Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links
Paper Citation Record · LEDGER
The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
As of 7 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2108.12447.
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 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T19:53:51.398917Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-23T18:45:46.055977Z
Reference resolution
0 of 0 outbound references displayed
- verified exact0
- verified fuzzy0
- unresolved0
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
No outbound reference observations are available for this paper version.
Pith citing papers
Observation a2c5a795-0745-4cbe-8df5-c8d19570b931 · inbound
A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold cites this paper.
A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
Reference 9
- Resolution
- verified exact
- arxiv_id, observed 2026-05-23T18:45:46.058833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 7aec8cfc-3479-4e86-8f7a-9accfd6d68f9 · inbound
Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks cites this paper.
Reduced-order modeling of Hamiltonian dynamics based on symplectic neural networks The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
Reference 38
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T19:53:51.398917Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cb0cc5f9-456b-449e-994c-f725071dfc71 · inbound
An inexact variable metric proximal linearization method for composite optimization on manifolds cites this paper.
An inexact variable metric proximal linearization method for composite optimization on manifolds The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
Reference 8
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-05-18T23:11:53.600151Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation f3df2214-1a38-4355-b571-f1bf105156f2 · inbound
A generalized canonical metric for optimization on the indefinite Stiefel manifold cites this paper.
A generalized canonical metric for optimization on the indefinite Stiefel manifold The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
Reference 5
- Resolution
- verified exact
- arxiv_id, observed 2026-05-18T15:31:33.494806Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4c36d248-148b-42aa-a79e-91c12217b6e8 · inbound
A polar-factor retraction on the symplectic Stiefel manifold with closed-form inverse cites this paper.
A polar-factor retraction on the symplectic Stiefel manifold with closed-form inverse The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications
Reference 7
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-05-11T21:11:20.195886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.