Paper Citation Record · LEDGER

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds

As of 16 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:1909.00410.

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

pith.paper-citation-record.v1
1909.00410 v2

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T06:04:05.341919Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:57:57.667307Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-14T13:57:58.201165Z

Reference resolution

30 of 30 outbound references displayed

verified exact0
verified fuzzy28
unresolved2
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 92193ee0-25ea-455c-a581-a2750c02fa36 · outbound

This paper cites Riemannian Lp center of mass: existence, uniqueness, and convexity.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Riemannian Lp center of mass: existence, uniqueness, and convexity

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.933383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2223cf0d-1100-4259-ba88-42bf56b7a590 · outbound

This paper cites Cut and singular loc i up to codimension 3.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Cut and singular loc i up to codimension 3

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.916935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2c24d55a-63fa-49ac-9936-995e25c91d8b · outbound

This paper cites Some consequences of the nat ure of the distance function on the cut locus in a Riemannian manifold.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Some consequences of the nat ure of the distance function on the cut locus in a Riemannian manifold

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.900376Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f82bfbb8-ec5a-4793-bf96-3ba6d77c16f5 · outbound

This paper cites A panoramic view of Riemannian geometry.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds A panoramic view of Riemannian geometry

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.883209Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6d0404ae-29f8-4c53-8f8b-330d2057ff55 · outbound

This paper cites Nonparame tric inference on manifolds.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Nonparame tric inference on manifolds

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.867827Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 77208d32-e2e0-45fc-b826-432144d883ef · outbound

This paper cites Omnibus CLTs for Fr´ echet means and nonparametric inference on non-Euclidean spaces.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Omnibus CLTs for Fr´ echet means and nonparametric inference on non-Euclidean spaces

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.852275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation eb406780-2b94-4825-b7bf-3a6374336438 · outbound

This paper cites Large sample the ory of intrinsic and extrinsic sample means on manifolds.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Large sample the ory of intrinsic and extrinsic sample means on manifolds

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.835080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation b5632ffa-eebc-4c4b-83f1-21b6cab6557c · outbound

This paper cites Large sample the ory of intrinsic and extrinsic sample means on manifolds.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Large sample the ory of intrinsic and extrinsic sample means on manifolds

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.819174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7a6a9b4f-7e5f-4593-9d24-f740226e3193 · outbound

This paper cites A course in metric geometry.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds A course in metric geometry

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.801358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6aa77daf-31ef-4b27-9b58-b1194116d043 · outbound

This paper cites Riemannian geometry.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Riemannian geometry

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.769760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 95f063ed-4302-4fd3-874e-18c939b478e2 · outbound

This paper cites Huckemann.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Huckemann

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.752358Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5af254b1-fd4f-45de-bfd5-2d0377bd14ae · outbound

This paper cites On the convergence of some Procrustean averaging algorithms.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds On the convergence of some Procrustean averaging algorithms

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.734971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 42d85fe5-3f22-46f1-858b-3e646f242771 · outbound

This paper cites How to conjugate C 1-close group actions.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds How to conjugate C 1-close group actions

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.718240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1ec1330b-5e2a-4e98-ae03-0a3baffdc18d · outbound

This paper cites Parallel translation of curvature along geodesics.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Parallel translation of curvature along geodesics

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.701010Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 8dffce9d-1149-4eaf-b7a8-8cd38bc72389 · outbound

This paper cites Intrinsic Means on t he Circle: Uniqueness, Locus and Asymptotics.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Intrinsic Means on t he Circle: Uniqueness, Locus and Asymptotics

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.684312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation df035f17-3a07-4b58-8542-6acf9fd0d723 · outbound

This paper cites Intrinsic inference on the mean ge odesic of planar shapes and tree discrimination by leaf growth.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Intrinsic inference on the mean ge odesic of planar shapes and tree discrimination by leaf growth

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.668804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 10c6de36-8097-4fe2-8f2f-bc46829723df · outbound

This paper cites The dimension of a cut lo cus on a smooth Riemannian manifold.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds The dimension of a cut lo cus on a smooth Riemannian manifold

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.648080Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f6bd82f9-a3e4-4a95-a86c-d30dbf0ef63d · outbound

This paper cites Riemannian center of mass and molliﬁer smoot hing.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Riemannian center of mass and molliﬁer smoot hing

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.604824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4d1a948b-415b-4a45-96ab-467480a418ef · outbound

This paper cites Riemannian Center of Mass and so called karcher mean.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Riemannian Center of Mass and so called karcher mean

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-14T06:04:05.285835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4bc0447c-a5d0-4652-9543-b27e5f1f5d5b · outbound

This paper cites Fuchsian groups.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Fuchsian groups

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.581885Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1aa7cc75-66b7-4009-b8d6-d95ae28cfd34 · outbound

This paper cites Probability, Convexity, and Harmo nic Maps with Small Image I: Uniqueness and Fine Existence.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Probability, Convexity, and Harmo nic Maps with Small Image I: Uniqueness and Fine Existence

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.562008Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 341d6550-ec08-4ec7-9ffd-3dc62344db73 · outbound

This paper cites On the consistency of Procrustean mean shap es.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds On the consistency of Procrustean mean shap es

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.544793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9146528a-ff04-4a1f-a2e9-a25af7e9244a · outbound

This paper cites On the measure of the cut loc us of a Fr´ echet mean.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds On the measure of the cut loc us of a Fr´ echet mean

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.524814Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c2325a57-c4eb-4ac9-a336-e87613c3a843 · outbound

This paper cites The distance function to t he boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds The distance function to t he boundary, Finsler geometry, and the singular set of viscosity solutions of some Hamilton-Jacobi equations

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.503420Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3cb6bc47-5170-4a2b-84ee-196ddb039049 · outbound

This paper cites Barycenters in Alexandrov spaces of cu rvature bounded below.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Barycenters in Alexandrov spaces of cu rvature bounded below

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.483065Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d3b7dff0-6e19-4b48-9c1f-7b49abed6eb6 · outbound

This paper cites Riemannian geometry.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Riemannian geometry

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.464609Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation ff0c0565-bb9c-40d4-a7d6-106389fef8a9 · outbound

This paper cites Geometry of surfaces.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Geometry of surfaces

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.444750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 014734e7-3d63-4621-95f6-493f1dd4aa44 · outbound

This paper cites Probability measures on metric sp aces of nonpositive curvature.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Probability measures on metric sp aces of nonpositive curvature

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.425376Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 78dd1731-7855-48be-b5ed-f1d6092c81ac · outbound

This paper cites On expected ﬁgures and a strong law of l arge numbers for random elements in quasi-metric spaces.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds On expected ﬁgures and a strong law of l arge numbers for random elements in quasi-metric spaces

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T06:04:05.402774Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 96d483c9-1429-44a7-9409-741389dd65c5 · outbound

This paper cites an unresolved cited work.

Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-14T06:04:05.785217Z

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No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

Observation 08011350-0299-4fde-9610-ed958495417d · inbound

Geometrical Smeariness -- A new Phenomenon of Fr\'echet Means cites this paper.

Geometrical Smeariness -- A new Phenomenon of Fr\'echet Means Stability of the Cut Locus and a Central Limit Theorem for Fr\'echet Means of Riemannian Manifolds

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-14T13:57:58.211225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.