Paper Citation Record · LEDGER

Bilinear Quadratic Output Systems and Balanced Truncation

As of 23 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 1 inbound Pith citation observation for arXiv:2507.03684.

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

pith.paper-citation-record.v1
2507.03684 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:18:29.084167Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T12:44:24.413557Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-01T18:16:15.623592Z

Reference resolution

42 of 42 outbound references displayed

verified exact5
verified fuzzy7
unresolved20
parse uncertain0
malformed identifier8
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2b766fbb-f69e-4441-8958-b00d2b36fad6 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:18:35.615844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6d17d01c-eb77-4613-9e6b-7fa701211ceb · outbound

This paper cites Al-Baiyat and M.

Bilinear Quadratic Output Systems and Balanced Truncation Al-Baiyat and M

Reference 2

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T20:18:31.035051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 62c4ce02-3022-4e3c-b6c8-d535d74f46a6 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:25.036326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 256de59d-f903-4e96-a6a5-5ec8a7ae5cde · outbound

This paper cites Bai and D.

Bilinear Quadratic Output Systems and Balanced Truncation Bai and D

Reference 4

Resolution: malformed identifier; no resolver link, observed 2026-08-06T20:18:25.208296Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9a61d81a-87e1-427b-b0c7-bcfab0eb738a · outbound

This paper cites Benner and T.

Bilinear Quadratic Output Systems and Balanced Truncation Benner and T

Reference 5

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:35.353335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7aa0b860-ae20-42b6-b838-498ffcedb07e · outbound

This paper cites Benner and T.

Bilinear Quadratic Output Systems and Balanced Truncation Benner and T

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:25.509201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02c756fc-6fc8-4c93-bd7f-6f928bcfc826 · outbound

This paper cites Benner and T.

Bilinear Quadratic Output Systems and Balanced Truncation Benner and T

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:25.646269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eed5559c-b72d-40df-9765-446d3136afb0 · outbound

This paper cites Benner and H.

Bilinear Quadratic Output Systems and Balanced Truncation Benner and H

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:25.757130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09f1c554-2b91-4b6f-a5fc-b35a7fb40edd · outbound

This paper cites Benner and P.

Bilinear Quadratic Output Systems and Balanced Truncation Benner and P

Reference 10

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:35.081571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7deabc91-7920-42b4-9a83-3a48454a22b9 · outbound

This paper cites Benner, P.

Bilinear Quadratic Output Systems and Balanced Truncation Benner, P

Reference 11

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T20:18:30.780900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d1ad2702-eb80-4067-8ffb-67a05bec4dc7 · outbound

This paper cites Benner, P.

Bilinear Quadratic Output Systems and Balanced Truncation Benner, P

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:26.026203Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d5750a1-2cd2-486b-8842-205841b058eb · outbound

This paper cites Breiten and T.

Bilinear Quadratic Output Systems and Balanced Truncation Breiten and T

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:26.180979Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b87d6730-cb63-40c7-b8b3-d7074f7b0774 · outbound

This paper cites Condon and R.

Bilinear Quadratic Output Systems and Balanced Truncation Condon and R

Reference 14

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:34.819755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c42c5d70-2fcb-4b3a-8842-65955f96c391 · outbound

This paper cites Damm , Rational Matrix Equations in Stochastic Control , Lecture Notes in Control and Information Sciences, 297 (2004).

Bilinear Quadratic Output Systems and Balanced Truncation Damm , Rational Matrix Equations in Stochastic Control , Lecture Notes in Control and Information Sciences, 297 (2004)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:34.700138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b5473dab-a187-4936-b023-adaf34c407f5 · outbound

This paper cites Damm , Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations, Numerical Linear Algebra with Applications, 15 (2008), pp.

Bilinear Quadratic Output Systems and Balanced Truncation Damm , Direct methods and ADI-preconditioned Krylov subspace methods for generalized Lyapunov equations, Numerical Linear Algebra with Applications, 15 (2008), pp

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:26.570817Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d02864bb-fc5e-4011-8f58-1bd9a2ddb09f · outbound

This paper cites Fujimoto, J.

Bilinear Quadratic Output Systems and Balanced Truncation Fujimoto, J

Reference 17

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:34.502618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 15c85d8c-dd17-41a3-8189-77c4ee9efde4 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:26.852514Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f214a987-b47b-46d5-a59a-a6d3a822315d · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 19

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:34.317687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 87a6dc75-d763-42f0-9e31-2d8ad3a4e628 · outbound

This paper cites Gugercin and A.

Bilinear Quadratic Output Systems and Balanced Truncation Gugercin and A

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:34.128578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 89e7da84-999c-448a-a5b9-b2c2d516e857 · outbound

This paper cites Hartmann, C.

Bilinear Quadratic Output Systems and Balanced Truncation Hartmann, C

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:33.761910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 99a1fab1-0403-4328-b071-8996407ad3b4 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:18:33.429861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 41bd0efc-0cbe-4f95-9ee2-ed949e6f48ac · outbound

This paper cites Lancaster and M.

Bilinear Quadratic Output Systems and Balanced Truncation Lancaster and M

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:33.250138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 88796d6e-38a1-4106-88e5-f74309c7a2c2 · outbound

This paper cites Mehrmann and B.

Bilinear Quadratic Output Systems and Balanced Truncation Mehrmann and B

Reference 24

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:33.103012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation cd980e17-cd77-40a1-84aa-1f48478eebe0 · outbound

This paper cites Mohler , Nonlinear systems (vol.

Bilinear Quadratic Output Systems and Balanced Truncation Mohler , Nonlinear systems (vol

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:32.876159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c2117c57-c8a5-4e7b-a0f8-cd4fad1a72c0 · outbound

This paper cites Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control, 26 (1981), pp.

Bilinear Quadratic Output Systems and Balanced Truncation Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control, 26 (1981), pp

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:27.582165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a8926ef-18b4-4e73-9b86-951015bb4707 · outbound

This paper cites Mullis and R.

Bilinear Quadratic Output Systems and Balanced Truncation Mullis and R

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:27.666337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 153defa1-3e3d-4628-9b79-3054895c1733 · outbound

This paper cites Padhi, Model Order Reduction of Nonlinear Dynamical Systems , master’s thesis, Indian Institute of Science Education and Research Pune, Pashan, Pune India, May 2024.

Bilinear Quadratic Output Systems and Balanced Truncation Padhi, Model Order Reduction of Nonlinear Dynamical Systems , master’s thesis, Indian Institute of Science Education and Research Pune, Pashan, Pune India, May 2024

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:32.681167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f3c06329-3042-466b-92ed-c5898cb9713e · outbound

This paper cites Pulch, Energy-based model order reduction for linear stochastic Galerkin systems of second order, PAMM, 23 (2023), p.

Bilinear Quadratic Output Systems and Balanced Truncation Pulch, Energy-based model order reduction for linear stochastic Galerkin systems of second order, PAMM, 23 (2023), p

Reference 29

Resolution: verified exact; doi, observed 2026-08-06T20:18:30.144571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e49dba0d-4ca4-47e3-a816-b703f365f82f · outbound

This paper cites Pulch and A.

Bilinear Quadratic Output Systems and Balanced Truncation Pulch and A

Reference 30

Resolution: verified exact; doi, observed 2026-08-06T20:18:29.849952Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c99adf05-ef62-4eae-8564-0395b57f2970 · outbound

This paper cites Interpolatory model reduction of dynamical systems with root mean squared error.

Bilinear Quadratic Output Systems and Balanced Truncation Interpolatory model reduction of dynamical systems with root mean squared error

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:18:30.372365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d75a5195-406c-47dd-8e25-f298721b44b5 · outbound

This paper cites Reiter and S.

Bilinear Quadratic Output Systems and Balanced Truncation Reiter and S

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:18:32.523520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f561454b-8f06-458e-ab4f-3e270e0ee925 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:18:32.333691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d0ec282d-7e79-414c-ace0-6d66486fe002 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:28.413600Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a550365-9bfb-4da2-9b9b-5675dda8e905 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:28.486811Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a0fdf97-e3be-4bc7-bc56-8a9ce65f6ae4 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 36

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T20:18:32.084660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 97890a0a-7aa9-4521-841c-99f50c9d1477 · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:18:31.781223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 24fe31bc-c56b-4b1c-9d67-7efc84012ebc · outbound

This paper cites V an Beeumen, K.

Bilinear Quadratic Output Systems and Balanced Truncation V an Beeumen, K

Reference 38

Resolution: verified exact; doi, observed 2026-08-06T20:18:29.633369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 3443854f-f9e1-4b75-9153-ddcb1ee31789 · outbound

This paper cites van der Schaft, Port-Hamiltonian systems: an introductory survey , in International con- gress of mathematicians, European Mathematical Society Publishing House (EMS Ph), 2006, pp.

Bilinear Quadratic Output Systems and Balanced Truncation van der Schaft, Port-Hamiltonian systems: an introductory survey , in International con- gress of mathematicians, European Mathematical Society Publishing House (EMS Ph), 2006, pp

Reference 39

Resolution: verified exact; doi, observed 2026-08-06T20:18:29.322390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9b0a7795-28e7-4683-b163-615e5317367b · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:18:31.584183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 11860b0c-1fee-45b1-bdb6-dbfa96db8a92 · outbound

This paper cites Yue and K.

Bilinear Quadratic Output Systems and Balanced Truncation Yue and K

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:28.956989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f869ec6-fce3-4cad-ba88-6551cc8ea3f7 · outbound

This paper cites Zhang and J.

Bilinear Quadratic Output Systems and Balanced Truncation Zhang and J

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T20:18:29.028698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91b1c70b-d21b-43db-8733-94dd6217e5ee · outbound

This paper cites an unresolved cited work.

Bilinear Quadratic Output Systems and Balanced Truncation Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:18:31.363646Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

Observation e7831d0b-f8b7-42fd-89e7-4e9c5f4f73f3 · inbound

Bilinear Systems with Quadratic Outputs: $\mathcal{H}_2$ Analysis, Optimality Conditions for Model Reduction, and Algorithmic Solutions cites this paper.

Bilinear Systems with Quadratic Outputs: $\mathcal{H}_2$ Analysis, Optimality Conditions for Model Reduction, and Algorithmic Solutions Bilinear Quadratic Output Systems and Balanced Truncation

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-01T12:50:03.227331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.