Paper Citation Record · LEDGER

Sharp perturbation bounds on the Frobenius norm of subunitary and positive polar factor

As of 10 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.

pith.paper-citation-record.v1
2507.14940 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:15:05.034933Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T11:25:45.070762Z

measured 0 of 1 external citation measurements

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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+00:00.