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Commutative Partial Differential Operators

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Alex Kasman, Emma Previato

Rings and Algebras · Submitted 14 Jul 1999

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

The authors' main claim In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed.

how it is stated · asserted 0.67 read the record →

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arXiv IDmath/9907097 (version 1)
Pith ID4EPSVIBP, Pith's permanent record of this paper and its review
CitationAlex Kasman, Emma Previato. "Commutative Partial Differential Operators." arXiv:math/9907097 (1999). https://pith.science/paper/4EPSVIBP
Claim paper

The compiled record

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,904 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.50 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed. In particular, we address the existence of a ``spectral variety'' generalizing the spectral curve of the one dimensional theory and the role of the differential resultant.

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 In one variable, there exists a satisfactory classification of commutative rings of differential operators. background 1.00 0.05 0.05 asserted 1.00
s1 In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed. gap 0.61 0.49 0.11 asserted 0.67
s2 In particular, we address the existence of a ``spectral variety'' generalizing the spectral curve of the one dimensional theory and the role of the differential resultant. contribution 0.99 0.51 0.15 asserted 0.65

What kind of paper the classifier reports this is: position or commentary 0.96 · evidence from argument 0.58.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions that may suggest a theory to be developed. In particular, we address the existence of a ``spectral variety'' generalizing the spectral curve of the one dimensional theory and the role of the differential resultant.

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