Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:30:25.202721Z
Paper Citation Record · LEDGER
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics
As of 16 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:1908.09275.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
22 of 22 outbound references displayed
- verified exact0
- verified fuzzy19
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 554aad67-1015-43a4-857f-5b55e5292a75 · outbound
This paper cites Letters i n Mathematical Physics 19(2), 167–170 (1990) 20 H` a Quang Minh.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Letters i n Mathematical Physics 19(2), 167–170 (1990) 20 H` a Quang Minh
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.601379Z
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 0860eca8-f56d-4d56-8138-3ab44428219a · outbound
This paper cites an unresolved cited work.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:30:25.579908Z
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 2331e6fc-c91b-4627-a0c1-ed81f6b50571 · outbound
This paper cites Expositiones Mathematicae (2018).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Expositiones Mathematicae (2018)
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.563972Z
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 1b9de1c9-106c-4fb9-bb34-bbc96dd983c6 · outbound
This paper cites Journal of Multivariate Analysis 12(3), 450 – 455 (1982).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Journal of Multivariate Analysis 12(3), 450 – 455 (1982)
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.547916Z
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 ec63062a-f1dd-413e-9b43-6b46e0250fc9 · outbound
This paper cites Anna ls of Applied Statistics 3, 1102–1123 (2009).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Anna ls of Applied Statistics 3, 1102–1123 (2009)
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.531755Z
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 1485c151-0d27-42be-b011-4dd394a6512e · outbound
This paper cites Mathematische Nachrichten 147(1), 185–203 (1990).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Mathematische Nachrichten 147(1), 185–203 (1990)
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.518264Z
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 dea1e457-9ef8-49b3-b44a-713ee632a6d3 · outbound
This paper cites Michigan Math.
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.503981Z
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 8365e626-53e9-4836-bbe6-9a033a26d9e7 · outbound
This paper cites Differential Geometry and its Applications 25, 679–700 (2007).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Differential Geometry and its Applications 25, 679–700 (2007)
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.490549Z
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 d9e429ae-2564-4b13-81c1-23eefbb0f7b0 · outbound
This paper cites In: Lieb, E., S.B., Wrightman, A.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics In: Lieb, E., S.B., Wrightman, A
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.476811Z
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 cb6ea591-60d6-464f-bf5d-d412eb06f2ac · outbound
This paper cites Information Geometry 1(2), 137–179 (Dec 2018).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Information Geometry 1(2), 137–179 (Dec 2018)
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.453846Z
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 ccf408f7-0a0f-4428-9c6c-a29f8ee3befd · outbound
This paper cites San khya A pp.
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.435473Z
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 f9e43afa-b285-49ab-81c5-a6c3b907d67a · outbound
This paper cites In: Advances in Ne ural Information Pro- cessing Systems 27 (NIPS 2014), pp.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics In: Advances in Ne ural Information Pro- cessing Systems 27 (NIPS 2014), pp
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.416721Z
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 c7443f35-1569-4bf9-a1ce-e24a4207d3db · outbound
This paper cites Linear Algebra and Its Applicat ions 528, 331–383 (2017).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Linear Algebra and Its Applicat ions 528, 331–383 (2017)
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.401664Z
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 a6dac983-3bbd-4042-b336-e3122fb0be32 · outbound
This paper cites In: Information Geo metry and its Appli- cations IV.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics In: Information Geo metry and its Appli- cations IV
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.384784Z
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 a4549b5a-d6f0-49ad-b7e0-8bde6d28bb5e · outbound
This paper cites In: International Conference on Geometric Science of Information.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics In: International Conference on Geometric Science of Information
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.368869Z
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 941b88ca-d689-4e37-a26c-29cfe4428b12 · outbound
This paper cites Syn- thesis Lectures on Computer Vision 7(4), 1–170 (2017).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Syn- thesis Lectures on Computer Vision 7(4), 1–170 (2017)
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.351422Z
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 e7c29cf0-b00e-4ad4-a2cd-f6761fafcb88 · outbound
This paper cites Linear Algebra and its Applications 48, 257 – 263 (1982).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Linear Algebra and its Applications 48, 257 – 263 (1982)
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.327564Z
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 e237a58f-8d6b-4452-bfef-1ac4aeb020d0 · outbound
This paper cites Springer Science & Busi- ness Media (2008).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Springer Science & Busi- ness Media (2008)
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.312349Z
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 5919cc19-abad-4628-a3fc-e04390c2a272 · outbound
This paper cites Osaka Journal of Math- ematics 48(4), 1005–1026 (2011).
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Osaka Journal of Math- ematics 48(4), 1005–1026 (2011)
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.297010Z
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 2cc16333-b7e8-471e-88e4-3e55964bbfef · outbound
This paper cites an unresolved cited work.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:30:25.281036Z
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 684c7e3d-1d53-404b-af3f-d2e244686f7c · outbound
This paper cites an unresolved cited work.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:30:25.265882Z
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 d32049c2-ab76-4223-92a8-e46a4c728119 · outbound
This paper cites For any A0 ∈ Sym++(n), D log(A0) : Sym( n) → Sym(n) and D exp(log(A0)) : Sym(n) → Sym(n) are invertible operators, thus they both have zero null spaces.
Alpha Procrustes metrics between positive definite operators: a unifying formulation for the Bures-Wasserstein and Log-Euclidean/Log-Hilbert-Schmidt metrics For any A0 ∈ Sym++(n), D log(A0) : Sym( n) → Sym(n) and D exp(log(A0)) : Sym(n) → Sym(n) are invertible operators, thus they both have zero null spaces
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:30:25.251079Z
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.
Pith citing papers
No inbound Pith citation observations are available.