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Paper Citation Record · LEDGER

Stability and Synchronization of Kuramoto Oscillators

As of 13 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2411.17925.

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

pith.paper-citation-record.v1
2411.17925 v2

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T11:53:24.565038Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

26 of 26 outbound references displayed

  • verified exact0
  • verified fuzzy13
  • unresolved13
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a9c6794d-15a0-4e51-8167-8ed799efa4b8 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.254757Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.601352Z digest=sha256:92f7e84fcf870000821183c9a2ef3d685c6c01f824349c84e2fe1b866929eb5b

Observation 2fe3ebdf-c16b-417c-ac92-afa92559943d · outbound

This paper cites In essence, sufficiently strong coupling ensures the existence (and, at an even higher threshold, unique- ness) of a stable phase-locked solution.

Stability and Synchronization of Kuramoto Oscillators In essence, sufficiently strong coupling ensures the existence (and, at an even higher threshold, unique- ness) of a stable phase-locked solution

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:26.241714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.647517Z digest=sha256:9c04e4ce67fffc0f868a09d06335efbd5ed337663cf73c5a1a7c247d0560e04c

Observation c51cbefe-67ba-4e78-a2ed-33e99475faa4 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.225959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.710593Z digest=sha256:7a3ba64856d1f13745a0acff4c1ed0d060ffb4cc4707ddd88e85c64c61212a7f

Observation 1c31ad93-29c8-40a6-8c65-0dd3bd3fcbf3 · outbound

This paper cites Before moving to the next notion of synchronization, let us look at a few mathematical preliminaries.

Stability and Synchronization of Kuramoto Oscillators Before moving to the next notion of synchronization, let us look at a few mathematical preliminaries

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:26.185427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.774262Z digest=sha256:f2ac9a55374ed373d235ceabdda72b2f3e0ebd246840be29005871c4bda5d19a

Observation 94bd220e-4089-4c1e-a691-a1718a31dee2 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.075786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.806895Z digest=sha256:f72ced5244da664646a1d0c5d2e0b622f7968143b4b98edc5edd7b34d28e1f88

Observation 748675df-7e30-48d3-b5b6-b104359a0a50 · outbound

This paper cites For example, a solution θ : R≥0 → Tn achieves phase synchronization if limι→∞ |θi(t) − θj(t)| = 0.

Stability and Synchronization of Kuramoto Oscillators For example, a solution θ : R≥0 → Tn achieves phase synchronization if limι→∞ |θi(t) − θj(t)| = 0

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:26.029428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.837979Z digest=sha256:0cab8dbe90c0245287fbda1557d5a658eea31c08587ec973dac4673b14e17f9d

Observation 59b7265d-d51b-41a1-b2df-f5be71c366c1 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:26.015879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.851501Z digest=sha256:80e02aaafeca57019b3ab802ca1668bcf5b117d18bf4b7d36a7f6edb4a142b95

Observation a41f9fd7-a2ca-4ee4-bcea-9e106be84331 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.999644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.857035Z digest=sha256:3b4e31e2e215eb12d07a3d1ef5023bf69c37ace6809f8e6314d92b2af0e70b9d

Observation 776a7684-11f8-4938-b94b-b37785bda508 · outbound

This paper cites Proof: Given θ ∈ Tn, we define the undirected graph Gcosine (θ) with the same nodes and edges as G and with edge weights aij cos (θi − θj).

Stability and Synchronization of Kuramoto Oscillators Proof: Given θ ∈ Tn, we define the undirected graph Gcosine (θ) with the same nodes and edges as G and with edge weights aij cos (θi − θj)

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.911693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.898311Z digest=sha256:620e9bf3f03e2c3e8704c15303acee3f50a0b2ee6d52c573eaae8881825e13b5

Observation 14a1bdd9-9618-4a56-9d07-f7ea89ca8101 · outbound

This paper cites Strogatz, ”From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators”, Physica D: Nonlinear Phenomena, Volume 143, Issues 1–4, 2000.

Stability and Synchronization of Kuramoto Oscillators Strogatz, ”From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators”, Physica D: Nonlinear Phenomena, Volume 143, Issues 1–4, 2000

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.804586Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:23.963578Z digest=sha256:1401026d819ae975e1ef94c60ed9ed0c5a212705ac998f878dc365e338e561ed

Observation 63f2757b-a2ae-4a09-a6dc-c73cf4c34281 · outbound

This paper cites Godsil and G.

Stability and Synchronization of Kuramoto Oscillators Godsil and G

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-12T11:53:24.023948Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T11:53:24.023948Z digest=sha256:dafade58251c10938aaca4efde52e0156659055d1bcbf43065b5f5208d1058f2

Observation ccfbdefa-f528-42f7-87fa-b499804eeed9 · outbound

This paper cites Biggs, Algebraic Graph Theory, Cambridge University Press, 1993.

Stability and Synchronization of Kuramoto Oscillators Biggs, Algebraic Graph Theory, Cambridge University Press, 1993

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.777977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.089395Z digest=sha256:71fe9f9c72c2a4ccacb10635815c878b62b5626e6300b994f8bf0da3c788b73c

Observation 71702fcc-fba8-414c-9bdd-0ec42eb905c0 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.728850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.125902Z digest=sha256:741cfa814953ed1182c59137af290f4d762c19af434acf2e38e34198d8fb48fd

Observation 50f3300c-80b3-43da-bdc6-4f14c8b4f5cf · outbound

This paper cites Chopra and M.

Stability and Synchronization of Kuramoto Oscillators Chopra and M

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-12T11:53:24.191645Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T11:53:24.191645Z digest=sha256:bb42c5c8d996d6707c81c64df0d31d70b3e290454dc9454ec26eddfec8c38770

Observation 7d8da27b-ffae-4310-b671-5e1fcab123df · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.609506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.230088Z digest=sha256:7a8080bbe74a2bc0359396ca6d237deba504187568e53ffc13a18250796bd2bc

Observation a3046708-4302-4b34-8429-d6877d3e427a · outbound

This paper cites D¨ orfler, M.

Stability and Synchronization of Kuramoto Oscillators D¨ orfler, M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.489704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.252517Z digest=sha256:6532dd53dd02c3075c5ad983098c8ccdd71d8c9bf017b2b8e1e4560bc82ded1d

Observation 7226edea-8714-4b7f-9b34-d3b96b50d751 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.476039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.279042Z digest=sha256:7adc93012ddb5400834d084983050bec9115e5b6e0ec8c0d040d728635b0259d

Observation 8a619fa8-b299-42b0-aad6-73fbc209711c · outbound

This paper cites Chepizhko, V.L.

Stability and Synchronization of Kuramoto Oscillators Chepizhko, V.L

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.456720Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.288168Z digest=sha256:b4c1a0a3949b04712ca24f43e5a14fe36aecec6e36a4737d2259bd1c36e2faa7

Observation ea115649-4389-466a-ad60-b0be28fc86cc · outbound

This paper cites The Kuramoto Model.

Stability and Synchronization of Kuramoto Oscillators The Kuramoto Model

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.408079Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.292457Z digest=sha256:303f4a5144613e32394b028c74f68ef560cc812f0f7dd6032967dfea00b62a52

Observation af9591bd-5733-4456-9c29-9e29aa6aeae1 · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.361758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.296805Z digest=sha256:a3c7d7aa043c3f56835f89487058632d95924dd21a83153afe31f25968d9ba2f

Observation c7567a3f-13ec-431e-836c-16a37d33d83b · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:25.238470Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.301287Z digest=sha256:d3d2ca65e1caab7f8b71a938853cc9e4f715e02df1eeef12b233dbbabe687cb3

Observation 42242f9b-1465-424f-9aa7-0522719904e4 · outbound

This paper cites Strogatz.

Stability and Synchronization of Kuramoto Oscillators Strogatz

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.105216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.310169Z digest=sha256:e340965f97cc69a7b99f3d743741e34b7ff37eed822b9bd2dec7e77a9163083b

Observation f46012c9-3e0f-4603-b84d-973845188395 · outbound

This paper cites Synchronization: From Simple to Complex.

Stability and Synchronization of Kuramoto Oscillators Synchronization: From Simple to Complex

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:25.052640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.403393Z digest=sha256:e7ae9100991c4026f6bcb61dfadbc865deb87cce0a7a4393d3059634c3dbb728

Observation 556e907d-1f8d-450e-8624-96bb59cba5d3 · outbound

This paper cites Acebr, L.L.

Stability and Synchronization of Kuramoto Oscillators Acebr, L.L

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:24.896053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.478508Z digest=sha256:e56137eb6afbe32c002637c7c2d237653aa05a7186c96be4a19d40dc5e801b8e

Observation 0b855058-08ce-415a-a567-cc339680b89f · outbound

This paper cites an unresolved cited work.

Stability and Synchronization of Kuramoto Oscillators Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-12T11:53:24.831705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.525943Z digest=sha256:a88620e1bdfeec4d6f981a869d4ee30856a4d49ad807cc3f0cc6512425e6dbf4

Observation 7f5c1611-904d-4f39-a9f3-c98afec4b301 · outbound

This paper cites optimal,” (1994) 21.

Stability and Synchronization of Kuramoto Oscillators optimal,” (1994) 21

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T11:53:24.730006Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-12T11:53:24.565038Z digest=sha256:6b61d1ef488e1e3aa2a36fc370e00de902518113c74553df6b58ea86b6f37418

Pith citing papers

No inbound Pith citation observations are available.