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Paper Citation Record · LEDGER

A variational formulation for steady surface water waves on a Beltrami flow

As of 16 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 0 inbound Pith citation observations for arXiv:1908.09386.

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

pith.paper-citation-record.v1
1908.09386 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:22:28.754725Z

measured 14 of 14 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

14 of 14 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation df8dacf6-3dd4-4fbc-9ef2-995f68523a26 · outbound

This paper cites 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid.

A variational formulation for steady surface water waves on a Beltrami flow 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 9a0aed38-fed3-4867-a6f3-a1163139f4cc · outbound

This paper cites 1993 Numerical simulation of gravity waves.

A variational formulation for steady surface water waves on a Beltrami flow 1993 Numerical simulation of gravity waves

Reference 2

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verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.997863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 17a00d13-1cbd-42df-a60f-1665017b33b8 · outbound

This paper cites 1967 A variational principle for a fluid with a free surface.

A variational formulation for steady surface water waves on a Beltrami flow 1967 A variational principle for a fluid with a free surface

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.981727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation b625137a-ebfc-41b2-94a0-e92f5255398f · outbound

This paper cites 2015 A kinematic conservation law in free surface flow.

A variational formulation for steady surface water waves on a Beltrami flow 2015 A kinematic conservation law in free surface flow

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.966527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation abf6bc85-63a8-4bd0-ae0a-a64574376ba5 · outbound

This paper cites 2015 Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity.

A variational formulation for steady surface water waves on a Beltrami flow 2015 Well-posedness and shallow-water stability for a new Hamiltonian formulation of the water waves equations with vorticity

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.951111Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T11:22:28.703200Z digest=sha256:3dc62f22943591956d7eef5ff9f9fe2af403a2d71cc0758dce1e717063880544

Observation 631c84d1-e6ec-47ff-b1b5-6a6c258188b9 · outbound

This paper cites 1958 A theorem on force-free magnetic fields.

A variational formulation for steady surface water waves on a Beltrami flow 1958 A theorem on force-free magnetic fields

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.935540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation f2738b3e-4897-4a83-885b-75d1b7267c38 · outbound

This paper cites 1991 On Woltjer’s variational principle for force-free fields.J.

A variational formulation for steady surface water waves on a Beltrami flow 1991 On Woltjer’s variational principle for force-free fields.J

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.919863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T11:22:28.714989Z digest=sha256:5e57c34621fbef2f2e5db9cecb0083df6e381f9c1e56152eb1d576bdd9f86943

Observation 14b9bdee-964d-4d6d-83f0-1629fb2170f6 · outbound

This paper cites 1984 Impulse, flow-force and variational principles.

A variational formulation for steady surface water waves on a Beltrami flow 1984 Impulse, flow-force and variational principles

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.903583Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation ec8f9078-e504-4a06-9eb0-25027ca9cb78 · outbound

This paper cites 2019 A variational principle for three-dimensional water waves over Beltrami flows.

A variational formulation for steady surface water waves on a Beltrami flow 2019 A variational principle for three-dimensional water waves over Beltrami flows

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.885824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 4b40368a-503a-47d8-bb10-5337cc441555 · outbound

This paper cites 1988 Mathematical Analysis and Numerical Methods for Science and Technology, Volume 3: Spectral Theory and Applications.

A variational formulation for steady surface water waves on a Beltrami flow 1988 Mathematical Analysis and Numerical Methods for Science and Technology, Volume 3: Spectral Theory and Applications

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.865889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 2c20e0dc-28c4-4bdc-9643-b753ac385019 · outbound

This paper cites 2013 The Water Waves Problem: Mathematical Analysis and Asymptotics.

A variational formulation for steady surface water waves on a Beltrami flow 2013 The Water Waves Problem: Mathematical Analysis and Asymptotics

Reference 11

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 476ab60d-c6b3-4279-ab54-09edf118c39a · outbound

This paper cites 1975 Sobolev Spaces.

A variational formulation for steady surface water waves on a Beltrami flow 1975 Sobolev Spaces

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.831740Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T11:22:28.743685Z digest=sha256:5e387da666a0faeaa5e3d51333c7275bf362916f25aff2f8f655d30f016b187d

Observation f9a0d840-809b-4a90-ba5d-158d57eab974 · outbound

This paper cites 1997 Lectures on Nonlinear Hyperbolic Differential Equations.

A variational formulation for steady surface water waves on a Beltrami flow 1997 Lectures on Nonlinear Hyperbolic Differential Equations

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.814164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Observation 14893b39-04e7-4adc-9f18-49f9feb15609 · outbound

This paper cites 2003 Analytic Theory of Global Bifurcation.

A variational formulation for steady surface water waves on a Beltrami flow 2003 Analytic Theory of Global Bifurcation

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:22:28.796342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

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Pith citing papers

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