78e03dee7ff12b0231e346a8f694ebd4b4efde29d1222

Observation f58ce9da-537f-43b2-a5a5-1d5e8789b9ee · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.698733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.627523Z digest=sha256:0197afc89d79b7837b65e7012924cada8e710ae68890d8f3f879742d85c737c9

Observation 94958ca2-4f9d-4201-b0ad-2b4a1a21932e · outbound

This paper cites Bo et al.

Learning Laplacian Positional Encodings for Heterophilous Graphs Bo et al

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:36:25.807033Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.592965Z digest=sha256:91f8fadca9285415e383e1031d4b9289cdf4cc8b651d736612f109860d0ecd86

Observation fbf87df4-45ea-40aa-a9a7-88f61ba0c551 · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.789790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.598304Z digest=sha256:6e86dcebe20c830e99348ceb9ee14857f4877840e857de0c6127ed2e84259026

Observation 4a2e834e-ea4b-44b2-8e4c-4f099f12be82 · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.772088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.603995Z digest=sha256:994dfe8512542d6d8c219cef7d6dc3a86421a240ad06a5c0ebc55a6ee9f42144

Observation f49637b4-4ff5-4048-b3d4-7e2944e9e8f5 · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.753687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.609612Z digest=sha256:7f39e51fd9c1c295dda98d05f8aa80e56fbcaee0e68410144cbc6de1ec918fa0

Observation 4aea1d8a-e8ca-4439-afb5-9073a20a5770 · outbound

This paper cites (2023) with a learnable linear projection matrix.

Learning Laplacian Positional Encodings for Heterophilous Graphs (2023) with a learnable linear projection matrix

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:36:25.735745Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.615547Z digest=sha256:a5af063fd80765cd283ad8abd3532cb3882b1e1f927759fceacc74b99a35aa79

Observation 4dfd5b55-42af-423c-914f-a0559d57c433 · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.717798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.621289Z digest=sha256:24b24cdb0cd9d44d74bf984aea6c19ade53a103744fad16ad225f1d87d0e9dfe

Observation df6838c9-88e6-4cd8-88ab-7a47abf713cb · outbound

This paper cites For LPE-FK, LPE-FLK, Elastic-PE, SignNet, and SAN-PE, we search across the number of eigenvector and eigenvalue pairsk∈ [8, 16, 32, 64, 128, 256, 512].

Learning Laplacian Positional Encodings for Heterophilous Graphs For LPE-FK, LPE-FLK, Elastic-PE, SignNet, and SAN-PE, we search across the number of eigenvector and eigenvalue pairsk∈ [8, 16, 32, 64, 128, 256, 512]

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:36:25.679956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.632802Z digest=sha256:681662585cdd32bd10ea47b42be6690c54190a690195dd4d06cdf72646187db6

Observation e89966c7-a116-426d-9ff8-03de3dfb1e9b · outbound

This paper cites an unresolved cited work.

Learning Laplacian Positional Encodings for Heterophilous Graphs Unresolved cited work

Reference 2022

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:36:25.824239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-16T05:36:25.587491Z digest=sha256:cd36ec5ad888853779139075134b6e5343511e48f8b4783076354e433bf8af17

Pith citing papers

No inbound Pith citation observations are available.