Paper Citation Record · LEDGER

Robust computation of higher-dimensional invariant tori from individual trajectories

As of 23 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2505.08715.

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

pith.paper-citation-record.v1
2505.08715 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:53:42.202998Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

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External citation measurements

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Outbound references

Observation 42d8ef5f-130e-4d48-8014-ebeb470bb838 · outbound

This paper cites Murray and Stanley F.

Robust computation of higher-dimensional invariant tori from individual trajectories Murray and Stanley F

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.634727Z

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Observation afec59de-f7d0-4100-abe5-91a7832dcde3 · outbound

This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:44.617314Z

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Observation 36d80e6b-cd87-4a74-aff0-664d6b213c53 · outbound

This paper cites An Introduction to Stellarators: From Magnetic Fields to Symmetries and Optimization.

Robust computation of higher-dimensional invariant tori from individual trajectories An Introduction to Stellarators: From Magnetic Fields to Symmetries and Optimization

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.595082Z

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This paper cites The Parameterization Method for Invariant Manifolds: From Rigorous Results to Effective Computations , volume 195 of Applied Mathematical Sciences.

Robust computation of higher-dimensional invariant tori from individual trajectories The Parameterization Method for Invariant Manifolds: From Rigorous Results to Effective Computations , volume 195 of Applied Mathematical Sciences

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.452204Z

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Observation 7c51233d-e64a-48fb-989f-35b322286567 · outbound

This paper cites Haro and R.

Robust computation of higher-dimensional invariant tori from individual trajectories Haro and R

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.434737Z

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Observation db5954cf-dadc-4149-90f1-fef5d07c23c8 · outbound

This paper cites A parameterization method for the computation of invariant tori andtheir whiskers in quasi-periodic maps: Numerical algorithms.

Robust computation of higher-dimensional invariant tori from individual trajectories A parameterization method for the computation of invariant tori andtheir whiskers in quasi-periodic maps: Numerical algorithms

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.417001Z

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Observation 27759277-a80f-4578-b7e7-59e5db9c7d23 · outbound

This paper cites Haro and R.

Robust computation of higher-dimensional invariant tori from individual trajectories Haro and R

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.384419Z

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This paper cites A tutorial on KAM theory.

Robust computation of higher-dimensional invariant tori from individual trajectories A tutorial on KAM theory

Reference 8

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Observation 766a9639-3f47-4477-bff7-d3df54d25ef0 · outbound

This paper cites On conservation of conditionally periodic motions for a small change in Hamilton’s function.

Robust computation of higher-dimensional invariant tori from individual trajectories On conservation of conditionally periodic motions for a small change in Hamilton’s function

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.262014Z

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Observation 55b8c0d4-2a5d-4907-8d80-15d2a76a006f · outbound

This paper cites Proof of a theorem of AN Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian.

Robust computation of higher-dimensional invariant tori from individual trajectories Proof of a theorem of AN Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.245659Z

Source-reported events for the cited work

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Observation 6a42beed-b1d9-4163-9832-d0f47a277335 · outbound

This paper cites On invariant curves of area-preserving mappings of an annulus.

Robust computation of higher-dimensional invariant tori from individual trajectories On invariant curves of area-preserving mappings of an annulus

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.227053Z

Source-reported events for the cited work

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Observation 8d480728-9d80-4e7a-b9ad-41c623416874 · outbound

This paper cites Figueras, A.

Robust computation of higher-dimensional invariant tori from individual trajectories Figueras, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.209961Z

Source-reported events for the cited work

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Observation 91abbe09-f9ec-4dbf-9aa2-89fb1e4fdf1b · outbound

This paper cites Olikara, and Daniel J.

Robust computation of higher-dimensional invariant tori from individual trajectories Olikara, and Daniel J

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.190705Z

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Observation e7b6a6ba-3368-4d0c-ba26-676e641755af · outbound

This paper cites Jeremy Kasdin, and Pini Gurfil.

Robust computation of higher-dimensional invariant tori from individual trajectories Jeremy Kasdin, and Pini Gurfil

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:44.079314Z

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Observation 8b83ef3c-69ef-4263-a6e8-7c2121dc3aab · outbound

This paper cites On the computation of reducible invariant tori on a parallel computer.

Robust computation of higher-dimensional invariant tori from individual trajectories On the computation of reducible invariant tori on a parallel computer

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.956694Z

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Observation 3202120d-4f18-4d75-b407-8dc92002f558 · outbound

This paper cites Leveraging quasi-periodic orbits for trajectory design in cislunar space.

Robust computation of higher-dimensional invariant tori from individual trajectories Leveraging quasi-periodic orbits for trajectory design in cislunar space

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.940799Z

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.925512Z

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This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.908271Z

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.891114Z

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Observation b19985c9-0b7f-4ade-bc27-06642bde36b8 · outbound

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.872975Z

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This paper cites Direct com- putation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry.

Robust computation of higher-dimensional invariant tori from individual trajectories Direct com- putation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.846923Z

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Observation 0b73ea5b-97d8-4e88-93e5-e3cb87dda8aa · outbound

This paper cites Introduction to Frequency Map Analysis.

Robust computation of higher-dimensional invariant tori from individual trajectories Introduction to Frequency Map Analysis

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.748194Z

Source-reported events for the cited work

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Observation 1639aa8c-aae6-4bb5-97f2-84ee96c491fd · outbound

This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.614539Z

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Observation b0fe0153-11c2-4a30-96c2-a7ed13e527ab · outbound

This paper cites Quantitative quasiperiodicity.

Robust computation of higher-dimensional invariant tori from individual trajectories Quantitative quasiperiodicity

Reference 24

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Observation 15a3c35d-cc36-4deb-94d7-60816431ee84 · outbound

This paper cites Sander and J.D.

Robust computation of higher-dimensional invariant tori from individual trajectories Sander and J.D

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.576062Z

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Observation bcb57a04-d88f-4809-9ce0-f630be56fbf1 · outbound

This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.558259Z

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Observation 8c8bbe7d-a0b3-4821-ad67-8db21b3ef4c8 · outbound

This paper cites Exponential convergence of the weighted Birkhoff average.

Robust computation of higher-dimensional invariant tori from individual trajectories Exponential convergence of the weighted Birkhoff average

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.540250Z

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Observation 0cf19647-3a85-4a93-96ca-2fec2100b727 · outbound

This paper cites Quantitative uniform exponential acceleration of averages along decaying waves, September 2024.

Robust computation of higher-dimensional invariant tori from individual trajectories Quantitative uniform exponential acceleration of averages along decaying waves, September 2024

Reference 28

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.521292Z

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Observation f5f61da2-0c5f-4bf0-958f-66593f1a27a0 · outbound

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Robust computation of higher-dimensional invariant tori from individual trajectories Ruth and D

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.502790Z

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Observation c48f5666-643b-4cf0-9f20-f90b52da1922 · outbound

This paper cites The High-Order Magnetic Near-Axis Expansion: Ill-Posedness and Regularization.

Robust computation of higher-dimensional invariant tori from individual trajectories The High-Order Magnetic Near-Axis Expansion: Ill-Posedness and Regularization

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T21:53:41.842630Z

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Observation a8ea80c8-d390-42c0-b09c-2e56537435ec · outbound

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.484878Z

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Observation 18e7fdcc-18a9-44f2-ac6d-83d5c8129cf8 · outbound

This paper cites Numerical computation of rotation numbers of quasi-periodic planar curves.

Robust computation of higher-dimensional invariant tori from individual trajectories Numerical computation of rotation numbers of quasi-periodic planar curves

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.369928Z

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Observation 32cd5752-288b-4f7d-bd50-c4c8a7cee5d5 · outbound

This paper cites SymplecticMapTools.jl.

Robust computation of higher-dimensional invariant tori from individual trajectories SymplecticMapTools.jl

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:43.268484Z

Source-reported events for the cited work

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Observation e6bc376b-dab3-456c-b6c2-e47af179d7ee · outbound

This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:43.100600Z

Source-reported events for the cited work

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 36

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Observation 8cad665c-d1c6-424f-b508-a2270f909022 · outbound

This paper cites Geometricintegrators.jl: Geometric numerical integration in julia.

Robust computation of higher-dimensional invariant tori from individual trajectories Geometricintegrators.jl: Geometric numerical integration in julia

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.960971Z

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Observation aec37869-5dd3-457d-b325-f1c678e41180 · outbound

This paper cites Trefethen and J.

Robust computation of higher-dimensional invariant tori from individual trajectories Trefethen and J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.943221Z

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Observation 7438f97b-e88c-4298-ae20-4b68f37ce20c · outbound

This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:42.926894Z

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Observation fae4247d-9ef7-47ac-9bc7-d629e8609cc6 · outbound

This paper cites Complexity of Lattice Problems.

Robust computation of higher-dimensional invariant tori from individual trajectories Complexity of Lattice Problems

Reference 40

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Observation 75ed2db4-c9f5-474c-9075-c4de4e058614 · outbound

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 41

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Observation e9c10f6c-4ec6-4c7f-8eb4-606d2a40334b · outbound

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Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:42.867137Z

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Observation 4d6672b7-8d5e-4fe2-a0d1-6af879d7ec67 · outbound

This paper cites HKZ and Minkowski Reduction Algorithms for Lattice- Reduction-Aided MIMO Detection.

Robust computation of higher-dimensional invariant tori from individual trajectories HKZ and Minkowski Reduction Algorithms for Lattice- Reduction-Aided MIMO Detection

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.815999Z

Source-reported events for the cited work

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Observation 88bb42c0-417c-4198-a663-cefb179e179d · outbound

This paper cites an unresolved cited work.

Robust computation of higher-dimensional invariant tori from individual trajectories Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-15T21:53:42.679641Z

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

Observation 10f6515e-203d-4b3b-8fad-049c09007a25 · outbound

This paper cites Dynamical systems, the three-body problem and space mission design.

Robust computation of higher-dimensional invariant tori from individual trajectories Dynamical systems, the three-body problem and space mission design

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.573667Z

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 48ae68fc-cd9e-4bbf-a924-e8d5e8f39426 · outbound

This paper cites Numerical exploration of the restricted problem, v.Astronomy and Astrophysics, 1:223– 238, 1969.

Robust computation of higher-dimensional invariant tori from individual trajectories Numerical exploration of the restricted problem, v.Astronomy and Astrophysics, 1:223– 238, 1969

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.555088Z

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 aea22d7a-9581-4d3d-a379-186af20d0882 · outbound

This paper cites Exploration of distant retrograde orbits around moon.

Robust computation of higher-dimensional invariant tori from individual trajectories Exploration of distant retrograde orbits around moon

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.533448Z

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 3b461759-e4f0-4be4-b875-bd8ca9fbf553 · outbound

This paper cites https://ssd.jpl.nasa.gov/tools/periodic_orbits.html.

Robust computation of higher-dimensional invariant tori from individual trajectories https://ssd.jpl.nasa.gov/tools/periodic_orbits.html

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.514185Z

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 d666e9ad-9762-4fe9-a4e9-0eb009497c8b · outbound

This paper cites Golub and Charles F.

Robust computation of higher-dimensional invariant tori from individual trajectories Golub and Charles F

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:53:42.436155Z

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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