Hamilton-Jacobi theory in Cauchy data space

C\'edirc M. Campos; David Mart\'in de Diego; Manuel de Le\'on; Miguel Vaquero

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Hamilton-Jacobi theory in Cauchy data space

Cédirc M. Campos, Manuel de León, David Martín de Diego, Miguel Vaquero

Mathematical Physics · Submitted 14 Nov 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our purpose in the current paper is to establish the corresponding Hamilton-Jacobi theory in the Cauchy data space, and relate both approaches.

how it is stated · asserted 0.86 read the record →

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arXiv ID1411.3959 (version 1)

Pith IDYLZDYSQD, Pith's permanent record of this paper and its review

CitationC\'edirc M. Campos, David Mart\'in de Diego, Manuel de Le\'on, Miguel Vaquero. "Hamilton-Jacobi theory in Cauchy data space." arXiv:1411.3959 (2014). https://pith.science/paper/YLZDYSQD

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,861 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.88 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Recently, M. de Le\'on el al. ([9]) have developed a geometric Hamilton-Jacobi theory for Classical Field Theories in the setting of multisymplectic geometry. Our purpose in the current paper is to establish the corresponding Hamilton-Jacobi theory in the Cauchy data space, and relate both approaches.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Recently, M. de Le\'on el al.	background 1.00	0.03	0.01	unclear 0.95
s1	([9]) have developed a geometric Hamilton-Jacobi theory for Classical Field Theories in the setting of multisymplectic geometry.	background 1.00	0.03	0.04	asserted 1.00
s2	Our purpose in the current paper is to establish the corresponding Hamilton-Jacobi theory in the Cauchy data space, and relate both approaches.	contribution 0.99	0.42	0.24	asserted 0.86

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.94.

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sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Recently, M. de Le\'on el al. ([9]) have developed a geometric Hamilton-Jacobi theory for Classical Field Theories in the setting of multisymplectic geometry. Our purpose in the current paper is to establish the corresponding Hamilton-Jacobi theory in the Cauchy data space, and relate both approaches.

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How the literature uses it

3 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 5 sentences without a confident label

Cites as background 2 papers

In this section we are going to introduce the phase space $$, which in the terminology of [ref] is the space denoted by “$T^*ℰ^t$”.

Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory · The space $𝕋^*Ẽ$ ($T^*ℰ^τ$) · 0.87
Let us notice that an alternative approach to the Hamilton-Jacobi theory for Classical Field Theories has been developed in the context of $k$-symplectic and $k$-cosymplectic structures (see [ref] ).

Methods of Differential Geometry in Classical Field Theories: k-symplectic and k-cosymplectic approaches · Introduction · 0.87

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