Paper Citation Record · LEDGER

Brockett cost function for symplectic eigenvalues

As of 7 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2506.07560.

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

pith.paper-citation-record.v1
2506.07560 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:44:05.312230Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

33 of 33 outbound references displayed

verified exact9
verified fuzzy5
unresolved14
parse uncertain0
malformed identifier4
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 16064296-3f33-4992-895a-ec3df297c9ea · outbound

This paper cites Absil, R.

Brockett cost function for symplectic eigenvalues Absil, R

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:00.584834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f65dee55-19e8-4523-9db5-eebce6ed50f6 · outbound

This paper cites Adesso and F.

Brockett cost function for symplectic eigenvalues Adesso and F

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:10.982975Z

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 3a4231c9-4c09-468f-be73-97df0bd0ab14 · outbound

This paper cites Amodio, On the computation of few eigenvalues of positive definite Hamiltonian matrices , Future Gener.

Brockett cost function for symplectic eigenvalues Amodio, On the computation of few eigenvalues of positive definite Hamiltonian matrices , Future Gener

Reference 3

Resolution: malformed identifier; no resolver link, observed 2026-08-07T05:44:00.913177Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12c8623f-c80a-49a7-bd20-ef3d401d9d43 · outbound

This paper cites Banchi, S.

Brockett cost function for symplectic eigenvalues Banchi, S

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:01.059862Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6404e4cc-050c-4639-b472-b5b4c964b1d3 · outbound

This paper cites Benner, D.

Brockett cost function for symplectic eigenvalues Benner, D

Reference 5

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:44:10.736040Z

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 207bf8ff-a766-434a-83a0-9f703640022b · outbound

This paper cites an unresolved cited work.

Brockett cost function for symplectic eigenvalues Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:44:10.480399Z

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 43e8561f-c39f-49a1-bdc2-2d5985a1572a · outbound

This paper cites Bhatia and T.

Brockett cost function for symplectic eigenvalues Bhatia and T

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:01.465455Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a47fbd45-c9b0-42b7-9f6a-2eceff224cf1 · outbound

This paper cites Birtea, I.

Brockett cost function for symplectic eigenvalues Birtea, I

Reference 8

Resolution: verified exact; doi, observed 2026-08-07T05:44:07.998706Z

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 4e13a436-313c-4d24-a88c-4e93866b891a · outbound

This paper cites Brockett, Least squares matching problems, Linear Algebra Appl., 122-124 (1989), pp.

Brockett cost function for symplectic eigenvalues Brockett, Least squares matching problems, Linear Algebra Appl., 122-124 (1989), pp

Reference 9

Resolution: verified exact; doi, observed 2026-08-07T05:44:07.752740Z

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 471e9995-641e-4b94-84c4-386a5b55fb87 · outbound

This paper cites Brockett, Dynamical systems that sort lists, diagonalize matrices, and solve linear pro- gramming problems, Linear Algebra Appl., 146 (1991), pp.

Brockett cost function for symplectic eigenvalues Brockett, Dynamical systems that sort lists, diagonalize matrices, and solve linear pro- gramming problems, Linear Algebra Appl., 146 (1991), pp

Reference 10

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:44:10.173948Z

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 bc748b71-22a0-4aec-a876-44db249ac85d · outbound

This paper cites Chakraborty, A.

Brockett cost function for symplectic eigenvalues Chakraborty, A

Reference 11

Resolution: metadata mismatch; raw_fallback, observed 2026-08-07T05:44:08.451236Z

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 418ffb19-150a-4039-89dc-28b56c2d34de · outbound

This paper cites de Gosson, Symplectic Geometry and Quantum Mechanics, Advances in Partial Differential Equations, Birkh¨ auser, Basel, 2006.

Brockett cost function for symplectic eigenvalues de Gosson, Symplectic Geometry and Quantum Mechanics, Advances in Partial Differential Equations, Birkh¨ auser, Basel, 2006

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:09.865929Z

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 76d211d2-0362-45ba-9da7-58e1031b9a12 · outbound

This paper cites Eisert, T.

Brockett cost function for symplectic eigenvalues Eisert, T

Reference 13

Resolution: verified exact; doi, observed 2026-08-07T05:44:07.497494Z

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 61878ad5-ace3-4366-ab99-679388870fcc · outbound

This paper cites an unresolved cited work.

Brockett cost function for symplectic eigenvalues Unresolved cited work

Reference 14

Resolution: malformed identifier; raw_fallback, observed 2026-08-07T05:44:09.615562Z

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 7d35dbf1-a9ee-4108-977f-7570d1adbdf3 · outbound

This paper cites Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods.

Brockett cost function for symplectic eigenvalues Symplectic Stiefel manifold: tractable metrics, second-order geometry and Newton's methods

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:02.642509Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7eeffae-b798-4469-acf9-8f14e375146c · outbound

This paper cites Golub and C.

Brockett cost function for symplectic eigenvalues Golub and C

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:02.828999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e4f04f5-3797-4a6b-bf0c-8f852e0cb999 · outbound

This paper cites Hardy, J.

Brockett cost function for symplectic eigenvalues Hardy, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:09.343252Z

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 812b3f44-d5f8-49e7-99e1-b329baf9806d · outbound

This paper cites Hiroshima, Additivity and multiplicativity properties of some Gaussian channels for Gauss- ian inputs , Phys.

Brockett cost function for symplectic eigenvalues Hiroshima, Additivity and multiplicativity properties of some Gaussian channels for Gauss- ian inputs , Phys

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.175440Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88fbfade-bc58-4758-ac9f-7f0b073309ec · outbound

This paper cites Jain and H.

Brockett cost function for symplectic eigenvalues Jain and H

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.282951Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0cebb0e0-d4e5-4ae3-94cf-bab1c210829c · outbound

This paper cites Riemannian optimization on the symplectic Stiefel manifold using second-order information.

Brockett cost function for symplectic eigenvalues Riemannian optimization on the symplectic Stiefel manifold using second-order information

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.433628Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b935d159-99ab-4136-bdbb-37bd6728da1d · outbound

This paper cites Kovaˇc-Striko and K.

Brockett cost function for symplectic eigenvalues Kovaˇc-Striko and K

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:03.601530Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5634f40a-90d9-45fb-a1f3-799e783f6015 · outbound

This paper cites Krbek, T.

Brockett cost function for symplectic eigenvalues Krbek, T

Reference 22

Resolution: verified exact; doi, observed 2026-08-07T05:44:07.174699Z

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 873c2e51-6ca4-453e-9a8d-7828766e6354 · outbound

This paper cites Liang and R.-C.

Brockett cost function for symplectic eigenvalues Liang and R.-C

Reference 23

Resolution: verified exact; doi, observed 2026-08-07T05:44:06.890279Z

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 fc98b06f-aaed-48ce-b1fa-904bf4bde34a · outbound

This paper cites Liang, L.

Brockett cost function for symplectic eigenvalues Liang, L

Reference 24

Resolution: verified exact; doi, observed 2026-08-07T05:44:06.522393Z

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 76d31b6d-e646-43d3-90dc-b47b69d15120 · outbound

This paper cites an unresolved cited work.

Brockett cost function for symplectic eigenvalues Unresolved cited work

Reference 25

Resolution: verified exact; doi, observed 2026-08-07T05:44:06.217422Z

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 4f1afa0a-a5d4-4a09-ab94-44e3e7b8fec6 · outbound

This paper cites an unresolved cited work.

Brockett cost function for symplectic eigenvalues Unresolved cited work

Reference 26

Resolution: verified exact; doi, observed 2026-08-07T05:44:05.893939Z

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 12244014-2059-4426-9d58-d0dd029ad77b · outbound

This paper cites On generalization of Williamson's theorem to real symmetric matrices.

Brockett cost function for symplectic eigenvalues On generalization of Williamson's theorem to real symmetric matrices

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-07T05:44:05.645251Z

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 004bd476-8861-4378-8ccf-6bd5bc4d57e1 · outbound

This paper cites Ortega and D.

Brockett cost function for symplectic eigenvalues Ortega and D

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:09.068671Z

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 49b124ac-ef9b-42c7-82ed-3667f04e5c97 · outbound

This paper cites an unresolved cited work.

Brockett cost function for symplectic eigenvalues Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:04.765318Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c03bb99-1daf-40c4-8c7e-4fd5b21faed9 · outbound

This paper cites an unresolved cited work.

Brockett cost function for symplectic eigenvalues Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:04.898931Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e152cf7-71a5-4edd-b39b-7c41842665eb · outbound

This paper cites Weedbrook, S.

Brockett cost function for symplectic eigenvalues Weedbrook, S

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:05.039746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c89ab2e-f7d4-4a60-847a-486b88bf66f8 · outbound

This paper cites Williamson , On the algebraic problem concerning the normal forms of linear dynamical systems, Am.

Brockett cost function for symplectic eigenvalues Williamson , On the algebraic problem concerning the normal forms of linear dynamical systems, Am

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:44:08.749190Z

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 a6640a5b-f327-4ae9-9135-b7411736bc24 · outbound

This paper cites Yamada and H.

Brockett cost function for symplectic eigenvalues Yamada and H

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T05:44:05.312230Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

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