Paper Citation Record · LEDGER

A Mathematical Framework for Topological Causal Data Analysis

As of 8 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2607.28161.

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

pith.paper-citation-record.v1
2607.28161 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-31T15:58:53.131228Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

39 of 39 outbound references displayed

verified exact3
verified fuzzy0
unresolved35
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f3f2b6cf-8b3f-496f-9fce-33ed4c8cf7c0 · outbound

This paper cites Persis- 34 tence images: A stable vector representation of persistent homology.Journal of Machine Learning Research, 18(8):1–35, 2017.

A Mathematical Framework for Topological Causal Data Analysis Persis- 34 tence images: A stable vector representation of persistent homology.Journal of Machine Learning Research, 18(8):1–35, 2017

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.112094Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94209f7a-12b4-4e68-9e3e-81dcbe8bacb4 · outbound

This paper cites Cambridge University Press, 2018.

A Mathematical Framework for Topological Causal Data Analysis Cambridge University Press, 2018

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.190619Z

Source-reported events for the cited work

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Observation bc4bf50d-e134-4fc2-a38c-d00262a223cc · outbound

This paper cites Statistical topological data analysis using persistence landscapes.J.

A Mathematical Framework for Topological Causal Data Analysis Statistical topological data analysis using persistence landscapes.J

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.279828Z

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Observation 4e8aa261-db32-438a-9128-36504ac25b88 · outbound

This paper cites A persistence landscapes toolbox for topological statis- tics.Journal of Symbolic Computation, 78:91–114, January 2017.

A Mathematical Framework for Topological Causal Data Analysis A persistence landscapes toolbox for topological statis- tics.Journal of Symbolic Computation, 78:91–114, January 2017

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.381848Z

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Observation 597b6da5-171e-4a0d-811a-a32be11ab789 · outbound

This paper cites Oudot, and Donald R.

A Mathematical Framework for Topological Causal Data Analysis Oudot, and Donald R

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.475692Z

Source-reported events for the cited work

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Observation 28493e09-da30-4b7a-a7ee-a82218c889ce · outbound

This paper cites Topology and data.Bulletin of the American Mathematical Society, 46 (2):255–308, January 2009.

A Mathematical Framework for Topological Causal Data Analysis Topology and data.Bulletin of the American Mathematical Society, 46 (2):255–308, January 2009

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.535898Z

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Observation aba6802d-8b6c-48cb-93f8-cba305a3d88f · outbound

This paper cites SlicedWassersteinkernelforpersistence diagrams.

A Mathematical Framework for Topological Causal Data Analysis SlicedWassersteinkernelforpersistence diagrams

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.634580Z

Source-reported events for the cited work

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Observation 26f9a457-6a12-448e-a8a3-c91816c31e13 · outbound

This paper cites Persistence stability for geometric com- plexes.Geometriae Dedicata, 173:193–214, 2014.

A Mathematical Framework for Topological Causal Data Analysis Persistence stability for geometric com- plexes.Geometriae Dedicata, 173:193–214, 2014

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.699435Z

Source-reported events for the cited work

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Observation 4541624a-c246-404f-b14a-7a0722edeea2 · outbound

This paper cites Springer, 2016.

A Mathematical Framework for Topological Causal Data Analysis Springer, 2016

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.807066Z

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Observation 51ef01be-9528-412e-94a4-3e1120cd3f2b · outbound

This paper cites An introduction to topological data analysis: Fun- damental and practical aspects for data scientists.Frontiers in Artificial Intelligence, 4,.

A Mathematical Framework for Topological Causal Data Analysis An introduction to topological data analysis: Fun- damental and practical aspects for data scientists.Frontiers in Artificial Intelligence, 4,

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.890470Z

Source-reported events for the cited work

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Observation a60b36f7-de01-4940-96fa-67f738100ccd · outbound

This paper cites Geometric inference for probability measures.Foundations of Computational Mathematics, 11(6):733–751, 2011.

A Mathematical Framework for Topological Causal Data Analysis Geometric inference for probability measures.Foundations of Computational Mathematics, 11(6):733–751, 2011

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.083538Z

Source-reported events for the cited work

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Observation 554f290e-8f7a-4fd3-af45-8671f4c012d6 · outbound

This paper cites Stochastic convergence of persistence landscapes and silhouettes.

A Mathematical Framework for Topological Causal Data Analysis Stochastic convergence of persistence landscapes and silhouettes

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.135932Z

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Observation b745b2bf-6c6e-4991-8d21-63da19705a1a · outbound

This paper cites Double/debiased machine learning for treatment and structural parameters.The Econometrics Journal, 21(1):C1–C68, January 2018.

A Mathematical Framework for Topological Causal Data Analysis Double/debiased machine learning for treatment and structural parameters.The Econometrics Journal, 21(1):C1–C68, January 2018

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.283241Z

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Observation e4bd8890-1595-457f-867a-24bf2b5fc736 · outbound

This paper cites Stability of persistence diagrams.

A Mathematical Framework for Topological Causal Data Analysis Stability of persistence diagrams

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.348892Z

Source-reported events for the cited work

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Observation ac6bf4eb-9f3d-45b4-83c1-c756f87fabe5 · outbound

This paper cites Lipschitz functions have l p -stable persistence.Foundations of Computational Mathematics, 10(2): 127–139, January 2010.

A Mathematical Framework for Topological Causal Data Analysis Lipschitz functions have l p -stable persistence.Foundations of Computational Mathematics, 10(2): 127–139, January 2010

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.414832Z

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Observation 819d2b46-2df5-4122-a9d1-b09d3ad77cdb · outbound

This paper cites Uhl.Vector Measures.

A Mathematical Framework for Topological Causal Data Analysis Uhl.Vector Measures

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.459844Z

Source-reported events for the cited work

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Observation 0d2704f6-b8a9-4876-add7-62ef99349226 · outbound

This paper cites Ameri- can Mathematical Society, 2010.

A Mathematical Framework for Topological Causal Data Analysis Ameri- can Mathematical Society, 2010

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.511736Z

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Observation 26ddb991-418a-4dd6-b58e-9c589ffaca86 · outbound

This paper cites Topological residual asymmetry for bivariate causal direction.

A Mathematical Framework for Topological Causal Data Analysis Topological residual asymmetry for bivariate causal direction

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.568283Z

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Observation d2956bf5-fa6a-42eb-9e90-522700f176ec · outbound

This paper cites Hernán and James M.

A Mathematical Framework for Topological Causal Data Analysis Hernán and James M

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.624828Z

Source-reported events for the cited work

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Observation c808713e-6fc2-4a88-b37d-e75f8ef841a6 · outbound

This paper cites A topological perspective on causal inference.

A Mathematical Framework for Topological Causal Data Analysis A topological perspective on causal inference

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.681750Z

Source-reported events for the cited work

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Observation 44c165f1-4299-49cf-b8cc-7a9e40dbda36 · outbound

This paper cites Imbens and Donald B.

A Mathematical Framework for Topological Causal Data Analysis Imbens and Donald B

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.774905Z

Source-reported events for the cited work

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Observation 994b7d2b-3213-4d56-9e90-1008d3e0727c · outbound

This paper cites Kennedy.Semiparametric Doubly Robust Targeted Double Machine Learning: A Review, page 207–236.

A Mathematical Framework for Topological Causal Data Analysis Kennedy.Semiparametric Doubly Robust Targeted Double Machine Learning: A Review, page 207–236

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:51.837110Z

Source-reported events for the cited work

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Observation 44f4d563-d097-4ff8-ba0e-3f558ac79afb · outbound

This paper cites Topological causal effects.Preprint, arXiv:2603.02289, 2026.

A Mathematical Framework for Topological Causal Data Analysis Topological causal effects.Preprint, arXiv:2603.02289, 2026

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-31T16:01:32.867116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a6b115b2-17d9-4d23-ba73-1905d755cc3e · outbound

This paper cites Kernel method for persistence diagrams via kernel embedding and weight factor.Journal of Machine Learning Research, 18(189):1–41, 2018.

A Mathematical Framework for Topological Causal Data Analysis Kernel method for persistence diagrams via kernel embedding and weight factor.Journal of Machine Learning Research, 18(189):1–41, 2018

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.012025Z

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Observation 6059f3f7-18f6-4bb1-b581-4786ef1522d2 · outbound

This paper cites Statisti- cal topological data analysis - a kernel perspective.

A Mathematical Framework for Topological Causal Data Analysis Statisti- cal topological data analysis - a kernel perspective

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.100882Z

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Observation f7ebaeef-f11b-4794-8991-9eb92e20ebb7 · outbound

This paper cites Persistence fisher kernel: A riemannian manifold kernel for persistence diagrams.

A Mathematical Framework for Topological Causal Data Analysis Persistence fisher kernel: A riemannian manifold kernel for persistence diagrams

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.183397Z

Source-reported events for the cited work

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Observation 5917fffa-0678-449f-a09e-82a6b29c3923 · outbound

This paper cites Probability measures on the space of persistence diagrams.Inverse Problems, 27(12):124007, November 2011.

A Mathematical Framework for Topological Causal Data Analysis Probability measures on the space of persistence diagrams.Inverse Problems, 27(12):124007, November 2011

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.239992Z

Source-reported events for the cited work

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Observation a463b5f5-f90b-4184-a34a-b250394e081a · outbound

This paper cites Oudot.Persistence Theory: From Quiver Representations to Data Analysis.

A Mathematical Framework for Topological Causal Data Analysis Oudot.Persistence Theory: From Quiver Representations to Data Analysis

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.343132Z

Source-reported events for the cited work

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Observation 62915a38-16d8-4478-a026-84015da14a79 · outbound

This paper cites Cambridge University Press, 2 edition, 2009.

A Mathematical Framework for Topological Causal Data Analysis Cambridge University Press, 2 edition, 2009

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.455505Z

Source-reported events for the cited work

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Observation b3fbb1e0-1084-4913-b20f-693d63fbaff5 · outbound

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A Mathematical Framework for Topological Causal Data Analysis Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.531573Z

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Observation 6669c8dd-bd06-4d47-b690-ee974e58b65e · outbound

This paper cites an unresolved cited work.

A Mathematical Framework for Topological Causal Data Analysis Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.631898Z

Source-reported events for the cited work

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Observation c156c098-21c9-40a6-8243-7b125fea67ba · outbound

This paper cites Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability.

A Mathematical Framework for Topological Causal Data Analysis Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-07-31T16:01:32.758808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4627f26e-6d7c-4291-9dc6-973ba8499f4a · outbound

This paper cites Absolute average and median treatment effects as causal estimands on metric spaces.

A Mathematical Framework for Topological Causal Data Analysis Absolute average and median treatment effects as causal estimands on metric spaces

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.770075Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e09cce0-7da6-47cf-8358-5e5721287bc0 · outbound

This paper cites Wasserstein Stability for Persistence Diagrams.

A Mathematical Framework for Topological Causal Data Analysis Wasserstein Stability for Persistence Diagrams

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.909005Z

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Observation 3dc9c3ee-1d9a-4025-92c5-42f3b0dae02f · outbound

This paper cites MIT Press, 2 edition, 2000.

A Mathematical Framework for Topological Causal Data Analysis MIT Press, 2 edition, 2000

Reference 35

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:52.980105Z

Source-reported events for the cited work

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Observation 04a1a305-cc45-441a-97d1-dc0e8c218a5a · outbound

This paper cites Fréchet means for distributions of persistence diagrams.Discrete & Computational Geometry, 52(1):44–70,.

A Mathematical Framework for Topological Causal Data Analysis Fréchet means for distributions of persistence diagrams.Discrete & Computational Geometry, 52(1):44–70,

Reference 36

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:53.046988Z

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Observation 7dcc4da3-6b4f-4cda-9e68-e394842a6875 · outbound

This paper cites doi: 10.1007/s00454-014-9604-7.

A Mathematical Framework for Topological Causal Data Analysis doi: 10.1007/s00454-014-9604-7

Reference 2014

Resolution: verified exact; doi, observed 2026-07-31T16:01:32.557565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dc8943e9-fa28-47e8-bbdf-649292f072b2 · outbound

This paper cites doi: 10.3389/frai.2021.667963.

A Mathematical Framework for Topological Causal Data Analysis doi: 10.3389/frai.2021.667963

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-07-31T15:58:50.983654Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 16a891fc-2f54-4fe6-99e5-53d1bb288eaf · outbound

This paper cites Absolute average and median treatment effects as causal estimands on metric spaces.

A Mathematical Framework for Topological Causal Data Analysis Absolute average and median treatment effects as causal estimands on metric spaces

Reference 2024

Resolution: metadata mismatch; local_arxiv, observed 2026-07-31T16:01:32.643266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

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