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On diffeological principal bundles of non-formal pseudo-differential operators over formal ones

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Jean-Pierre Magnot

Differential Geometry · Submitted 28 Jun 2022

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

The authors' main claim We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group.

how it is stated · asserted 1.00 read the record →

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arXiv ID2207.07015 (version 1)
Pith IDKLFSQFZX, Pith's permanent record of this paper and its review
CitationJean-Pierre Magnot. "On diffeological principal bundles of non-formal pseudo-differential operators over formal ones." arXiv:2207.07015 (2022). https://pith.science/paper/KLFSQFZX
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,319 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.72 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.19 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local trivialization, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. contribution 0.92 0.92 0.65 asserted 1.00
s1 For this, we give few results on diffeological principal bundles with (a priori) no local trivialization, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions. method 0.98 0.81 0.12 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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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

We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local trivialization, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions.

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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

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