Paper Citation Record · LEDGER

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2508.09627.

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

pith.paper-citation-record.v1
2508.09627 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T20:59:36.920210Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

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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

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Source: cited_works

Reference resolution

37 of 37 outbound references displayed

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External citation measurements

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Outbound references

Observation 309dc42d-5c34-4ea4-b840-7fbbe20d47fa · outbound

This paper cites Attention's forward pass and Frank-Wolfe.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Attention's forward pass and Frank-Wolfe

Reference 1

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Observation be0693ad-f159-4275-b699-ba59d30ccd26 · outbound

This paper cites France 2030.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs France 2030

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T20:59:37.558342Z

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Observation 5fa23a59-cbeb-47fe-9c9a-5a63fc776f71 · outbound

This paper cites What Does BERT Look At? An Analysis of BERT's Attention.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs What Does BERT Look At? An Analysis of BERT's Attention

Reference 8

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Observation 96c08972-70ad-4294-ae0f-2b6c2d5ef9ca · outbound

This paper cites Code available at https://github.com/borjanG/2025-transformers-frank-wolfe.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Code available at https://github.com/borjanG/2025-transformers-frank-wolfe

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T20:59:37.550089Z

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Observation 2e3fae44-e889-45c2-ac57-1e1517f784b5 · outbound

This paper cites Geometric Dynamics of Signal Propagation Predict Trainability of Transformers.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Geometric Dynamics of Signal Propagation Predict Trainability of Transformers

Reference 11

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Observation d49db9ff-bad3-421c-afac-c1727575192d · outbound

This paper cites Synchronization on circles and spheres with non- linear interactions.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Synchronization on circles and spheres with non- linear interactions

Reference 12

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Observation 04880a75-c3bb-4696-8674-9f8d69a99d5b · outbound

This paper cites Setting the Record Straight on Transformer Oversmoothing.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Setting the Record Straight on Transformer Oversmoothing

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.854088Z

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Observation 2476eea6-535a-476d-a5b6-38416a280c2e · outbound

This paper cites HashAttention: Semantic Sparsity for Faster Inference.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs HashAttention: Semantic Sparsity for Faster Inference

Reference 15

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Observation 5e7b399b-64c1-4f3a-8ec4-f96880616beb · outbound

This paper cites Large-time asymptotics in deep learning.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Large-time asymptotics in deep learning

Reference 16

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Observation a4db7592-1233-4ab9-a260-588d96f51ff7 · outbound

This paper cites Dynamic metastability in the self-attention model.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Dynamic metastability in the self-attention model

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.868654Z

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Observation 54808db1-4cb4-4349-9f62-84967e7c007f · outbound

This paper cites When Attention Sink Emerges in Language Models: An Empirical View.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs When Attention Sink Emerges in Language Models: An Empirical View

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.871722Z

Source-reported events for the cited work

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Observation 166a3f28-2f3e-4d48-baca-9238c483fb90 · outbound

This paper cites Measure-to-measure interpolation using Transformers.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Measure-to-measure interpolation using Transformers

Reference 20

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Observation 3502e52c-0527-4846-9369-9a8cab6009fa · outbound

This paper cites On the num- ber of modes of Gaussian kernel density estimators.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs On the num- ber of modes of Gaussian kernel density estimators

Reference 21

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Observation 184f4fac-3124-47f1-bf01-adafaa68cdad · outbound

This paper cites OT-Transformer: A Continuous-time Transformer Architecture with Optimal Transport Regularization.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs OT-Transformer: A Continuous-time Transformer Architecture with Optimal Transport Regularization

Reference 23

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Observation 0c488601-5e03-4c95-bbd9-e12079528d8f · outbound

This paper cites Convergence Rate of Frank-Wolfe for Non-Convex Objectives.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Convergence Rate of Frank-Wolfe for Non-Convex Objectives

Reference 24

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Observation a264f768-456a-4187-bdfd-e8c4215a6db4 · outbound

This paper cites The Sparse Frontier: Sparse Attention Trade-offs in Transformer LLMs.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs The Sparse Frontier: Sparse Attention Trade-offs in Transformer LLMs

Reference 26

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Observation fdd1b26f-6d48-4bf0-bc57-e1cdd0bc5170 · outbound

This paper cites Revisiting Over-smoothing in BERT from the Perspective of Graph.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Revisiting Over-smoothing in BERT from the Perspective of Graph

Reference 29

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Observation 0048375a-034c-445f-aa2a-f55b6ab1c697 · outbound

This paper cites Exploiting Sparsity for Long Context Inference: Million Token Contexts on Commodity GPUs.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Exploiting Sparsity for Long Context Inference: Million Token Contexts on Commodity GPUs

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.902216Z

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Observation e24cac0b-f4f2-49dc-8d33-b784f73db151 · outbound

This paper cites Prefixing Attention Sinks can Mitigate Activation Outliers for Large Language Model Quantization.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Prefixing Attention Sinks can Mitigate Activation Outliers for Large Language Model Quantization

Reference 31

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This paper cites Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Solutions of stationary McKean-Vlasov equation on a high-dimensional sphere and other Riemannian manifolds

Reference 32

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Observation e2419bc3-9a4d-446f-a74d-68c1c0a731ad · outbound

This paper cites Residual connections and normalization can provably pre- vent oversmoothing in gnns.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Residual connections and normalization can provably pre- vent oversmoothing in gnns

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.910294Z

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Observation a2254ff4-0335-4f5c-95cc-4fb38a9bded3 · outbound

This paper cites Recurrent self-attention dy- namics: An energy-agnostic perspective from Jacobians.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Recurrent self-attention dy- namics: An energy-agnostic perspective from Jacobians

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.912576Z

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Observation e6bff8e5-8ac2-47ed-ac17-06cfee5527ce · outbound

This paper cites Transformer-based Causal Language Models Perform Clustering.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Transformer-based Causal Language Models Perform Clustering

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-05T20:59:36.948538Z

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Observation 76b0351b-0473-4548-84ea-eaa5ed186703 · outbound

This paper cites Learning Gaussian Mixture Models via Transformer Mea- sure Flows.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Learning Gaussian Mixture Models via Transformer Mea- sure Flows

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T20:59:37.541550Z

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Observation 91051fea-5921-423c-b867-6be33b69a2fd · outbound

This paper cites Understanding Catastrophic Forgetting In LoRA via Mean-Field Attention Dynamics.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Understanding Catastrophic Forgetting In LoRA via Mean-Field Attention Dynamics

Reference 1973

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Observation 0bc11a14-fda1-4ea6-8bcc-333bb7caccd9 · outbound

This paper cites Finding Clustering Algorithms in the Transformer Architecture.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Finding Clustering Algorithms in the Transformer Architecture

Reference 1996

Resolution: verified exact; local_arxiv, observed 2026-08-05T20:59:37.495323Z

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Observation fee07a90-4ecf-40bd-90d4-d9cda2f960b3 · outbound

This paper cites Two failure modes of deep transformers and how to avoid them: a unified theory of signal propagation at initialisation.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Two failure modes of deep transformers and how to avoid them: a unified theory of signal propagation at initialisation

Reference 2004

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Observation 8fe3d3f0-8c60-4bbc-929b-1897a9ec4116 · outbound

This paper cites Self-attention Networks Localize When QK-eigenspectrum Concentrates.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Self-attention Networks Localize When QK-eigenspectrum Concentrates

Reference 2005

Resolution: verified exact; local_arxiv, observed 2026-08-05T20:59:37.525796Z

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Observation 11e8aa8d-6699-4818-ae0e-f9f8a6e8f38f · outbound

This paper cites Synchronization of mean-field models on the circle.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Synchronization of mean-field models on the circle

Reference 2007

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.894338Z

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Observation fe4b9dc8-3e46-43ed-9d3a-6f8ce3ca128e · outbound

This paper cites Towards understanding how attention mechanism works in deep learning.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Towards understanding how attention mechanism works in deep learning

Reference 2012

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Observation ad0838aa-9c70-4d71-be19-d52d396ea4fc · outbound

This paper cites The Geometry of Tokens in Internal Representations of Large Language Models.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs The Geometry of Tokens in Internal Representations of Large Language Models

Reference 2015

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Observation 9e3340f0-fd96-4d64-8e81-f35743804b52 · outbound

This paper cites Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Understanding and Improving Transformer From a Multi-Particle Dynamic System Point of View

Reference 2016

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.888717Z

Source-reported events for the cited work

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Observation 210c3b96-5b53-405f-800b-56aa795a4958 · outbound

This paper cites Continuum attention for neural operators.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Continuum attention for neural operators

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.843044Z

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Observation c3e72879-24cc-4739-b007-0fda49998b22 · outbound

This paper cites DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.857122Z

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Observation 7dca149c-b4ac-4c9e-8db8-4bdf0d50a1f1 · outbound

This paper cites A Unified Perspective on the Dynamics of Deep Transformers.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs A Unified Perspective on the Dynamics of Deep Transformers

Reference 2022

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Observation 11f2bcab-7eac-4ab1-b450-47ea94c8730c · outbound

This paper cites Quantitative Clustering in Mean-Field Transformer Models.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Quantitative Clustering in Mean-Field Transformer Models

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-05T20:59:36.845608Z

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Observation 5575d3cf-34d6-46d8-980d-275027b37d83 · outbound

This paper cites Breaking BERT: Evaluating and Optimizing Sparsified Attention.

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs Breaking BERT: Evaluating and Optimizing Sparsified Attention

Reference 2025

Resolution: verified exact; local_arxiv, observed 2026-08-05T20:59:37.514140Z

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