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Paper Citation Record · LEDGER

On phase in scaled graphs

As of 23 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 2 inbound Pith citation observations for arXiv:2504.21448.

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

pith.paper-citation-record.v1
2504.21448 v2

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T05:11:48.694792Z

measured 28 of 28 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-19T03:45:42.220147Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T03:47:01.702163Z

Reference resolution

26 of 26 outbound references displayed

  • verified exact0
  • verified fuzzy21
  • unresolved5
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e5d2c441-2e7b-40c3-9cf2-8b1c4dec6a15 · outbound

This paper cites Skogestad and I.

On phase in scaled graphs Skogestad and I

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.985108Z

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.

source=pdf_text observed=2026-08-16T05:11:48.598425Z digest=sha256:2af9d81f3d8c2f0fe58119da4d697e2d9c25c09f723750bd1b9cc8d425635085

Observation d141a17a-7b92-4254-a5e0-a79779271a43 · outbound

This paper cites an unresolved cited work.

On phase in scaled graphs Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:11:48.975217Z

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.

source=pdf_text observed=2026-08-16T05:11:48.603088Z digest=sha256:03be3b60db2ba7c78bd80fc47aacab187de9f0e944c1705be1e77ac8ff0648ab

Observation 99482aa0-a6b6-4ffc-92f2-0a0ccc052373 · outbound

This paper cites Scaled relative graphs: Non- expansive operators via 2D Euclidean geometry,.

On phase in scaled graphs Scaled relative graphs: Non- expansive operators via 2D Euclidean geometry,

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.965491Z

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.

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Observation 0dff2cad-8646-4062-ae1b-c252a594e8eb · outbound

This paper cites Scaled relative g raphs for system analysis,.

On phase in scaled graphs Scaled relative g raphs for system analysis,

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.955577Z

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.

source=pdf_text observed=2026-08-16T05:11:48.610491Z digest=sha256:96732a01aa56aac02c3ff56b846c67ea19bb807110297fe4f319028f49381eb1

Observation f07e2903-49f0-4cf6-ae97-af549639fe3e · outbound

This paper cites A rolled-off passivity theorem,.

On phase in scaled graphs A rolled-off passivity theorem,

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.945744Z

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.

source=pdf_text observed=2026-08-16T05:11:48.614318Z digest=sha256:8c22a8c405732d66e2aa88362cce8de6c00495a95809c5d0bc416f894a9d9711

Observation 23eb788a-9e43-4f5f-aa9b-8bb05ac63732 · outbound

This paper cites Graphical Nonli near System Analysis,.

On phase in scaled graphs Graphical Nonli near System Analysis,

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.935017Z

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.

source=pdf_text observed=2026-08-16T05:11:48.617767Z digest=sha256:d882744dbefcb4fd8added3c1c7a92be976ff357f4cd1bbc2e4f990dc2e78313

Observation 746f074a-e239-4548-8f8c-393d02232282 · outbound

This paper cites Scaled graphs for reset control system analysis,.

On phase in scaled graphs Scaled graphs for reset control system analysis,

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.923854Z

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.

source=pdf_text observed=2026-08-16T05:11:48.621675Z digest=sha256:084d8597ea11d81e11e876e0a7aa9aae01d6d1bce000ad61e81c70ea4db2d467

Observation bcd9f2c2-ea84-4077-9fb9-8261a18108e6 · outbound

This paper cites The Scaled Relative Graph of a Linear Operator.

On phase in scaled graphs The Scaled Relative Graph of a Linear Operator

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-16T05:11:48.625029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:11:48.625029Z digest=sha256:5d2df3e79ae6723b210cc3bf902f57e6288b330943043b1f404e5a69e59f400b

Observation 50baa2ba-c6d5-4125-916c-5120272945e1 · outbound

This paper cites van der Schaft, L2-Gain and Passivity Techniques in Non-linear Control, Springer, 2017.

On phase in scaled graphs van der Schaft, L2-Gain and Passivity Techniques in Non-linear Control, Springer, 2017

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.913201Z

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.

source=pdf_text observed=2026-08-16T05:11:48.628534Z digest=sha256:a2ed8580658029add00fbd1281a92ec28d2f60f335ed81c9282c504040d9c1ee

Observation 3b9b00dc-51f7-4553-816f-02c33a56a73d · outbound

This paper cites Wielandt, Topics in the Analytic Theory of Matrices.

On phase in scaled graphs Wielandt, Topics in the Analytic Theory of Matrices

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.903113Z

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.

source=pdf_text observed=2026-08-16T05:11:48.632005Z digest=sha256:950bfd5e63fc9f82e36407e469336d0fd31b412734628fa48ea351fd7b3dbd91

Observation c5187440-544e-4d69-b4c4-3511985707b6 · outbound

This paper cites Soft and hard scal ed relative graphs for nonlinear feedback stability.

On phase in scaled graphs Soft and hard scal ed relative graphs for nonlinear feedback stability

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.892176Z

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.

source=pdf_text observed=2026-08-16T05:11:48.639780Z digest=sha256:debb01bc9b0978c53417d437b918f07d7b7ac8f09ac792520bdbdbdc3ca1d92b

Observation 2c7f6b75-82f8-42ca-918f-139cbeee4dea · outbound

This paper cites On the input-output stability of time-varyi ng non-linear feedback systems Part one: Conditions derived using concep ts of loop gain, conicity, and positivity,.

On phase in scaled graphs On the input-output stability of time-varyi ng non-linear feedback systems Part one: Conditions derived using concep ts of loop gain, conicity, and positivity,

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.882094Z

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.

source=pdf_text observed=2026-08-16T05:11:48.643706Z digest=sha256:36c43ff6ad17d27b7e0816a6821cb6a32f66479513237812c1eada1762aabe53

Observation 90902ceb-a404-42f5-9f17-a4970428ecfe · outbound

This paper cites an unresolved cited work.

On phase in scaled graphs Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:11:48.871045Z

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.

source=pdf_text observed=2026-08-16T05:11:48.647121Z digest=sha256:412438cf85162b05f7a395379456ae2d79db17d6035cd498eb7deb8e816c52b3

Observation 314be589-d36d-4963-b833-672dafd91139 · outbound

This paper cites Astrom and T.

On phase in scaled graphs Astrom and T

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.859871Z

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.

source=pdf_text observed=2026-08-16T05:11:48.651430Z digest=sha256:bb6d45527cc0f78ec3f111541c4f93819ccc6e146cf357fced29293aebb47e72

Observation b7d46c69-1088-4683-aaec-17abc7418467 · outbound

This paper cites an unresolved cited work.

On phase in scaled graphs Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-16T05:11:48.849672Z

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.

source=pdf_text observed=2026-08-16T05:11:48.654848Z digest=sha256:9b394cdd8707d8937ab1515a77893e0202825a021f2ee48b1395cc2998773b23

Observation 730f64ba-77e4-460d-9e62-1dfc5526473e · outbound

This paper cites Phase of Nonlinear Systems.

On phase in scaled graphs Phase of Nonlinear Systems

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-16T05:11:48.658708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-16T05:11:48.658708Z digest=sha256:9ca0d9d56537cd97c9c6e514a11c56f8ee88792504d52395459abfb2789c74b0

Observation b5b71c9a-735f-4df5-90d7-bf791724d72f · outbound

This paper cites Khalil, Non-linear Systems (3rd ed.).

On phase in scaled graphs Khalil, Non-linear Systems (3rd ed.)

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.840303Z

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.

source=pdf_text observed=2026-08-16T05:11:48.662040Z digest=sha256:d7646bf5c9f4958b6f2c734b02553ba95894d22abaaa36a27b3fb51727bf18fe

Observation 57efbadc-f5ad-4671-8748-ada0c525a0f0 · outbound

This paper cites Extendi ng negative imaginary systems theory to nonlinear systems,.

On phase in scaled graphs Extendi ng negative imaginary systems theory to nonlinear systems,

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.830339Z

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.

source=pdf_text observed=2026-08-16T05:11:48.665413Z digest=sha256:9ba0bb11e18c5aeab5f2acb0b03ac5569b22f66ccc94f1dabf95318122195873

Observation 64b6060a-5622-4dd6-92b1-1bc6923a5ea1 · outbound

This paper cites Stability analysis of intercon nected systems with “mixed.

On phase in scaled graphs Stability analysis of intercon nected systems with “mixed

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.820743Z

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.

source=pdf_text observed=2026-08-16T05:11:48.669122Z digest=sha256:9ae40b7dc2d1ca6a55aecfd31ab857bda18d044cf5761b78108efd05fecc619b

Observation 6e59de57-b1fe-4d41-85ef-76fffc0150ac · outbound

This paper cites Characterization of input- output neg- ative imaginary systems in a dissipative framework,.

On phase in scaled graphs Characterization of input- output neg- ative imaginary systems in a dissipative framework,

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.810783Z

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.

source=pdf_text observed=2026-08-16T05:11:48.672848Z digest=sha256:cc6a9e9ea2076eaea54bcc884e6d8105001a143d60e275a37c0a2cfdf8973a4a

Observation 6c38ab74-d3f3-4dc0-92af-b7a695a85e17 · outbound

This paper cites A frequency-domain ap proach to nonlinear negative imaginary systems analysis,.

On phase in scaled graphs A frequency-domain ap proach to nonlinear negative imaginary systems analysis,

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.800409Z

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.

source=pdf_text observed=2026-08-16T05:11:48.676769Z digest=sha256:639f153652e32fce38c9d3e98b5ef2f084da8f3f5b862eed0d761df55ad6bc2d

Observation 3b97d68a-6288-4f18-a940-21cd74a8ab1f · outbound

This paper cites Stability robustness of a feedback inter- connection of systems with negative imaginary frequency re sponse,.

On phase in scaled graphs Stability robustness of a feedback inter- connection of systems with negative imaginary frequency re sponse,

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.789907Z

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.

source=pdf_text observed=2026-08-16T05:11:48.680503Z digest=sha256:cdeea1008b3b50ee7eb8f6df8a8dbbd92318f8c84575ab38290255eeb3d928c1

Observation db284b57-9ad0-4d46-b120-14592946375b · outbound

This paper cites System analysis via integ ral quadratic constraints,.

On phase in scaled graphs System analysis via integ ral quadratic constraints,

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.779316Z

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.

source=pdf_text observed=2026-08-16T05:11:48.684008Z digest=sha256:fdebbce1b916035355ef360649cf432f458868f65290098a4e8a5beccbe0ca4a

Observation f8c1163a-756c-4af1-87f4-dc470ba90c6b · outbound

This paper cites On a larg e-gain theorem,.

On phase in scaled graphs On a larg e-gain theorem,

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.768269Z

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.

source=pdf_text observed=2026-08-16T05:11:48.687411Z digest=sha256:3dcad7f2c5b42171ac42f2d03ef60f7b0835b408e330d8b535ba858096ef9abf

Observation f62429bc-0259-46eb-8b6e-eee2e41ab9f3 · outbound

This paper cites On the input- output stability of nonlinear systems: Large gain theorem.

On phase in scaled graphs On the input- output stability of nonlinear systems: Large gain theorem

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.758014Z

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.

source=pdf_text observed=2026-08-16T05:11:48.690529Z digest=sha256:2fe8d86d19ada99806a5120179a080f2b7950b8e266ddb1f4729f26a414e694e

Observation 4135a80d-38e7-49bc-a829-c4170249c327 · outbound

This paper cites Freeman, ‘On the Role of Well-Posedness in Homotop y Methods for the Stability Analysis of non-linear Feedback Systems’ , In Lecture Notes in Control and Information Sciences, pp.

On phase in scaled graphs Freeman, ‘On the Role of Well-Posedness in Homotop y Methods for the Stability Analysis of non-linear Feedback Systems’ , In Lecture Notes in Control and Information Sciences, pp

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-16T05:11:48.745829Z

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.

source=pdf_text observed=2026-08-16T05:11:48.694792Z digest=sha256:e7736f449f925f52862267e34ff11a8ff1acf0d493fce97631cd12baa0d910ec

Pith citing papers

Observation e88db15f-7b54-4737-b730-220a6fd695c2 · inbound

Analysis of Non-Square Nonlinear MIMO Systems using Scaled Relative Graphs cites this paper.

Analysis of Non-Square Nonlinear MIMO Systems using Scaled Relative Graphs On phase in scaled graphs

Reference 8

Resolution
verified exact
arxiv_id, observed 2026-05-19T03:47:01.705413Z

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.

source=pdf_text observed=2026-05-19T03:45:42.220147Z digest=sha256:c118bbbe4dc6847ba643a44a4c09ab19de2e974e5f1ac311b816fa91732e4a05

Observation 77b57148-4f1c-44b9-9477-84b4a1941e55 · inbound

Symmetry Is Almost All You Need: Robust Stability with Uncertainty Induced by Symmetric SRG Regions cites this paper.

Symmetry Is Almost All You Need: Robust Stability with Uncertainty Induced by Symmetric SRG Regions On phase in scaled graphs

Reference 26

Resolution
verified exact
arxiv_id, observed 2026-05-10T14:35:34.330273Z

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.

source=pdf_text observed=2026-05-10T14:33:50.293127Z digest=sha256:db3fe7bc63f855c6e80a5f52c06b3f3ada27ba05c79973a20b994526293b7ae1