Paper Citation Record · LEDGER

Isotropic randomization for one-sample testing in metric spaces

As of 11 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2501.15945.

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

pith.paper-citation-record.v1
2501.15945 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T13:54:17.104542Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+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 exact4
verified fuzzy25
unresolved10
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7301acbc-51cf-4684-9616-c5a38b7e3106 · outbound

This paper cites Computing Medians and Means in Hadamard Spaces.

Isotropic randomization for one-sample testing in metric spaces Computing Medians and Means in Hadamard Spaces

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.728720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d2815654-0abe-4880-a153-4308aad229a0 · outbound

This paper cites Riemannian geometry and matrix geometric means.

Isotropic randomization for one-sample testing in metric spaces Riemannian geometry and matrix geometric means

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.717242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 491c96af-a02c-4d66-99e3-3f3f45c4e366 · outbound

This paper cites On the Bu- res–Wasserstein distance between positive definite matrices.

Isotropic randomization for one-sample testing in metric spaces On the Bu- res–Wasserstein distance between positive definite matrices

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.706132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 61d63f26-ae6b-47a2-b1ae-46215498724a · outbound

This paper cites Omnibus Clts for Fr´ echet Means and Nonparametric Inference on Non-Euclidean Spaces.

Isotropic randomization for one-sample testing in metric spaces Omnibus Clts for Fr´ echet Means and Nonparametric Inference on Non-Euclidean Spaces

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.694950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 05594bc7-b600-48a3-831b-f44138bf7794 · outbound

This paper cites Concentration of empirical barycenters in metric spaces.

Isotropic randomization for one-sample testing in metric spaces Concentration of empirical barycenters in metric spaces

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-10T13:54:17.351498Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f06b1486-40f5-4b88-89cd-bf3474f32ec7 · outbound

This paper cites An Autoregressive Model for Time Series of Random Objects.

Isotropic randomization for one-sample testing in metric spaces An Autoregressive Model for Time Series of Random Objects

Reference 6

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cce36085-a4e8-439f-af84-39566bbba943 · outbound

This paper cites Medoid splits for efficient random forests in metric spaces.

Isotropic randomization for one-sample testing in metric spaces Medoid splits for efficient random forests in metric spaces

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.683392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2dc46e80-333f-4bdd-a4c5-08b24f605076 · outbound

This paper cites Cambridge studies in advanced mathematics: Riemannian geometry: A modern introduction series number 98.

Isotropic randomization for one-sample testing in metric spaces Cambridge studies in advanced mathematics: Riemannian geometry: A modern introduction series number 98

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.672128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 071195ff-0264-493a-ad13-ae651eb506a0 · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-10T13:54:17.659568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dd50576f-48ce-4daa-af24-a6d0ae8775ed · outbound

This paper cites Fr´ echet analysis of variance for random objects.

Isotropic randomization for one-sample testing in metric spaces Fr´ echet analysis of variance for random objects

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.633542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 344c78b9-b39a-4970-b038-02cba77443d2 · outbound

This paper cites Fr´ echet change-point detec- tion.

Isotropic randomization for one-sample testing in metric spaces Fr´ echet change-point detec- tion

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.621584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4a9cb47e-fb1f-46ee-b2fd-619f2abb5649 · outbound

This paper cites A Smeary Central Limit Theorem for Manifolds with Application to High Dimensional Spheres.

Isotropic randomization for one-sample testing in metric spaces A Smeary Central Limit Theorem for Manifolds with Application to High Dimensional Spheres

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-10T13:54:17.321800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 601cc5d2-2ccf-4588-8c0c-eed85393b598 · outbound

This paper cites Les ´ el´ ements al´ eatoires de nature quelconque dans un espace distanci´ e.

Isotropic randomization for one-sample testing in metric spaces Les ´ el´ ements al´ eatoires de nature quelconque dans un espace distanci´ e

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.609667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0b40387-1446-4dba-829e-0eb059cc5317 · outbound

This paper cites Uni- versal Bayes consistency in metric spaces.

Isotropic randomization for one-sample testing in metric spaces Uni- versal Bayes consistency in metric spaces

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.597604Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 0543e189-1c0f-4df0-a8ec-ce4e7ac2b39f · outbound

This paper cites Differential geometry, lie groups and symmetric spaces.

Isotropic randomization for one-sample testing in metric spaces Differential geometry, lie groups and symmetric spaces

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.584493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 79acbd0e-077f-449c-bedc-b63b90e5d53d · outbound

This paper cites A Lower Bound for Estimating Fr\'echet Means.

Isotropic randomization for one-sample testing in metric spaces A Lower Bound for Estimating Fr\'echet Means

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T13:54:17.304343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3ca37196-0fa8-4471-8a78-b756ef4695d6 · outbound

This paper cites Testing serial indepen- dence of object-valued time series.

Isotropic randomization for one-sample testing in metric spaces Testing serial indepen- dence of object-valued time series

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.572954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e56fd8d5-b805-4cd1-8a58-18a3d6c5e979 · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 18

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abfa9076-43dc-4398-b770-11d4d482d4d5 · outbound

This paper cites Robust Signal Recovery in Hadamard Spaces.

Isotropic randomization for one-sample testing in metric spaces Robust Signal Recovery in Hadamard Spaces

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-10T13:54:17.033775Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94a22895-7c61-46f2-8662-511d4cc22b7b · outbound

This paper cites On the Consistency of Procrustean Mean Shapes.

Isotropic randomization for one-sample testing in metric spaces On the Consistency of Procrustean Mean Shapes

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.561540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 80d15112-bf8c-4605-b4d0-38a0d8802f39 · outbound

This paper cites Testing statistical hypotheses.

Isotropic randomization for one-sample testing in metric spaces Testing statistical hypotheses

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.549759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e96b9ead-6146-4891-882e-5d82226f06e8 · outbound

This paper cites Wasserstein Riemannian geometry of Gaussian densities.

Isotropic randomization for one-sample testing in metric spaces Wasserstein Riemannian geometry of Gaussian densities

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.538578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f06226f6-c4ff-44df-a6b7-2c60da9036fe · outbound

This paper cites Directional statistics.

Isotropic randomization for one-sample testing in metric spaces Directional statistics

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-10T13:54:17.048630Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a0df62d-9a3a-4052-98fb-2349603eca62 · outbound

This paper cites Equivariant estimation of Fr´ echet means.

Isotropic randomization for one-sample testing in metric spaces Equivariant estimation of Fr´ echet means

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.519297Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5a368d9a-277a-4030-8c11-a9b652e0def4 · outbound

This paper cites The Stein effect for Fr´ echet means.

Isotropic randomization for one-sample testing in metric spaces The Stein effect for Fr´ echet means

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.508007Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6b0bbfaa-e709-4468-b2d5-aaded28455c9 · outbound

This paper cites Panaretos and Yoav Zemel.

Isotropic randomization for one-sample testing in metric spaces Panaretos and Yoav Zemel

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.495877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3d40960f-6c8a-4e66-9d9f-264edbbb8b30 · outbound

This paper cites Frechet regression for ran- dom objects with Euclidean predictors.

Isotropic randomization for one-sample testing in metric spaces Frechet regression for ran- dom objects with Euclidean predictors

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.485442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 46b49761-e950-4cd4-b63f-48c2d7686092 · outbound

This paper cites Functional data analysis for density functions by transformation to a Hilbert space.

Isotropic randomization for one-sample testing in metric spaces Functional data analysis for density functions by transformation to a Hilbert space

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-10T13:54:17.271877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d668583e-1e19-4a15-9d4f-36c951b481aa · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-10T13:54:17.474272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4b4d6dc6-9166-4ee0-85f7-cd22255d24c0 · outbound

This paper cites Convergence rates for the generalized Fr´ echet mean via the quadruple inequality.

Isotropic randomization for one-sample testing in metric spaces Convergence rates for the generalized Fr´ echet mean via the quadruple inequality

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.462638Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1cef9ede-dba2-4946-89e4-14354703f131 · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-10T13:54:17.450425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 231a5e0c-1ac3-4944-ad23-3437082704ac · outbound

This paper cites Probability measures on metric spaces of non- positive curvature.

Isotropic randomization for one-sample testing in metric spaces Probability measures on metric spaces of non- positive curvature

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.438261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation bd933d05-81c1-453f-8313-84c845765868 · outbound

This paper cites Theoretically and Computation- ally Convenient Geometries on Full-Rank Correlation Matrices.

Isotropic randomization for one-sample testing in metric spaces Theoretically and Computation- ally Convenient Geometries on Full-Rank Correlation Matrices

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.414189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation c6282169-ea99-4466-a1af-77d629d55c0b · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-10T13:54:17.400876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e2a2453b-b15f-4960-9eff-c5609f2dfd2c · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-10T13:54:17.389318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 79d82f86-1b70-4451-a4a3-3330c0a697c8 · outbound

This paper cites Bayes Hilbert Spaces.

Isotropic randomization for one-sample testing in metric spaces Bayes Hilbert Spaces

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.377465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation a8e9e88a-5f89-4087-800c-495ab4a56dd2 · outbound

This paper cites Law of large numbers in CAT(1)-spaces of small radii.

Isotropic randomization for one-sample testing in metric spaces Law of large numbers in CAT(1)-spaces of small radii

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.364521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ae68fdcc-6e49-420d-a549-45c581e4efed · outbound

This paper cites an unresolved cited work.

Isotropic randomization for one-sample testing in metric spaces Unresolved cited work

Reference 390

Resolution: unresolved; raw_fallback, observed 2026-08-10T13:54:17.426744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2e53a557-b04d-4551-af79-ab19ecf98a86 · outbound

This paper cites ISSN: 2640-3498.

Isotropic randomization for one-sample testing in metric spaces ISSN: 2640-3498

Reference 1304

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T13:54:17.646685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

No inbound Pith citation observations are available.