Paper Citation Record · LEDGER

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects

As of 20 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2606.10212.

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

pith.paper-citation-record.v1
2606.10212 v2

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T14:24:01.541464Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T03:22:14.173149Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy0
unresolved11
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7dea801f-bbd8-4c34-af3c-063bf1308706 · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4005e8c0-0038-4018-a5a8-9b2f017ff0d0 · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71d17f5b-9951-4fa0-8505-379e26b617ce · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec171988-90bd-4bca-b966-c428b146b062 · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb71d2ca-f3c2-4578-a7d5-f86ad7fd811c · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ce6381a-b2a5-4a64-bdb2-c75faa0355bb · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6aa1c76-a37f-4daa-84c9-5efa2e3d0fd5 · outbound

This paper cites More generally, Cov  X i aiXi, X j bjYj   = X i X j aibj Cov(Xi, Yj).

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects More generally, Cov  X i aiXi, X j bjYj   = X i X j aibj Cov(Xi, Yj)

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3347698f-097e-4f34-bfae-7e4d7f4729bd · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 8

Resolution: parse uncertain; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32a4c5dd-b239-4aa6-b001-241f2a9fe563 · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48afb277-02d5-4946-933b-87577a499bef · outbound

This paper cites an unresolved cited work.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6bbb0d0-ee4b-4478-b444-7300a9450ff5 · outbound

This paper cites 16 D Covariance Under Basis Rotation The parallel transport can be interpreted as a rotation of basis when the manifold is viewed as embedded in some ambient space, i.e.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects 16 D Covariance Under Basis Rotation The parallel transport can be interpreted as a rotation of basis when the manifold is viewed as embedded in some ambient space, i.e

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6085955-8da2-4b30-9377-cfe59aa133e8 · outbound

This paper cites Proof of Theorem 3.6.

Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects Proof of Theorem 3.6

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T14:24:01.541464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation bfa13f27-e028-4c2f-9161-a275debc21c1 · inbound

A Riemannian View on Active Subspaces cites this paper.

A Riemannian View on Active Subspaces Intrinsic Riemannian Cross-covariance for Manifold-valued Random Objects

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-01T03:22:14.173149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.