Degenerations of invariant lagrangian manifolds

Mauricio Garay

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Degenerations of invariant lagrangian manifolds

Mauricio Garay

Dynamical Systems · Submitted 16 Sep 2013

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

The authors' main claim We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can "integrated" as a deformation of (H,I).

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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, 2,299 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.51 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider a pair (H,I) where I is an involutive ideal of a Poisson algebra and H lies in I. We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can "integrated" as a deformation of (H,I).

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	We consider a pair (H,I) where I is an involutive ideal of a Poisson algebra and H lies in I.	background 0.78	0.45	0.03	asserted 0.78
s1	We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can "integrated" as a deformation of (H,I).	result 0.97	0.92	0.87	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v2

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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

We consider a pair (H,I) where I is an involutive ideal of a Poisson algebra and H lies in I. We show that if I defines a 2n-gon singularity then, under arithmetical conditions on H, any deformation of H can "integrated" as a deformation of (H,I).

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What this paper does with the arXiv papers it cites

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

Cites as background 1 paper

We assume the reader is acquainted with the notions introduced in it (see [ref] for details).

Espaces vectoriels \'echelonn\'es · Statement of the theorem · 0.96

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