Pith. sign in

Paper Citation Record · LEDGER

Learning Laplacian Positional Encodings for Heterophilous Graphs

As of 23 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 2026-08-23T06:30:58.430688+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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.557067Z digest=sha256:5e8918bd798fd3c1270a274af70bd1a62277d55aecf05782bdc56d1d0d433bc1

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.563852Z digest=sha256:c3dda078e505dab261b9234442edc2b8944079c467634d284ef5a96c6c95e07f

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.569174Z digest=sha256:aca0f93975e117db931960d554e3feb534a317d088e91882bf5e418a80f9a0dc

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.574457Z digest=sha256:23616f67e571f0777d7327de3ca382f8db48e249beb5d9d82fe364ac37d432b0

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.579886Z digest=sha256:7e31faebf415e28b0c314e0d5c69d52accef04a18745726ef8fcb1bfdd6265a1

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.627523Z digest=sha256:b3a7d6ea547207b8d3ed6548ac3934599c5b6490271ffe0162f9af9a1fee391d

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.592965Z digest=sha256:861813d375312a7fdc489cf455811d918aec41d87cd432d60dfec8b0d3d0a223

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.598304Z digest=sha256:6ea107483da4d9f5cc388ceaa0a443260b48277fa69501e98fac457d8ec3e7e2

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.603995Z digest=sha256:3a90356b91f0454d0258e2c0c4343739023f71733466d31cda9cd55cec5638f7

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.609612Z digest=sha256:6eb3d08bef519339d60461ea9b34b937ecd6cf19101cb594aa1b95c6f563f2c8

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.615547Z digest=sha256:e05ed8676b56501abdbc6cad5555090bc8a16272fe91e9938e2ae3c62c42b9ef

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.621289Z digest=sha256:1858293b14bb21c069a9b29ea8120f2619ab07e3382d68f7df3e979c8c60fa9d

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.632802Z digest=sha256:03c1d9eb6ffcfc610d9712a9a3475b0ee1ea5f2c3ac3efc75f1a0254fe54f9d0

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 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-16T05:36:25.587491Z digest=sha256:d82b41ccb444f88d1da5a5bcb0c89e7883be1c6beef7f430518b1b3537aa01ac

Pith citing papers

No inbound Pith citation observations are available.