Paper Citation Record · LEDGER

Data-driven balanced truncation for second-order systems via the approximate Gramians

As of 8 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2506.03855.

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

pith.paper-citation-record.v1
2506.03855 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:00:39.071894Z

measured 35 of 35 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-25T07:58:48.667349Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

34 of 34 outbound references displayed

verified exact0
verified fuzzy21
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 019a44b8-9d80-4a47-bde8-0f9142724703 · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.626191Z

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 d32a6d28-cf6e-42ca-9c1e-8f68b37f0bfe · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.611442Z

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 81d8c2fe-212a-496e-a48e-72f3493c4a7c · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.596627Z

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 26146bcf-d7bc-49d3-9512-10c0b4f26e4c · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.581757Z

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 92ee281a-aef6-4c45-9fde-d07ad9ad1624 · outbound

This paper cites Meyer, S.

Data-driven balanced truncation for second-order systems via the approximate Gramians Meyer, S

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.566048Z

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 09fb4c3b-fd20-43af-87b6-f7d85e502c61 · outbound

This paper cites Chahlaoui, D.

Data-driven balanced truncation for second-order systems via the approximate Gramians Chahlaoui, D

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.550834Z

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 a87e4768-20fb-43d7-a66c-6139ea6e9eb0 · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.536413Z

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 e244ba4e-8637-4c87-a54d-002c828050d3 · outbound

This paper cites Benner, P.

Data-driven balanced truncation for second-order systems via the approximate Gramians Benner, P

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.520896Z

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 5f2812c5-b3b3-468b-aec2-682ed1bb94f1 · outbound

This paper cites Hartmann, V.

Data-driven balanced truncation for second-order systems via the approximate Gramians Hartmann, V

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.505273Z

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 e481efc3-f791-473e-acb6-1a36b9d9ba69 · outbound

This paper cites Sato, Riemannian optimal model reduction of linear s econd-order systems, IEEE Control Systems Letters 1 (1) (2017) 2–7.

Data-driven balanced truncation for second-order systems via the approximate Gramians Sato, Riemannian optimal model reduction of linear s econd-order systems, IEEE Control Systems Letters 1 (1) (2017) 2–7

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.490549Z

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 5aea5347-2a7a-4c86-a6a8-a2c985c0d7d5 · outbound

This paper cites Mlinaric, P.

Data-driven balanced truncation for second-order systems via the approximate Gramians Mlinaric, P

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.474847Z

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 c234c70f-9b2b-489c-9e4b-11898da2fe54 · outbound

This paper cites Pulch, Stochastic Galerkin method and port-Hamilto nian form for linear dynamical systems of second order, Mathematics and Computers in Simulation 216 (2024) 187–197.

Data-driven balanced truncation for second-order systems via the approximate Gramians Pulch, Stochastic Galerkin method and port-Hamilto nian form for linear dynamical systems of second order, Mathematics and Computers in Simulation 216 (2024) 187–197

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.460414Z

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 985b69ed-9db4-4217-8660-7032dd0832c6 · outbound

This paper cites Beattie, S.

Data-driven balanced truncation for second-order systems via the approximate Gramians Beattie, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.444771Z

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 36aaf3fd-19b8-4cd8-b636-d6136886ca42 · outbound

This paper cites Goyal, B.

Data-driven balanced truncation for second-order systems via the approximate Gramians Goyal, B

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.429680Z

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 28d8e9dc-972e-426c-b118-b15291031555 · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.414523Z

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 5f8babf6-3ad1-471b-b9fe-7c5ef02535ee · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.397298Z

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 f313c503-9aad-4882-9de0-c2116966052e · outbound

This paper cites Moreschini, J.

Data-driven balanced truncation for second-order systems via the approximate Gramians Moreschini, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.382868Z

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 3d71744e-57ab-412e-8e8a-8c4e9dd3d67b · outbound

This paper cites Peherstorfer, K.

Data-driven balanced truncation for second-order systems via the approximate Gramians Peherstorfer, K

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.367678Z

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 d94b041e-4a8b-4d13-a238-1c6c8b19c032 · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.351842Z

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 b57d7f48-b23a-4aee-a511-cc95426956ad · outbound

This paper cites Schwerdtner, M.

Data-driven balanced truncation for second-order systems via the approximate Gramians Schwerdtner, M

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.336330Z

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 e285d4ae-ccf3-419f-8059-2e38b7ea304b · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.318064Z

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 a1450282-b7e7-4b11-b073-7d252913b67f · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.301531Z

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 dac0348f-3a1e-4125-ae80-406f3805b57f · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.284138Z

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 cd3fe5d0-e952-42fd-9fef-1757cf9a35de · outbound

This paper cites Boyd, Exponentially convergent fourier-chebshev q uadrature schemes on bounded and inﬁnite intervals, Journal of Scientiﬁc Computing 2 (1987) 99–109.

Data-driven balanced truncation for second-order systems via the approximate Gramians Boyd, Exponentially convergent fourier-chebshev q uadrature schemes on bounded and inﬁnite intervals, Journal of Scientiﬁc Computing 2 (1987) 99–109

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.268046Z

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 9b3cd92f-3102-4305-ab8d-4b30a046cad5 · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.252565Z

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 77486898-6d25-45cc-bac9-927e8b3d7c24 · outbound

This paper cites Meirovitch, Principles and Techniques of Vibration s, Prentice Hall, New Jersey, 1997.

Data-driven balanced truncation for second-order systems via the approximate Gramians Meirovitch, Principles and Techniques of Vibration s, Prentice Hall, New Jersey, 1997

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.237096Z

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 3b726535-b4b2-4ce4-b183-56b660907879 · outbound

This paper cites an unresolved cited work.

Data-driven balanced truncation for second-order systems via the approximate Gramians Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-07T11:00:39.220628Z

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 fa967f14-3766-4898-aecb-c207dc9eea4c · outbound

This paper cites Bonin, H.

Data-driven balanced truncation for second-order systems via the approximate Gramians Bonin, H

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.205293Z

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 b2362f07-895c-4d87-8c99-28b415306532 · outbound

This paper cites Schulze, B.

Data-driven balanced truncation for second-order systems via the approximate Gramians Schulze, B

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.188927Z

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 d8bbcb2b-12ac-4646-9bee-7d35e75a84af · outbound

This paper cites Hamadi, K.

Data-driven balanced truncation for second-order systems via the approximate Gramians Hamadi, K

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.171492Z

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 503ee4cd-2732-40b3-8ceb-edc4edca597c · outbound

This paper cites Sinomcini, A new iterative method for solving large- scale lyapunov matrix equations, SIAM Journal on Scientiﬁc Computing 29 (3) (2007) 1268–1288.

Data-driven balanced truncation for second-order systems via the approximate Gramians Sinomcini, A new iterative method for solving large- scale lyapunov matrix equations, SIAM Journal on Scientiﬁc Computing 29 (3) (2007) 1268–1288

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.156607Z

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 14067ae6-e0d5-43ff-8f7d-089b1d0daa01 · outbound

This paper cites Sinomcini, Computational methods for linear matrix equations, SIAM Review 58 (3) (2016) 377–441.

Data-driven balanced truncation for second-order systems via the approximate Gramians Sinomcini, Computational methods for linear matrix equations, SIAM Review 58 (3) (2016) 377–441

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.141084Z

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 0ea1a767-0358-4b19-920d-276b9272403e · outbound

This paper cites Chahlaoui, P.

Data-driven balanced truncation for second-order systems via the approximate Gramians Chahlaoui, P

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.125059Z

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 c1591cf4-a7e8-43b5-90ff-00638db91e20 · outbound

This paper cites Benner, D.

Data-driven balanced truncation for second-order systems via the approximate Gramians Benner, D

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T11:00:39.108970Z

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 237be3bf-7a2b-4258-bec0-92fd82be700d · inbound

Data-driven balanced truncation for second-order systems with generalized proportional damping cites this paper.

Data-driven balanced truncation for second-order systems with generalized proportional damping Data-driven balanced truncation for second-order systems via the approximate Gramians

Reference 45

Resolution: verified exact; arxiv_id, observed 2026-05-25T08:00:29.219390Z

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.