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Paper Citation Record · LEDGER

Geometrical optics in phase space

As of 23 August 2026, this Paper Citation Record lists 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2509.08098.

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

pith.paper-citation-record.v1
2509.08098 v1

Coverage vector

measured 30 of 30 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T21:22:25.489364Z

measured 31 of 31 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 2026-05-18T15:17:51.128999Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T15:21:32.974621Z

Reference resolution

30 of 30 outbound references displayed

  • verified exact7
  • verified fuzzy14
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9ec06715-25b7-4bec-a290-88c49f357924 · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 1

Resolution
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raw_fallback, observed 2026-08-04T21:22:31.015048Z

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 43f7073c-4d10-4f45-8229-c5c390aec166 · outbound

This paper cites A geometric theory of waves and its applications to plasma physics.

Geometrical optics in phase space A geometric theory of waves and its applications to plasma physics

Reference 23

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verified exact
local_arxiv, observed 2026-08-04T21:22:25.794969Z

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=2026-08-04T21:22:24.927013Z digest=sha256:70b9cdeab259c15b51baab8a671f165e3ba318a95a4217559fc99c7e22f05817

Observation 75f542ef-f8a5-49f7-a71a-4c8491756647 · outbound

This paper cites Ponderomotive forces on waves in modulated media.

Geometrical optics in phase space Ponderomotive forces on waves in modulated media

Reference 35

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:22:26.485405Z

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=2026-08-04T21:22:23.353539Z digest=sha256:cb91d25b4762ed6de09e9d7095427974cbe60ec5492cc5ebe21c8d94c155bbbc

Observation 3a1b15b7-2d5a-464b-bd00-d19123ca9f8b · outbound

This paper cites & Kopeck ´y, V.1973 Penetration of high-frequency waves into a weakly inhomogeneous magnetized plasma at oblique incidence and their transformation to Bernstein modes.J.

Geometrical optics in phase space & Kopeck ´y, V.1973 Penetration of high-frequency waves into a weakly inhomogeneous magnetized plasma at oblique incidence and their transformation to Bernstein modes.J

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:27.796856Z

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=2026-08-04T21:22:24.857660Z digest=sha256:f44e2da66d7356865728f5628216cd5d1945f7a5fbd429cd7933b1649da74194

Observation 9cc1dc60-eedb-47c1-bbfd-79dac7d20c3b · outbound

This paper cites & Glogower, J.1964 Quantum mechanical phase and time operator.Physics 1,.

Geometrical optics in phase space & Glogower, J.1964 Quantum mechanical phase and time operator.Physics 1,

Reference 37

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verified fuzzy
raw_fallback, observed 2026-08-04T21:22:27.580224Z

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=2026-08-04T21:22:25.016694Z digest=sha256:0eda1e54d0f9a95899c6ad52a68d7518616b2f580e6f599e970d0ebd76c1b7ba

Observation 5de7737b-f590-4abb-807d-1cfec98e3d10 · outbound

This paper cites The Hidden Ontological Variable in Quantum Harmonic Oscillators.

Geometrical optics in phase space The Hidden Ontological Variable in Quantum Harmonic Oscillators

Reference 49

Resolution
unresolved
no resolver link, observed 2026-08-04T21:22:25.114482Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-04T21:22:25.114482Z digest=sha256:a42e064f541dc0834031f20dcaa87d0539bb61ed3363f381250458f37cd8051f

Observation 7b539c27-fb64-4447-a74b-9ba05fbee91e · outbound

This paper cites R., Brizard, A.

Geometrical optics in phase space R., Brizard, A

Reference 143

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:27.338248Z

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=2026-08-04T21:22:25.209939Z digest=sha256:ab6200c1c3e96041242c151d17bc6e03a0b3cdb5f224e4a4eef4f3096ff8e25c

Observation a62b56d1-3048-4802-8787-a8429ff378b4 · outbound

This paper cites & Ferry, D.

Geometrical optics in phase space & Ferry, D

Reference 156

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:26.914822Z

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=2026-08-04T21:22:25.333907Z digest=sha256:451e03004cc03adf88d835813aaba773e1417c627ce3b1cb16b543d1cf3cc600

Observation 715add45-47ed-4879-af09-37779865e1cc · outbound

This paper cites G.1985 Symplectically invariant WKB wave functions.Phys.

Geometrical optics in phase space G.1985 Symplectically invariant WKB wave functions.Phys

Reference 193

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:29.174658Z

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=2026-08-04T21:22:24.090599Z digest=sha256:e041292eaafdf2286637da10eb367b540bc78d011dd5b1cdf4ed5045af615f7c

Observation 1cbfd919-dd1a-4b91-a03a-be58a9b37c63 · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 199

Resolution
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raw_fallback, observed 2026-08-04T21:22:29.930038Z

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=2026-08-04T21:22:23.700935Z digest=sha256:3141822475db2e1a568dd2378bfd1a49d40501a94165c8016a590dfdfb9e6f5d

Observation 2d41615e-0f7a-426d-b511-a07be2e38340 · outbound

This paper cites Quasioptical modeling of wave beams with and without mode conversion: II. Numerical simulations of single-mode beams.

Geometrical optics in phase space Quasioptical modeling of wave beams with and without mode conversion: II. Numerical simulations of single-mode beams

Reference 271

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:22:25.650172Z

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=2026-08-04T21:22:25.398579Z digest=sha256:a9ef8c7fb350b0970881d9cdc75e434ec1d45e122e4691455edecfe34b941dec

Observation c67ae1ec-ed8c-483a-a56e-ead592078a42 · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 337

Resolution
unresolved
raw_fallback, observed 2026-08-04T21:22:28.505396Z

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=2026-08-04T21:22:24.446933Z digest=sha256:4c336246c41a065d09667be64be4ea600182251d4d9b5587d5a4520b64b7850c

Observation 59888a6f-42bf-4583-87c4-331d3f5b5cc0 · outbound

This paper cites & Ursell, F.1957 An extension of the method of steepest descents.Math.

Geometrical optics in phase space & Ursell, F.1957 An extension of the method of steepest descents.Math

Reference 517

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:30.347380Z

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=2026-08-04T21:22:23.073861Z digest=sha256:cc7aef5d21351ff737b7362ae95e8f489218befc07d529d6b2ffbf303985f4c9

Observation 1d12d6b9-7095-4036-9391-1a0b55091777 · outbound

This paper cites Quasilinear theory for inhomogeneous plasma.

Geometrical optics in phase space Quasilinear theory for inhomogeneous plasma

Reference 599

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:22:26.609811Z

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=2026-08-04T21:22:23.235030Z digest=sha256:46fb5cf24864d960d12c9969b5548ea2562800597c2202cdc10b4fba5dd5a965

Observation 07ace0e7-f98d-4b6c-ad5b-733fbdd421cd · outbound

This paper cites Rep.138,.

Geometrical optics in phase space Rep.138,

Reference 669

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:29.472317Z

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=2026-08-04T21:22:23.983152Z digest=sha256:5a8d4f6c66592fe96e00f77e24af56094c01f09e416eeb7e9ec89fe89c46340a

Observation 0d37ed69-1331-4486-b71a-90df5e6e80b9 · outbound

This paper cites & Kay, K.

Geometrical optics in phase space & Kay, K

Reference 1001

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:26.759114Z

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=2026-08-04T21:22:25.489364Z digest=sha256:85036ce16bab3fc83ce2104d18e8ed4d2bdd835843313b271410a7e395a108f2

Observation bd03693d-3ad5-4937-9327-dedb8ab0a912 · outbound

This paper cites D.1973 Group velocity and nonlinear dispersive wave propagation.Proc.

Geometrical optics in phase space D.1973 Group velocity and nonlinear dispersive wave propagation.Proc

Reference 1077

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:30.152559Z

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=2026-08-04T21:22:23.605251Z digest=sha256:a5cfe0e9fcc782b0f6cc73915b7120ad314dca21c36f27858687a3c78db23518

Observation ed163bfb-e50a-4b1d-bc5f-049e8b4ab871 · outbound

This paper cites Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation.

Geometrical optics in phase space Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation

Reference 1139

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:22:25.916730Z

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 62826c23-0b76-47c6-9dee-0ed824689481 · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 1279

Resolution
unresolved
raw_fallback, observed 2026-08-04T21:22:30.871483Z

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=2026-08-04T21:22:22.760895Z digest=sha256:248124814a2368c4ed112230430dbc3c16a84b3ad69561dd9ecfbfa7f96915bc

Observation 9e11a6ea-f412-4f4c-bcab-a87d25ca6c55 · outbound

This paper cites Wigner Function for Harmonic Oscillator and The Classical Limit.

Geometrical optics in phase space Wigner Function for Harmonic Oscillator and The Classical Limit

Reference 1321

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:22:26.060368Z

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=2026-08-04T21:22:24.596778Z digest=sha256:a2272a71baba403aa3e8082397ee87199c3e32a3c90888aff674f9d0f87ccf84

Observation 432a3c89-fa37-4f53-ae5d-7b2e32a8561f · outbound

This paper cites A., Balakina, M.

Geometrical optics in phase space A., Balakina, M

Reference 1699

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verified fuzzy
raw_fallback, observed 2026-08-04T21:22:30.678013Z

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=2026-08-04T21:22:22.861678Z digest=sha256:14f7e008c068bc62f3a58d2258b61f41ed12f60a2b5b357a3d9489348cafd879

Observation f0e46d26-1fc9-4899-a37f-ab88b1933e1c · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 1742

Resolution
unresolved
raw_fallback, observed 2026-08-04T21:22:28.969255Z

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=2026-08-04T21:22:24.195488Z digest=sha256:dc63724d1bd0dcf6626d2bfbec6874bd10e0af62a58a6983ec6189624ea066a0

Observation 260dc121-2219-4445-a350-04a664b25e0d · outbound

This paper cites H.1974 Classical-limit quantum mechanics and the theory of molecular collisions.

Geometrical optics in phase space H.1974 Classical-limit quantum mechanics and the theory of molecular collisions

Reference 2017

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:28.277297Z

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=2026-08-04T21:22:24.526572Z digest=sha256:8ea946bc5b3bbdd43250d9fa40be6a5b5d55765062a75a1dc1dff822fdf2e6c6

Observation 9a2e27a4-d8be-46ca-a7d5-e0827223cb68 · outbound

This paper cites & de Izarra, C.1997 An integral representation for the product of Airy functions.Z.

Geometrical optics in phase space & de Izarra, C.1997 An integral representation for the product of Airy functions.Z

Reference 2147

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:27.148388Z

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=2026-08-04T21:22:25.279017Z digest=sha256:5240bc719e44a991001f5e9a634e751bccf0f2de2f329efa6422028c81573caf

Observation b671e8e5-79e8-433b-81cb-61dd11c6a89b · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 2644

Resolution
unresolved
raw_fallback, observed 2026-08-04T21:22:28.721675Z

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=2026-08-04T21:22:24.344811Z digest=sha256:d74805069e95333093c302b3390f6ab33b0da7aa3ce3166dee0d75a665fcccdc

Observation a0ea0a20-5472-4dc2-8578-5911533ceee0 · outbound

This paper cites Spin Hall effect of radiofrequency waves in magnetized plasmas.

Geometrical optics in phase space Spin Hall effect of radiofrequency waves in magnetized plasmas

Reference 2727

Resolution
verified exact
local_arxiv, observed 2026-08-04T21:22:26.363143Z

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=2026-08-04T21:22:23.441647Z digest=sha256:38fe02b56d3900ac4f1900e8f3781b95a74d527df43f86b38ace16b1343e897a

Observation f337ecd3-6b24-410f-b153-d612e7ea0b3f · outbound

This paper cites D., F arina, D., Felici, F., Figini, L., Fischer, R., Galperti, C., Happel, T., Lin-Liu, Y.

Geometrical optics in phase space D., F arina, D., Felici, F., Figini, L., Fischer, R., Galperti, C., Happel, T., Lin-Liu, Y

Reference 3529

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:28.041181Z

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=2026-08-04T21:22:24.759371Z digest=sha256:70dbad391397fd214740ade243beeeb9d86f72c8c67689d65e836bfd026545e0

Observation b1323708-61e7-4637-b1bf-985f69456d0a · outbound

This paper cites D.2022 The Van Vleck formula on Ehrenfest time scales and stationary phase asymptotics for frequency-dependent phases.Commun.

Geometrical optics in phase space D.2022 The Van Vleck formula on Ehrenfest time scales and stationary phase asymptotics for frequency-dependent phases.Commun

Reference 4285

Resolution
verified fuzzy
raw_fallback, observed 2026-08-04T21:22:30.519745Z

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=2026-08-04T21:22:22.975849Z digest=sha256:3f42e7d3d22019942dc2a6cb20ecae24308b48d5c939deb9a66101ba28da4398

Observation da2a6b33-aa2c-4226-a72b-4c5ea7f85e6a · outbound

This paper cites an unresolved cited work.

Geometrical optics in phase space Unresolved cited work

Reference 4432

Resolution
unresolved
raw_fallback, observed 2026-08-04T21:22:29.697745Z

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=2026-08-04T21:22:23.863712Z digest=sha256:b30364c3423fea32e5e9de7a18356db563789c6410b55940544efba22fc9307e

Observation 8ead196a-b97b-4945-a483-89db40e66b15 · outbound

This paper cites Pseudo-differential representation of the metaplectic transform and its application to fast algorithms.

Geometrical optics in phase space Pseudo-differential representation of the metaplectic transform and its application to fast algorithms

Reference 5239

Resolution
metadata mismatch
local_arxiv, observed 2026-08-04T21:22:26.213476Z

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=2026-08-04T21:22:24.270990Z digest=sha256:67906345d131a110adb6c09a2f2e5a2f2d8db08100106b499cefa81cd248329b

Pith citing papers

Observation eae826bf-8fae-4e84-b473-0ab3e687a0c5 · inbound

A Doppler backscattering diagnostic for the EXL-50U spherical tokamak: plasma considerations and preliminary quasioptical design cites this paper.

A Doppler backscattering diagnostic for the EXL-50U spherical tokamak: plasma considerations and preliminary quasioptical design Geometrical optics in phase space

Reference 33

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verified exact
arxiv_id, observed 2026-05-18T15:21:32.977200Z

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=2026-05-18T15:17:51.128999Z digest=sha256:949825345add9635e55f5f93c68aa5b7dc60ce7f2974145d3a480b979f43283c