Paper Citation Record · LEDGER

Optimization of geometric hypergraph embedding

As of 22 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2509.08772.

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

pith.paper-citation-record.v1
2509.08772 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:10:56.984191Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

38 of 38 outbound references displayed

verified exact3
verified fuzzy26
unresolved7
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 95cf5469-f8b0-404b-829f-2f93cb22dad1 · outbound

This paper cites Evolutionary dynamics of higher-order interactions in social networks.

Optimization of geometric hypergraph embedding Evolutionary dynamics of higher-order interactions in social networks

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.624321Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b4d1e7dd-a1ac-48ed-b518-01b0ed85ceee · outbound

This paper cites A Survey on Hypergraph Representation Learning.

Optimization of geometric hypergraph embedding A Survey on Hypergraph Representation Learning

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T16:10:56.502785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cde99f0d-690e-429f-8fd4-989bc8a421f9 · outbound

This paper cites Minimization of functions having Lipschitz continuous first partial derivatives.

Optimization of geometric hypergraph embedding Minimization of functions having Lipschitz continuous first partial derivatives

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.594222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ad56ac9c-01ba-4491-9f4c-99b37165b4ae · outbound

This paper cites Class of models for random hypergraphs.

Optimization of geometric hypergraph embedding Class of models for random hypergraphs

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.571553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 50f7bc28-e00a-44b1-abdb-00304019b866 · outbound

This paper cites The physics of higher-order interactions in complex systems.

Optimization of geometric hypergraph embedding The physics of higher-order interactions in complex systems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.535603Z

Source-reported events for the cited work

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Observation 1d56a1cd-47e3-4d1a-9eb0-2f1be29b9e3b · outbound

This paper cites Networks beyond pairwise interactions: Structure and dynamics.

Optimization of geometric hypergraph embedding Networks beyond pairwise interactions: Structure and dynamics

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.508322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 56bbcf01-b204-429f-829c-0b5b7e5add96 · outbound

This paper cites Towards a theoretical foundation for Laplacian- based manifold methods.

Optimization of geometric hypergraph embedding Towards a theoretical foundation for Laplacian- based manifold methods

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.470201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fa306ee8-7812-4699-a480-aa2bf7338f23 · outbound

This paper cites Higher-order organization of complex networks.

Optimization of geometric hypergraph embedding Higher-order organization of complex networks

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.435910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a390d1c1-737a-437e-bd89-fb0be769b5d8 · outbound

This paper cites Three Hypergraph Eigenvector Centralities.

Optimization of geometric hypergraph embedding Three Hypergraph Eigenvector Centralities

Reference 9

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Source-reported events for the cited work

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Observation 677f2408-d0e6-4002-85cb-fdcc4cf4c8c8 · outbound

This paper cites What Are Higher- Order Networks?.

Optimization of geometric hypergraph embedding What Are Higher- Order Networks?

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.388795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dfae5ace-fd5d-40bd-aa7b-538f4daab58b · outbound

This paper cites The use of the area under the ROC curve in the evaluation of machine learning algorithms.

Optimization of geometric hypergraph embedding The use of the area under the ROC curve in the evaluation of machine learning algorithms

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.358868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d7c50260-ea82-4f8d-8db5-3d8403764ea2 · outbound

This paper cites Hypergraph clustering: from blockmodels to modularity.

Optimization of geometric hypergraph embedding Hypergraph clustering: from blockmodels to modularity

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.332354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dc24205d-7cdd-4ff2-9e22-1a6f57375cde · outbound

This paper cites A spatial hypergraph model where epidemic spread demonstrates clear higher-order effects.

Optimization of geometric hypergraph embedding A spatial hypergraph model where epidemic spread demonstrates clear higher-order effects

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.290692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0f78ed75-0493-4d6d-b49b-bcdfa01c8acd · outbound

This paper cites Estimating the intrinsic dimension of datasets by a minimal neighbourhood information.

Optimization of geometric hypergraph embedding Estimating the intrinsic dimension of datasets by a minimal neighbourhood information

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.253803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 41b30280-4b94-4abb-b17c-d5420a2590b9 · outbound

This paper cites A Representation of Hypergraphs in the Euclidean Space.

Optimization of geometric hypergraph embedding A Representation of Hypergraphs in the Euclidean Space

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.227916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 070c8f69-b624-48a4-9661-0e73c9745009 · outbound

This paper cites Random plane networks.

Optimization of geometric hypergraph embedding Random plane networks

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.186097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation dd8ae1d3-6e87-47c7-8d75-fb1f0870166b · outbound

This paper cites Generative hypergraph models and spectral embedding.

Optimization of geometric hypergraph embedding Generative hypergraph models and spectral embedding

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T16:10:56.749215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca497cd4-e733-4b6d-b39b-7523374afe25 · outbound

This paper cites Estimating network dimension when the spectrum struggles.

Optimization of geometric hypergraph embedding Estimating network dimension when the spectrum struggles

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.149918Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8f48ec5c-201c-47ad-907e-21a675a32abd · outbound

This paper cites Periodic reordering.

Optimization of geometric hypergraph embedding Periodic reordering

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.112363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0a7f3fbf-ee61-4db3-9d6e-6804912af527 · outbound

This paper cites Epidemics on hypergraphs: Spectral thresholds for extinction.

Optimization of geometric hypergraph embedding Epidemics on hypergraphs: Spectral thresholds for extinction

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.065974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 11d58a7e-09f5-4a26-901a-033724f3194f · outbound

This paper cites Spectral clustering and its use in bioinformatics.

Optimization of geometric hypergraph embedding Spectral clustering and its use in bioinformatics

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:58.024166Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation db37dbb8-287d-4a32-9657-608c8b60558d · outbound

This paper cites Comparing partitions.

Optimization of geometric hypergraph embedding Comparing partitions

Reference 22

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T16:10:57.986728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4c2c13f6-50be-4912-8904-896dcce7bdf4 · outbound

This paper cites Connectivity of Random Geometric Hypergraphs.

Optimization of geometric hypergraph embedding Connectivity of Random Geometric Hypergraphs

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.793925Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 28067804-8aa2-4b48-adae-af3b556aa04b · outbound

This paper cites On spectral partitioning of signed graphs.

Optimization of geometric hypergraph embedding On spectral partitioning of signed graphs

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:10:57.438398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 835e4b78-f52f-4e58-b837-8b4af78ba745 · outbound

This paper cites The effect of heterogeneity on hypergraph contagion models.

Optimization of geometric hypergraph embedding The effect of heterogeneity on hypergraph contagion models

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.753551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 976bd0d6-b944-491a-b2fc-ceda8662c19b · outbound

This paper cites Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualiza- tion.

Optimization of geometric hypergraph embedding Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualiza- tion

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.713252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation fbe0bf68-82d0-4754-921d-e3355fbea34e · outbound

This paper cites A tutorial on spectral clustering.

Optimization of geometric hypergraph embedding A tutorial on spectral clustering

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.675641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 02f1ac98-7520-4b44-b85c-2302c60574c9 · outbound

This paper cites Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors, Contact Diaries and Friendship Surveys.

Optimization of geometric hypergraph embedding Contact Patterns in a High School: A Comparison between Data Collected Using Wearable Sensors, Contact Diaries and Friendship Surveys

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T16:10:56.875959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58a83da5-44e2-4ac3-bffd-8ce6187f315a · outbound

This paper cites Derivatives and Perturbations of Eigen- vectors.

Optimization of geometric hypergraph embedding Derivatives and Perturbations of Eigen- vectors

Reference 29

Resolution: verified exact; doi, observed 2026-08-15T16:10:57.129457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d1cf8f3f-049a-444c-bac7-be3629feb290 · outbound

This paper cites Learning the effective order of a hypergraph dynamical system.

Optimization of geometric hypergraph embedding Learning the effective order of a hypergraph dynamical system

Reference 30

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T16:10:57.628961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 676cd3d5-b436-42b7-b16c-04be175c10fe · outbound

This paper cites High-Resolution Measurements of Face-to-Face Contact Patterns in a Primary School.

Optimization of geometric hypergraph embedding High-Resolution Measurements of Face-to-Face Contact Patterns in a Primary School

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T16:10:56.910431Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a6c90566-d52a-4ed3-9fb2-78d62e97d7c5 · outbound

This paper cites FOBE and HOBE: First- and High-Order Bipartite Embeddings.

Optimization of geometric hypergraph embedding FOBE and HOBE: First- and High-Order Bipartite Embeddings

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T16:10:56.918717Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 065de508-f2ea-45fa-99e6-68d8a10b8a32 · outbound

This paper cites The why, how, and when of representations for complex systems.

Optimization of geometric hypergraph embedding The why, how, and when of representations for complex systems

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.589640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8f674b91-adf3-4059-9010-17361bad5383 · outbound

This paper cites Wilkinson and J.

Optimization of geometric hypergraph embedding Wilkinson and J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.542489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3186b895-1a4e-4aff-a823-f0f8a21264ab · outbound

This paper cites A novel hypergraph convolution network-based approach for predicting the material removal rate in chemi- cal mechanical planarization.

Optimization of geometric hypergraph embedding A novel hypergraph convolution network-based approach for predicting the material removal rate in chemi- cal mechanical planarization

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.508012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3b48e732-59a3-40f1-869d-83e13c05288b · outbound

This paper cites Hypergraph Convolutional Recurrent Neural Network.

Optimization of geometric hypergraph embedding Hypergraph Convolutional Recurrent Neural Network

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T16:10:56.957105Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8114fa04-e87b-483d-b755-674f20da3f82 · outbound

This paper cites Modeling signed social networks using spectral embedding.

Optimization of geometric hypergraph embedding Modeling signed social networks using spectral embedding

Reference 37

Resolution: verified exact; doi, observed 2026-08-15T16:10:57.068945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0eda51c3-f8ca-4e0f-9e79-999259ebd853 · outbound

This paper cites Heterogeneous hypergraph embedding for document recommendation.

Optimization of geometric hypergraph embedding Heterogeneous hypergraph embedding for document recommendation

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:10:57.464825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.