Paper Citation Record · LEDGER

On the approximation of the Riemannian barycenter

As of 17 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2504.15671.

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

pith.paper-citation-record.v1
2504.15671 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T11:25:44.049801Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

18 of 18 outbound references displayed

verified exact3
verified fuzzy2
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5180d9ad-e5de-4199-bfd9-7effe2eb1050 · outbound

This paper cites Princeton University Press, Princeton, NJ (2008), http://press.

On the approximation of the Riemannian barycenter Princeton University Press, Princeton, NJ (2008), http://press

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:44.353830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 70e5b995-643c-4557-98a6-9dfaf721a23d · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications46(2), 1145–1167 (2025), https://doi.org/10.1137/24M1644808.

On the approximation of the Riemannian barycenter SIAM Journal on Matrix Analysis and Applications46(2), 1145–1167 (2025), https://doi.org/10.1137/24M1644808

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.000992Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8491d93-7f85-49ec-aa12-fd842b98511c · outbound

This paper cites Proceedings of the American Mathematical Society139(2), 655–673 (2011),http: //www.jstor.org/stable/41059320.

On the approximation of the Riemannian barycenter Proceedings of the American Mathematical Society139(2), 655–673 (2011),http: //www.jstor.org/stable/41059320

Reference 3

Resolution: verified exact; raw_fallback, observed 2026-08-16T11:25:44.334435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation aeb7ce20-8835-48e8-aab4-3c6ea3149c72 · outbound

This paper cites SIAM Journal on Control and Optimization51(3), 2230–2260 (2013), https://doi.org/10.1137/12086282X.

On the approximation of the Riemannian barycenter SIAM Journal on Control and Optimization51(3), 2230–2260 (2013), https://doi.org/10.1137/12086282X

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.007693Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9fe712f6-dddc-4c8e-b5dc-d3a3e808b7eb · outbound

This paper cites Foundations of Computational Mathematics23(4), 1335–1380 (2023), https://doi.org/10.1007/s10208-022-09571-x.

On the approximation of the Riemannian barycenter Foundations of Computational Mathematics23(4), 1335–1380 (2023), https://doi.org/10.1007/s10208-022-09571-x

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.010834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e3e5a16-f195-47bf-ba96-92e29489bf55 · outbound

This paper cites Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds.

On the approximation of the Riemannian barycenter Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-16T11:25:44.276503Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2812bdd7-913f-4b15-a40a-5fdf523a3db3 · outbound

This paper cites The Annals of Statistics47(1), 415 – 438 (2019),https://doi.org/ 10.1214/18-AOS1692.

On the approximation of the Riemannian barycenter The Annals of Statistics47(1), 415 – 438 (2019),https://doi.org/ 10.1214/18-AOS1692

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.017552Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4bb3f037-1ee3-4073-96fd-803c7b455281 · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications20(2), 303–353 (1998), https://doi.org/10.1137/S0895479895290954.

On the approximation of the Riemannian barycenter SIAM Journal on Matrix Analysis and Applications20(2), 303–353 (1998), https://doi.org/10.1137/S0895479895290954

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.020443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b9b4840f-b489-4d11-9b19-4dc79f889c36 · outbound

This paper cites IEEE Transactions on Signal Processing 63(1), 155–168 (2015),https://doi.org/10.1109/TSP.2014.2365764.

On the approximation of the Riemannian barycenter IEEE Transactions on Signal Processing 63(1), 155–168 (2015),https://doi.org/10.1109/TSP.2014.2365764

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.023426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7486a522-41af-4703-88ed-e1db9b242c41 · outbound

This paper cites IEEE Transactions on Signal Processing61, 883–894 (02 2013), https://doi.org/10.1109/TSP.2012.2226167.

On the approximation of the Riemannian barycenter IEEE Transactions on Signal Processing61, 883–894 (02 2013), https://doi.org/10.1109/TSP.2012.2226167

Reference 10

Resolution: metadata mismatch; raw_fallback, observed 2026-08-16T11:25:44.215171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 942055e3-6d02-4a34-ae67-ee9db8603946 · outbound

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

On the approximation of the Riemannian barycenter Riemannian Center of Mass and so called karcher mean

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.028916Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ecd58575-3cc5-4c3b-8663-d33fbe643fc1 · outbound

This paper cites Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics.

On the approximation of the Riemannian barycenter Bounds on the geodesic distances on the Stiefel manifold for a family of Riemannian metrics

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.032285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b1cd36e-b3bc-4a56-8da3-13c1dfe0e34a · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications46(2), 879–905 (2025), https://doi.org/10.1137/24M1647801.

On the approximation of the Riemannian barycenter SIAM Journal on Matrix Analysis and Applications46(2), 879–905 (2025), https://doi.org/10.1137/24M1647801

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.035283Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd91934c-bbe8-47be-a163-f79dd05ec544 · outbound

This paper cites Journal of Mathematical Imaging and Vision25(1), 127–154 (2006), https://doi.org/10.1007/s10851-006-6228-4, a preliminary appeared as INRIA RR-5093, January 2004.

On the approximation of the Riemannian barycenter Journal of Mathematical Imaging and Vision25(1), 127–154 (2006), https://doi.org/10.1007/s10851-006-6228-4, a preliminary appeared as INRIA RR-5093, January 2004

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.038057Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2693fab-b2c3-4dc5-ab0f-c56e84dcdbac · outbound

This paper cites Fields Institute Communications, Amer- ican Mathematical Society (1996), https://books.google.be/books?id= ODDyngEACAAJ.

On the approximation of the Riemannian barycenter Fields Institute Communications, Amer- ican Mathematical Society (1996), https://books.google.be/books?id= ODDyngEACAAJ

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T11:25:44.343611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1c969a97-afd2-40bb-b665-a5da2896a7e4 · outbound

This paper cites Computational Optimization and Applications 77(3), 779–810 (2020), https:// doi.org/10.1007/s10589-020-00219-6 10 Simon Mataigne, P.-A.

On the approximation of the Riemannian barycenter Computational Optimization and Applications 77(3), 779–810 (2020), https:// doi.org/10.1007/s10589-020-00219-6 10 Simon Mataigne, P.-A

Reference 16

Resolution: verified exact; doi, observed 2026-08-16T11:25:44.088735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4f1f4f96-4863-4df7-a4c6-211a07ea243a · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications 43(2), 953–980 (2022),https://doi.org/10.1137/21M1425426.

On the approximation of the Riemannian barycenter SIAM Journal on Matrix Analysis and Applications 43(2), 953–980 (2022),https://doi.org/10.1137/21M1425426

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.046875Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac5ed818-d49a-493e-9b8f-08691decf502 · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications 46(1), 298–309 (2025),https://doi.org/10.1137/24M1663818.

On the approximation of the Riemannian barycenter SIAM Journal on Matrix Analysis and Applications 46(1), 298–309 (2025),https://doi.org/10.1137/24M1663818

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T11:25:44.049801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.