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Paper Citation Record · LEDGER

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions

As of 17 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2506.11414.

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

pith.paper-citation-record.v1
2506.11414 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:21:06.977963Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

31 of 31 outbound references displayed

  • verified exact6
  • verified fuzzy21
  • unresolved4
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6ac9ad38-cf0d-4923-9de0-2844639d5080 · outbound

This paper cites On the water-wave equations with surface tension.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions On the water-wave equations with surface tension

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.571644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.842487Z digest=sha256:7b70337a7a5379d2567a8c20d586059457527fd70826cd59573b0fe7de62acf0

Observation 6ddaf27b-9718-4a8d-a94b-0613743b8a17 · outbound

This paper cites an unresolved cited work.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Unresolved cited work

Reference 2

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verified exact
raw_fallback, observed 2026-08-07T04:21:07.262288Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.847580Z digest=sha256:e08283e52ce9f64ffdb182e5f9d3c6c79f2a72c89d88a5940a7cfb18f96a4e50

Observation a4c54919-1ae1-4cd9-a710-8e78e218eba5 · outbound

This paper cites Bifurcation from multiple eigenvalues of rotating traveling waves on a capillary liquid drop.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Bifurcation from multiple eigenvalues of rotating traveling waves on a capillary liquid drop

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-07T04:21:06.851991Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T04:21:06.851991Z digest=sha256:f46238525a1255e1308a8d9c55dcc1b8c688e690ed0888757e117066c26ddd79

Observation 7f58439e-1e2a-4c8e-9b33-62b668ed9ca1 · outbound

This paper cites Almost global solutions of capillary-gravity water waves equations on the circle.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Almost global solutions of capillary-gravity water waves equations on the circle

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.558659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.856939Z digest=sha256:0365fde9a78acc2057bc6c027c5f63f467ab870dc14de148315d73ad89482904

Observation a29364be-6a25-4feb-a45b-951671420de0 · outbound

This paper cites Quadratic life span of periodic gravity-capillary water waves.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Quadratic life span of periodic gravity-capillary water waves

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.545634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.861875Z digest=sha256:2de408f7821f9ddd7fde9e3077c7e05840c71d262810f3f1945ab8e6959fa20a

Observation 6666f748-a450-4f52-8fe8-690a7d10b37d · outbound

This paper cites On the cauchy problem for a capillary drop.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions On the cauchy problem for a capillary drop

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.532193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.866507Z digest=sha256:303fc06e82d7fee49baa77553ee8cb03da2453959ce10b43a83a896f694bf907

Observation a68a0d12-8bd6-4589-bddd-09c4c242ccd4 · outbound

This paper cites Finite time singularities for the free boundary incompressible euler equations.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Finite time singularities for the free boundary incompressible euler equations

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.518850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.871380Z digest=sha256:93ec14e082526513e0bd246932b0a5fe5da8a244600239fb32741104d905aea5

Observation 14d94efc-8232-40ef-a40d-a96627bdf64c · outbound

This paper cites Finite time singularities for water waves with surface tension.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Finite time singularities for water waves with surface tension

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.504814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.875558Z digest=sha256:fb94b2ff3dc47e930937093f361f44ae40f57e34858fecbfc072c8d26a2a3e96

Observation 655e1d5c-1b03-43cf-aab6-8131b7fce7fd · outbound

This paper cites L., Gancedo, F., and G ´omez-Serrano, J.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions L., Gancedo, F., and G ´omez-Serrano, J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.491175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.879525Z digest=sha256:a9eb1c8db3fb15d1c562bf5734a4d5857146aa78e89dbf94e4940d52e982aa82

Observation 9139c3f4-3aaa-4fd5-804d-6469c9fe036a · outbound

This paper cites Well-posedness of the free-surface incompressible euler equations with or without surface tension.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Well-posedness of the free-surface incompressible euler equations with or without surface tension

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.478078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.884587Z digest=sha256:e8686d000a1c62128bc61f854fd4897c6ec439dac7dc2329321c89d49a950a15

Observation fa419e63-415a-4d3a-bdfc-e3f2b3643afb · outbound

This paper cites On the finite-time splash and splat singularities for the 3-d free-surface euler equations.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions On the finite-time splash and splat singularities for the 3-d free-surface euler equations

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.464196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.889666Z digest=sha256:74bf1e292cf02236e17ce239a5af584a9dada1a1de502a9e923143b9d8ccdc76

Observation 33a8ce2d-8fde-40dc-8a57-1b3759b8d31a · outbound

This paper cites D., Pausader, B., and Pusateri, F.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions D., Pausader, B., and Pusateri, F

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.450905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.894060Z digest=sha256:33fafc222dde3bb8fc4e1b077829900cfecf9266a192d24531f03b1823d403c6

Observation ba0edf6b-bd1b-4c3a-a3d7-5c1b22f43f0c · outbound

This paper cites an unresolved cited work.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-07T04:21:07.436739Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.898062Z digest=sha256:4392de137589d482ceb237e2d0b0e916698599d447b2dc9c7ae357ea636eb31a

Observation 2377990e-108e-4338-b52b-ec61d82cdfec · outbound

This paper cites Regularity Theory for Elliptic PDE.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Regularity Theory for Elliptic PDE

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.423116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.902034Z digest=sha256:72a236e7a67abc4b4e9f427cfe12a52460a127e4740b2436d19f734b5b0bfc06

Observation 54c1c09d-caa0-47ea-863f-61b8a61e4d48 · outbound

This paper cites Classification of finite-time blow-up mechanisms for the incompressible free-boundary Euler equations with surface tension.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Classification of finite-time blow-up mechanisms for the incompressible free-boundary Euler equations with surface tension

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-07T04:21:06.906374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T04:21:06.906374Z digest=sha256:b54a620a83f51648d1ba45224aa1f7971857045eef6c24310ec61efcfa40995a

Observation 13962d71-5107-4828-9a4f-6cb23474f5c5 · outbound

This paper cites Small scale creation for 2d free boundary euler equations with surface tension.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Small scale creation for 2d free boundary euler equations with surface tension

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.409557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.911006Z digest=sha256:5e2b179904dfa29363a5816efa0692d40d4534b727de6d0c764117ba104a63e4

Observation ee3bd7a7-6f39-40b2-9ceb-69956b8c7241 · outbound

This paper cites The lifespan of small data solutions in two dimensional capillary water waves.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions The lifespan of small data solutions in two dimensional capillary water waves

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.395573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.915242Z digest=sha256:834d10c85ce58cfb8bfbc585d1398c317631cfaa657b7ad7bbd45e2678c48609

Observation 7e51edc6-9e23-42e1-8a0e-8cb1ca1e9a7f · outbound

This paper cites Global regularity for 2D water waves with surface tension , vol.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Global regularity for 2D water waves with surface tension , vol

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.381582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.919539Z digest=sha256:df5a63438b25a80420a2f969977f6c8f842123b7becb1245ace5c8fa6aaa5b49

Observation 712495da-5ffe-4b9e-b83c-306255b71b3d · outbound

This paper cites Small scale creation for solutions of the incompressible two- dimensional euler equation.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Small scale creation for solutions of the incompressible two- dimensional euler equation

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.366853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.923615Z digest=sha256:342a8f8f818b1415e4074b18a9dc2ccc5a670c33e177bf6e87535420da33f766

Observation d8d17cb6-b4b1-40a3-b44a-5fdcc4b5b97b · outbound

This paper cites Two-dimensional capillary liquid drop: Craig-Sulem formulation on $\mathbb{T}^1$ and bifurcations from multiple eigenvalues of rotating waves.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Two-dimensional capillary liquid drop: Craig-Sulem formulation on $\mathbb{T}^1$ and bifurcations from multiple eigenvalues of rotating waves

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-07T04:21:06.928058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T04:21:06.928058Z digest=sha256:4c594802f3fbefd0630fbb14d656502c3161518ed861a48c25a99d69331dde4e

Observation 970f40fa-569f-44e8-a200-3409cfbde490 · outbound

This paper cites Global Bifurcation of Steady Surface Capillary Waves on a $2D$ Droplet.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Global Bifurcation of Steady Surface Capillary Waves on a $2D$ Droplet

Reference 21

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:21:07.100187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.933165Z digest=sha256:3513c6a5cd7d05b272f6d9ce37eb8985302176d6cc5f1a09e56cc4d3593000fe

Observation 73de7ccf-baf7-4461-8344-aa7006f00619 · outbound

This paper cites Bonnesen-style isoperimetric inequalities.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Bonnesen-style isoperimetric inequalities

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.352951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.938018Z digest=sha256:a01ea2a07be5dc0aa9e9fb3b7cacb06de8c98cb34b1976908627fd064cde604d

Observation 16cbe15b-91cf-4ee4-8479-19d5ede48d73 · outbound

This paper cites Longtime Dynamics of Irrotational Spherical Water Drops: Initial Notes.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Longtime Dynamics of Irrotational Spherical Water Drops: Initial Notes

Reference 23

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:21:07.080201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.942299Z digest=sha256:3310feb79b93e6a68f043c682cd86bb4df75e695da782f3626f28672a8752086

Observation 5bdaffa8-e11d-4ef6-b05b-b665849feac3 · outbound

This paper cites On the Cauchy Problem of Spherical Capillary Water Waves.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions On the Cauchy Problem of Spherical Capillary Water Waves

Reference 24

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:21:07.059986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.947128Z digest=sha256:48a2e9ebf69dfdc6ec2f3cd7b978727eecf7d5c94933e0587aa889b4f23e6b4e

Observation 11fd7dae-515d-4af6-8e57-93da35e66357 · outbound

This paper cites Para-differential Calculus on Compact Lie Groups and Spherical Capillary Water Waves.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Para-differential Calculus on Compact Lie Groups and Spherical Capillary Water Waves

Reference 25

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:21:07.040265Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.951728Z digest=sha256:d53774c55faab31b521f1b9bbf0d51b00c3d68f8a14e9ad4211549a0e61822d8

Observation 15cb163c-7d43-4720-95f4-f11c59849b77 · outbound

This paper cites Toolbox of Para-differential Calculus on Compact Lie Groups.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Toolbox of Para-differential Calculus on Compact Lie Groups

Reference 26

Resolution
verified exact
local_arxiv, observed 2026-08-07T04:21:07.019607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.956387Z digest=sha256:f48463d42a4f89342216c2e684a578bfe00ff969325f66bb34530682d4277981

Observation 41d3dd18-c76b-4816-8780-acab072f9ca7 · outbound

This paper cites Geometry and a priori estimates for free boundary problems of the euler’s equation.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Geometry and a priori estimates for free boundary problems of the euler’s equation

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.338081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.960878Z digest=sha256:74463e0f5d53237887341d54cec67d0b4ba61b0ea2ddf34fe8a982daeff37c93

Observation 7aa971f3-493e-4b3c-89d9-d44e1f14a179 · outbound

This paper cites A priori estimates for fluid interface problems.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions A priori estimates for fluid interface problems

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.322386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.965297Z digest=sha256:06dda17301e840d0e4b76bdadf0768875150f3d1e95a89066ed4f9c6f483184b

Observation 517f6439-44e4-4d40-90f5-0090662b9a36 · outbound

This paper cites Local well-posedness for fluid interface problems.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Local well-posedness for fluid interface problems

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.307831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.969466Z digest=sha256:22a88c956d205c9984cb6241b04fdc2f0f9815724bf078861a731de74dbb1983

Observation d114e6f2-d4a9-4513-80d6-886fd3c6b678 · outbound

This paper cites A., and Brown, R.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions A., and Brown, R

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.292858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.973592Z digest=sha256:863e4ad3b84b80952b58987549466697bb954a2465bc72f89612124bca0db30b

Observation 0c966806-a391-452e-844f-a1d19b95c21c · outbound

This paper cites Exponential growth of the vorticity gradient for the euler equation on the torus.

Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions Exponential growth of the vorticity gradient for the euler equation on the torus

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T04:21:07.276921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-07T04:21:06.977963Z digest=sha256:5fe3b0ee3151388c97b5c249032d1b2dbaf9b78fc13e17399a766187a714b663

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