Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T16:15:05.034933Z
Paper Citation Record · LEDGER
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor
As of 7 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2507.14940.
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 2026-08-05T11:25:45.070762Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-05T11:25:45.116336Z
Reference resolution
30 of 30 outbound references displayed
- verified exact1
- verified fuzzy20
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation df8f6cf9-be80-42b9-9b1f-ccd6849fcf50 · outbound
This paper cites Araki, S.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Araki, S
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:09.823543Z
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 e08c3c74-cc7b-4eb1-8ce5-74e3343b78e7 · outbound
This paper cites Barrlund, Perturbation bounds on the polar decomposition, BIT 30 (1989) 101–113.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Barrlund, Perturbation bounds on the polar decomposition, BIT 30 (1989) 101–113
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:09.627485Z
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 65a6ba3b-2a09-4620-81bc-2538ae8a5d62 · outbound
This paper cites Bhatia, Matrix Analysis, Springer, New York, 1997.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Bhatia, Matrix Analysis, Springer, New York, 1997
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:09.472459Z
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 24848259-3873-4491-ae2e-9c44a4ed5e84 · outbound
This paper cites Boyd and L.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Boyd and L
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:09.285179Z
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 fa3ee925-9d8a-429f-904b-cbe246d448d0 · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:09.164895Z
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 fd985aea-f713-489b-b1ce-905dfc05fabb · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:08.969773Z
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 89901e30-b1d7-4ef9-b469-b59847a76af7 · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:08.792657Z
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 7fbe567e-9b2e-4d58-8313-cabea5706dc8 · outbound
This paper cites Golub, C.F.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Golub, C.F
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:08.634058Z
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 4669f2ac-e0e9-4ea1-97b9-7e437a8fe7aa · outbound
This paper cites Hardy, J.E.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Hardy, J.E
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:08.497300Z
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 b728134d-3709-4c6b-bde4-2e4cb91ec671 · outbound
This paper cites Higham, Computing the polar decomposition–with applications, SIAM J.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Higham, Computing the polar decomposition–with applications, SIAM J
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:08.336840Z
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 abb83a73-2798-4b6e-b2df-e814ee88d1a8 · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:08.195745Z
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 56700c52-5527-4dff-9774-18ad1e79be3f · outbound
This paper cites Kenney, A.J.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Kenney, A.J
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:08.026655Z
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 5b664aea-acad-4fe1-83f3-3d0cd36a887a · outbound
This paper cites Kittaneh, Inequalities for the Schatten p-norm.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Kittaneh, Inequalities for the Schatten p-norm
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:07.890925Z
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 566bc704-2c9f-4b62-b4d2-9725ff2c0e6a · outbound
This paper cites Lee, Rotfel’d type inequalities for norms, Linear Algebra Appl.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Lee, Rotfel’d type inequalities for norms, Linear Algebra Appl
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:07.767874Z
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 dbf4f0cd-70fd-48c7-a08c-47cb98b7a94e · outbound
This paper cites Li, A perturbation bound for the generalized polar decomposition, BIT 33 (1993) 304– 308.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Li, A perturbation bound for the generalized polar decomposition, BIT 33 (1993) 304– 308
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:07.594456Z
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 3e75cf34-7391-49e9-bf69-2f4b5a2e9d15 · outbound
This paper cites Li, New perturbation bounds for the unitary polar factor, SIAM J.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Li, New perturbation bounds for the unitary polar factor, SIAM J
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:07.430511Z
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 0696da2c-6fe5-40fc-b418-53a1814d1495 · outbound
This paper cites Li, Relative perturbation bounds for unitary polar factor, BIT 37 (1997) 67–75.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Li, Relative perturbation bounds for unitary polar factor, BIT 37 (1997) 67–75
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:07.285310Z
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 b4955b5d-cf0c-49ca-a9b7-577b0e93ffb2 · outbound
This paper cites Li, Relative perturbation bounds for positive polar factors of graded matrices, SIAM J.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Li, Relative perturbation bounds for positive polar factors of graded matrices, SIAM J
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:07.137107Z
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 4a5e5c16-0116-4d0c-ab49-f19538be26b6 · outbound
This paper cites Li, Some new perturbation bounds for subunitary polar factors, Acta Math.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Li, Some new perturbation bounds for subunitary polar factors, Acta Math
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:06.994062Z
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 74470d2c-39be-4193-a545-081c42b989eb · outbound
This paper cites Li, On the perturbation bound in unitarily invariant norms for subunitary polar factors, Linear Algebra Appl.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Li, On the perturbation bound in unitarily invariant norms for subunitary polar factors, Linear Algebra Appl
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:06.863417Z
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 0f1a1360-e736-48dd-9fed-07833f6f625e · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:06.655486Z
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 3c2f0af9-af38-427a-acf7-b6175fd1fadf · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:06.512215Z
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 5f3c6716-e72a-4760-b396-4383e31383ee · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:06.344061Z
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 70dd850f-ef2b-43e4-8dd0-086291ac5390 · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:06.168398Z
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 2ae21404-af2b-4db9-831b-f084a4cda043 · outbound
This paper cites Mathias, Perturbation bounds for the polar decomposition, SIAM J.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Mathias, Perturbation bounds for the polar decomposition, SIAM J
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:05.993772Z
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 15b3c3f6-bc6b-4ae1-a2c5-6cfdf24d3e06 · outbound
This paper cites Rudin, Principles of Mathematical Analysis, McGraw-Hill, 3rd ed.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Rudin, Principles of Mathematical Analysis, McGraw-Hill, 3rd ed
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:05.844476Z
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 af8ce2bc-cc07-4d2d-b271-6e4a5eb6e9a3 · outbound
This paper cites an unresolved cited work.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T16:15:05.713179Z
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 f7f80827-50e1-4d57-af42-dea72c712b39 · outbound
This paper cites Zhang, Matrix Theory: Basic Results and Techniques, second ed., Springer, New York, 2011.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Zhang, Matrix Theory: Basic Results and Techniques, second ed., Springer, New York, 2011
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:05.572732Z
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 02ddde09-4517-4c5a-bb66-b0916ddfd626 · outbound
This paper cites A new proof of Lee's conjecture on the Frobenius norm via the matrix Cauchy-Schwarz inequality.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor A new proof of Lee's conjecture on the Frobenius norm via the matrix Cauchy-Schwarz inequality
Reference 29
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T16:15:05.201680Z
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 2e8a732e-6cd4-40d7-bdb3-1d996e6e1f6c · outbound
This paper cites Zhu et al., New perturbation bounds in unitarily invariant norms for subunitary polar factors, Electron.
Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor Zhu et al., New perturbation bounds in unitarily invariant norms for subunitary polar factors, Electron
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T16:15:05.381073Z
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.
Pith citing papers
Observation 38273555-bdb7-4194-acbf-c247a59ad0b0 · inbound
AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates cites this paper.
AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor
Reference 36
- Resolution
- verified exact
- local_arxiv, observed 2026-08-05T11:25:45.121899Z
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.