Paper Citation Record · LEDGER

Magnitude homology and Euler characteristics of directed acyclic graphs

As of 21 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:2607.23357.

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pith.paper-citation-record.v1
2607.23357 v1

Coverage vector

measured 42 of 42 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-31T23:47:23.469264Z

measured 42 of 42 standing notices

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42 of 42 outbound references displayed

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Outbound references

Observation 18122463-fdaa-462d-b1c8-648f0225e0f0 · outbound

This paper cites The magnitude of metric spaces.Documenta Mathematica, 18:857–905, 2013.

Magnitude homology and Euler characteristics of directed acyclic graphs The magnitude of metric spaces.Documenta Mathematica, 18:857–905, 2013

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:19.675255Z

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Observation a2ef4e28-c2d4-43d9-b0b7-be67f3c76b0b · outbound

This paper cites The magnitude of a metric space: from category theory to geometric measure theory.

Magnitude homology and Euler characteristics of directed acyclic graphs The magnitude of a metric space: from category theory to geometric measure theory

Reference 2

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Observation 4dc37f9c-12e5-45e2-bdfe-a9befb6b999a · outbound

This paper cites Cambridge, 2021.

Magnitude homology and Euler characteristics of directed acyclic graphs Cambridge, 2021

Reference 3

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Observation dfc4ae4f-4034-412e-8467-4294b91c56fe · outbound

This paper cites Weighting vectors for machine learning: numerical harmonic analysis applied to boundary detection.

Magnitude homology and Euler characteristics of directed acyclic graphs Weighting vectors for machine learning: numerical harmonic analysis applied to boundary detection

Reference 4

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Observation 3a615ca1-b689-48ef-a50a-44a0b3a617c4 · outbound

This paper cites The magnitude vector of images.Journal of Applied and Computational Topology, 8(3):447–473, 2024.

Magnitude homology and Euler characteristics of directed acyclic graphs The magnitude vector of images.Journal of Applied and Computational Topology, 8(3):447–473, 2024

Reference 5

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Observation 4f6cd8f5-e792-49d7-a305-3beb5384d90b · outbound

This paper cites Metric space magnitude for evaluating the diversity of latent representations.

Magnitude homology and Euler characteristics of directed acyclic graphs Metric space magnitude for evaluating the diversity of latent representations

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:20.086467Z

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Observation cddedc95-be2d-476b-b700-d0c65515f585 · outbound

This paper cites Geometry-aware edge pooling for graph neural networks.

Magnitude homology and Euler characteristics of directed acyclic graphs Geometry-aware edge pooling for graph neural networks

Reference 7

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Observation 57726095-63f1-4426-b86e-3262a2b2d2c2 · outbound

This paper cites Comparative analysis of indicators for multi-objective diversity opti- mization.

Magnitude homology and Euler characteristics of directed acyclic graphs Comparative analysis of indicators for multi-objective diversity opti- mization

Reference 8

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Observation d203b664-2fd7-4f2d-9729-4c137e8f228e · outbound

This paper cites The Magnitude of Dominated Sets: A Pareto Compliant Indicator Grounded in Metric Geometry.

Magnitude homology and Euler characteristics of directed acyclic graphs The Magnitude of Dominated Sets: A Pareto Compliant Indicator Grounded in Metric Geometry

Reference 9

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Observation 058ad33a-4833-46c4-b6d0-7abf18c4d950 · outbound

This paper cites Persistent magnitude for the quantitative analysis of the structure and stability of carboranes.Journal of Computational Biophysics and Chemistry, 23(06):741–751, 2024.

Magnitude homology and Euler characteristics of directed acyclic graphs Persistent magnitude for the quantitative analysis of the structure and stability of carboranes.Journal of Computational Biophysics and Chemistry, 23(06):741–751, 2024

Reference 10

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Observation 38ba7015-cd27-4e7e-be03-4735cccb9068 · outbound

This paper cites Topological magnitude for protein flexibility analysis.Royal Society Open Science, 12(12), 2025.

Magnitude homology and Euler characteristics of directed acyclic graphs Topological magnitude for protein flexibility analysis.Royal Society Open Science, 12(12), 2025

Reference 11

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Observation c6b370ab-0f39-44f4-aac2-48bb7e19cf54 · outbound

This paper cites Categorifying the magnitude of a graph.Homology, Homotopy and Applications, 19(2):31–60, 2017.

Magnitude homology and Euler characteristics of directed acyclic graphs Categorifying the magnitude of a graph.Homology, Homotopy and Applications, 19(2):31–60, 2017

Reference 12

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Observation 42d42f2e-ca56-414a-b7fd-ba9c686e95f3 · outbound

This paper cites Magnitude homology of enriched categories and metric spaces.Algebraic & Geometric Topology, 21(5):2175–2221, 2021.

Magnitude homology and Euler characteristics of directed acyclic graphs Magnitude homology of enriched categories and metric spaces.Algebraic & Geometric Topology, 21(5):2175–2221, 2021

Reference 13

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Observation 139b4f0b-acdb-4107-90ae-0732915ec90d · outbound

This paper cites Blurred magnitude homology of functional connectome for ASD diagnosis.Frontiers in Psychiatry, 16: 1677282, 2025.

Magnitude homology and Euler characteristics of directed acyclic graphs Blurred magnitude homology of functional connectome for ASD diagnosis.Frontiers in Psychiatry, 16: 1677282, 2025

Reference 14

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Observation 81da6617-c4ea-4d3a-9866-eadaf555e580 · outbound

This paper cites Cambridge, 2002.

Magnitude homology and Euler characteristics of directed acyclic graphs Cambridge, 2002

Reference 15

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Observation c7d91eac-dff0-4384-95f5-f74a1d405e47 · outbound

This paper cites Springer Nature, 2026.

Magnitude homology and Euler characteristics of directed acyclic graphs Springer Nature, 2026

Reference 16

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Observation 2dccf909-6af4-4e0f-a6d4-c1fa9050adbe · outbound

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Magnitude homology and Euler characteristics of directed acyclic graphs Unresolved cited work

Reference 17

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Observation af67ce0d-1bf8-49f1-87dc-34f6464f74b1 · outbound

This paper cites Poset topology: tools and applications.

Magnitude homology and Euler characteristics of directed acyclic graphs Poset topology: tools and applications

Reference 18

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Observation f8a1a031-3ff6-4ec7-80c7-e0401d7afb84 · outbound

This paper cites Magnitude homology of metric spaces and order complexes.Bulletin of the London Mathematical Society, 53(3):893–905, 2021.

Magnitude homology and Euler characteristics of directed acyclic graphs Magnitude homology of metric spaces and order complexes.Bulletin of the London Mathematical Society, 53(3):893–905, 2021

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:21.102321Z

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Observation d90c24e3-b89c-49c6-83f4-9486714134cc · outbound

This paper cites Iterated magnitude homology.Advances in Mathematics, 468:110210, 2025.

Magnitude homology and Euler characteristics of directed acyclic graphs Iterated magnitude homology.Advances in Mathematics, 468:110210, 2025

Reference 20

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Observation d0601169-7390-48bc-9b9e-5852d9a2628e · outbound

This paper cites Fast M\"obius and Zeta Transforms.

Magnitude homology and Euler characteristics of directed acyclic graphs Fast M\"obius and Zeta Transforms

Reference 21

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Observation 90cde89b-af2a-4220-a38e-9c8e7f8ba1f5 · outbound

This paper cites Magnitude cohomology.Mathematische Zeitschrift, 301(4):3617–3640,.

Magnitude homology and Euler characteristics of directed acyclic graphs Magnitude cohomology.Mathematische Zeitschrift, 301(4):3617–3640,

Reference 22

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Observation c2dc83ec-5f1f-40b4-9b4d-c9409825533e · outbound

This paper cites Geometric approach to graph magnitude homology.

Magnitude homology and Euler characteristics of directed acyclic graphs Geometric approach to graph magnitude homology

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:21.447680Z

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Observation 3c983612-1a86-4f71-9b9c-8b48b5068cb6 · outbound

This paper cites Magnitude meets persistence: homology theories for filtered simplicial sets.

Magnitude homology and Euler characteristics of directed acyclic graphs Magnitude meets persistence: homology theories for filtered simplicial sets

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:21.539561Z

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Observation c8f1fe98-16df-4ee3-ae9a-52207854a50f · outbound

This paper cites Quantales, persistence, and magnitude homology.

Magnitude homology and Euler characteristics of directed acyclic graphs Quantales, persistence, and magnitude homology

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:21.654992Z

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Observation 7200c290-309f-42c3-8855-132d0e598c01 · outbound

This paper cites Persistent magnitude.Journal of Pure and Applied Algebra, 225(3):106517, 2021.

Magnitude homology and Euler characteristics of directed acyclic graphs Persistent magnitude.Journal of Pure and Applied Algebra, 225(3):106517, 2021

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:21.772837Z

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Observation e074b96e-d4d3-4a86-864b-23092f60a484 · outbound

This paper cites Magnitude homology and path homology.Bulletin of the London Mathematical Society, 55(1):375–398, 2023.

Magnitude homology and Euler characteristics of directed acyclic graphs Magnitude homology and path homology.Bulletin of the London Mathematical Society, 55(1):375–398, 2023

Reference 27

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Observation 599ac3bd-7af7-4b21-9458-73afa05b1840 · outbound

This paper cites Path homologies of deep feedforward networks.

Magnitude homology and Euler characteristics of directed acyclic graphs Path homologies of deep feedforward networks

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:22.023983Z

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Observation cf90bfda-4548-420d-88b5-9de3867b9f23 · outbound

This paper cites A unified framework for numerically inverting Laplace trans- forms.INFORMS Journal on Computing, 18(4):408–421, 2006.

Magnitude homology and Euler characteristics of directed acyclic graphs A unified framework for numerically inverting Laplace trans- forms.INFORMS Journal on Computing, 18(4):408–421, 2006

Reference 29

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Observation 87f2c300-dcfb-4670-8487-c8794a8ba27d · outbound

This paper cites An improved Talbot method for numerical Laplace transform inversion.Numerical Algorithms, 68(1):167–183, 2015.

Magnitude homology and Euler characteristics of directed acyclic graphs An improved Talbot method for numerical Laplace transform inversion.Numerical Algorithms, 68(1):167–183, 2015

Reference 30

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Observation 7144a82f-5d14-42c8-b6a4-3290d749599b · outbound

This paper cites Springer, 2018.

Magnitude homology and Euler characteristics of directed acyclic graphs Springer, 2018

Reference 31

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Observation e18aa1dd-cd7b-424c-96a2-7fdc3df8e468 · outbound

This paper cites Optimally scaled and optimally conditioned Vandermonde and Vandermonde- like matrices.BIT Numerical Mathematics, 51(1):103–125, 2011.

Magnitude homology and Euler characteristics of directed acyclic graphs Optimally scaled and optimally conditioned Vandermonde and Vandermonde- like matrices.BIT Numerical Mathematics, 51(1):103–125, 2011

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:22.521992Z

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Observation 41e2eab9-8e07-415c-bd4f-37dc055a2b70 · outbound

This paper cites Johns Hopkins, 2013.

Magnitude homology and Euler characteristics of directed acyclic graphs Johns Hopkins, 2013

Reference 33

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Observation b69b7068-a56d-4af4-8eee-2404be0f34d4 · outbound

This paper cites On Lovász’ lattice reduction and the nearest lattice point problem.Combinatorica, 6(1):1–13, 1986.

Magnitude homology and Euler characteristics of directed acyclic graphs On Lovász’ lattice reduction and the nearest lattice point problem.Combinatorica, 6(1):1–13, 1986

Reference 34

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Observation 0b709afc-ab50-4c6b-9d12-38e099cf8a51 · outbound

This paper cites Effects of the LLL reduction on the success probability of the Babai point and on the complexity of sphere decoding.IEEE Transactions on Information Theory, 59(8):4915–4926, 2013.

Magnitude homology and Euler characteristics of directed acyclic graphs Effects of the LLL reduction on the success probability of the Babai point and on the complexity of sphere decoding.IEEE Transactions on Information Theory, 59(8):4915–4926, 2013

Reference 35

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Observation 20999653-29aa-42b7-9d72-a701c6bba6e0 · outbound

This paper cites Springer, 2026.

Magnitude homology and Euler characteristics of directed acyclic graphs Springer, 2026

Reference 36

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Observation b3d1e23f-eecb-4dd3-a482-c1e4aeebd88c · outbound

This paper cites Bridging the black box: a survey on mechanistic interpretability in AI.ACM Computing Surveys, 58(8):1–35, 2026.

Magnitude homology and Euler characteristics of directed acyclic graphs Bridging the black box: a survey on mechanistic interpretability in AI.ACM Computing Surveys, 58(8):1–35, 2026

Reference 37

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Observation dafa85ef-4bc0-44f9-b189-68ca3489e3ad · outbound

This paper cites Euler calculus with applications to signals and sensing.Advances in Applied and Computational Topology, 70:75–145, 2012.

Magnitude homology and Euler characteristics of directed acyclic graphs Euler calculus with applications to signals and sensing.Advances in Applied and Computational Topology, 70:75–145, 2012

Reference 38

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Observation 92462245-f6de-4815-b468-4651d9a77b41 · outbound

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Magnitude homology and Euler characteristics of directed acyclic graphs Unresolved cited work

Reference 39

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Observation 1bb19434-b175-4192-a5b0-93ef198f02e3 · outbound

This paper cites An invitation to the Euler characteristic transform.The American Mathemati- cal Monthly, 132(1):15–25, 2025.

Magnitude homology and Euler characteristics of directed acyclic graphs An invitation to the Euler characteristic transform.The American Mathemati- cal Monthly, 132(1):15–25, 2025

Reference 40

Resolution: unresolved; no resolver link, observed 2026-07-31T23:47:23.272725Z

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Observation 289b58a3-bde7-4f77-b716-1f213675c363 · outbound

This paper cites Topology meets machine mearning: an introduction using the Euler characteristic transform.Notices of the American Mathematical Society, 72:719–727, 2025.

Magnitude homology and Euler characteristics of directed acyclic graphs Topology meets machine mearning: an introduction using the Euler characteristic transform.Notices of the American Mathematical Society, 72:719–727, 2025

Reference 41

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Observation 8e2c6af6-3973-452f-91a3-dd7d68fdea89 · outbound

This paper cites Peel neighborhoods.

Magnitude homology and Euler characteristics of directed acyclic graphs Peel neighborhoods

Reference 42

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